algorithmen für routenplanung · pdf filewheelchair users only ... verschiedene varianten...

INSTITUT FÜR THEORETISCHE INFORMATIK · ALGORITHMIK · PROF. DR. DOROTHEA WAGNER

Algorithmen für Routenplanung17. Vorlesung, Sommersemester 2017

Tobias Zündorf | 17. Juli 2017

KIT – Universität des Landes Baden-Württemberg undnationales Großforschungszentrum in der Helmholtz-Gemeinschaft

www.kit.edu

http://www.kit.edu

Fahrplanauskunft

Transport for London August 2011

Key to symbols Explanation of zones

1

3

45

6

2

7

8

9

Station in both zones



Station in Zone 9

Station in Zone 6

Station in Zone 5

Station in Zone 3Station in Zone 2

Station in Zone 1

Station in Zone 4

Station in Zone 8

Station in Zone 7

Station closed

Riverboat services

AirportTramlink

Interchange stations

Step-free access from street to platform

Step-free access from street to train

National Rail

Blackfriars

Check before you travel

Key to lines

Bank Waterloo & City line open 0615 until 2148 Mondays to Fridays and 0800 until 1830 Saturdays. Closed Sundays and Public Holidays---------------------------------------------------------------------------Blackfriars Underground station closed until late 2011---------------------------------------------------------------------------Camden Town From 1300 until 1730 Sundays open for interchange and exit only---------------------------------------------------------------------------Canary Wharf Step-free interchange between Underground, Canary Wharf DLR and Heron Quays DLR stations at street level---------------------------------------------------------------------------Cannon Street Open until 2100 Mondays to Fridays. Closed Saturdays and Sundays---------------------------------------------------------------------------Heron Quays Step-free interchange between Heron Quays and Canary Wharf Underground station at street level---------------------------------------------------------------------------Hounslow West Step-free access for wheelchair users only---------------------------------------------------------------------------Tottenham Northern line trains will not Court Road stop at Tottenham Court Road until late 2011 ---------------------------------------------------------------------------Turnham Green Served by Piccadilly line trains early mornings and late evenings only---------------------------------------------------------------------------Victoria Major escalator refurbishment works until early 2012. Use nearby stations or alternative routes---------------------------------------------------------------------------Waterloo Waterloo & City line open 0615 until 2148 Mondays to Fridays and 0800 until 1830 Saturdays. Closed Sundays and Public Holidays---------------------------------------------------------------------------West India Quay Not served by DLR trains from Bank towards Lewisham before 1900 on Mondays to Fridays---------------------------------------------------------------------------

Northern

Metropolitan

Victoria

District

Circle

Central

Bakerloo

DLR

London Overground

Piccadilly

Waterloo & City

Jubilee

Hammersmith & City

River Thames

A

B

C

D

E

F

1 2 3 4 5 6 7 8 9

1 2 3 4 5 76 8 9

A

B

C

D

E

F

2 2

22

2

5

8 8 6

2

4

4

65

41

3

2

43

3

36 3 1

1

3

3

59 7 7Special fares apply

5

5

4

4

4

AmershamChorleywood

Mill Hill East

Rickmansworth

Perivale

KentishTown West

CamdenRoad

Dalston Kingsland

Wanstead Park

Vauxhall

Hanger Lane

Edgware

Burnt Oak

Colindale

Hendon Central

Brent Cross

Golders Green

West Silvertown

Pontoon Dock

London City Airport

Woolwich Arsenal

King George V

Hampstead

Belsize Park

Chalk Farm

Chalfont &Latimer

Chesham

New Cross Gate

Moor Park

NorthwoodNorthwoodHills

Pinner

North Harrow

Custom House for ExCeL

Prince Regent

Royal Albert

Beckton Park

Cyprus

Gallions Reach

Beckton

Watford

Croxley

Fulham Broadway

LambethNorth

HeathrowTerminal 4

Harrow-on-the-Hill

KensalRise

BethnalGreen

Westferry

SevenSisters

Blackwall

BrondesburyPark

HampsteadHeath

HarringayGreen Lanes

LeytonstoneHigh Road

LeytonMidland Road

Hackney Central

NorthwickPark

PrestonRoad

RoyalVictoria

WembleyPark

Rayners Lane

Watford High Street

RuislipGardens

South Ruislip

Greenford

Northolt

South Harrow

Sudbury Hill

Sudbury Town

Alperton

Pimlico

Park Royal

North Ealing

Acton Central

South Acton

Ealing Broadway

Watford Junction

West Ruislip

Bushey

Carpenders Park

Hatch End

North Wembley

West Brompton

Ealing Common

South Kenton

Kenton

Wembley Central

Kensal Green

Queen’s Park

Gunnersbury

Kew Gardens

Richmond

Stockwell

Bow Church

Stonebridge Park

Harlesden

Camden Town

Willesden Junction

Headstone Lane

Parsons Green

Putney Bridge

East Putney

Southfields

Wimbledon Park

Wimbledon

Island Gardens

Greenwich

Deptford Bridge

South Quay

Crossharbour

Mudchute

Heron Quays

West India Quay

Elverson Road

Oakwood

Cockfosters

Southgate

Arnos Grove

Bounds Green

Theydon Bois

Epping

Debden

Loughton

Buckhurst Hill

WalthamstowQueen’s Road

Woodgrange Park

Leytonstone

Leyton

Wood Green

Turnpike Lane

Manor House

Stanmore

Canons Park

Queensbury

Kingsbury

High Barnet

Totteridge & Whetstone

Woodside Park

West Finchley

Finchley CentralWoodford

South Woodford

Snaresbrook

Hainault

Fairlop

Barkingside

Newbury Park

East Finchley

Highgate

Archway

Devons Road

Langdon Park

All Saints

Tufnell Park

Kentish Town

Neasden

Dollis Hill

Willesden Green

South Tottenham

Swiss Cottage

ImperialWharf

Brixton

Kilburn

West Hampstead

Blackhorse Road

Acton Town

CanningTown

Finchley Road

Highbury &Islington

Canary Wharf

Stratford

StratfordInternational

FinsburyPark

Elephant & Castle

Stepney Green

Barking

East Ham

Plaistow

Upton Park

Poplar

West Ham

Upper Holloway

PuddingMill Lane

Kennington

Borough

Elm ParkDagenham

East

DagenhamHeathway

Becontree

Upney

Heathrow Terminal 5

Finchley Road& Frognal

Crouch Hill

Northfields

Boston Manor

South Ealing

Osterley

Hounslow Central

Hounslow East

Clapham North

Oval

Clapham Common

Clapham South

Balham

Tooting Bec

Tooting Broadway

Colliers Wood

South Wimbledon

Arsenal

Holloway Road

Caledonian Road

Morden

West Croydon

HounslowWest

Hatton Cross

HeathrowTerminals 1, 2, 3

ClaphamJunction

WestHarrow

Brondesbury CaledonianRoad &

Barnsbury

TottenhamHale

WalthamstowCentral

HackneyWick

Homerton

WestActon

Limehouse EastIndia

Crystal Palace

ChiswickPark

RodingValley

GrangeHill

Chigwell

Redbridge

GantsHill

Wanstead

NorthGreenwichfor The O2

Ickenham

TurnhamGreen

Uxbridge

Hillingdon Ruislip

GospelOak

Mile End

Bow Road

Bromley-by-Bow

Upminster

Upminster Bridge

Hornchurch

Norwood Junction

Sydenham

Forest Hill

Anerley

Penge West

Honor Oak Park

Brockley

Harrow &Wealdstone

Cutty Sark for Maritime Greenwich

Ruislip Manor

Eastcote

Wapping

Shadwell

New Cross

CanadaWater

Surrey Quays

Whitechapel

Lewisham

Kilburn Park

Regent’s Park

KilburnHigh Road

EdgwareRoad

SouthHampstead

GoodgeStreet

Shepherd’s BushMarket

Goldhawk Road

Hammersmith

Bayswater

Warren Street

Aldgate

Euston

Farringdon

BarbicanRussellSquare

Kensington(Olympia)

MorningtonCrescent

High StreetKensington

Old Street

St. John’s Wood

Green Park

BakerStreet

NottingHill Gate

Victoria

AldgateEast

Blackfriars

Mansion House

Cannon Street

OxfordCircus

BondStreet

TowerHill

Westminster

PiccadillyCircus

CharingCross

Holborn

Tower Gateway

Monument

Moorgate

Leicester Square

London Bridge

St. Paul’s

Hyde Park Corner

Knightsbridge

StamfordBrook

RavenscourtPark

WestKensington

NorthActon

HollandPark

Marylebone

Angel

Queensway MarbleArch

SouthKensington

Earl’sCourt

SloaneSquare

Covent Garden

LiverpoolStreet

GreatPortland

Street

Bank

EastActon

ChanceryLane

LancasterGate

Warwick AvenueMaida Vale

Fenchurch Street

Paddington

BaronsCourt

GloucesterRoad St. James’s

Park Temple

Latimer Road

Ladbroke Grove

Royal Oak

Westbourne Park

Bermondsey

Rotherhithe

ShoreditchHigh Street

Dalston Junction

Haggerston

Hoxton

Wood Lane

Shepherd’sBush

WhiteCity

King’s CrossSt. Pancras

EustonSquareEdgware

Road

Southwark

Embankment

Stratford High Street

Abbey Road

Star Lane

Waterloo

TottenhamCourt Road

Canonbury

Tobias Zündorf – Algorithmen für RoutenplanungFolie 2 – 17. Juli 2017

Institut für Theoretische InformatikLehrstuhl Algorithmik

Wdh. Begriffe



Wdh. Begriffe

stop = Haltestelle



Wdh. Begriffe

stop = Haltestelle

9:00

9:05 9:08

9:17

9:23 9:31



Wdh. Begriffe

stop = Haltestelle

9:00

9:05 9:08

9:17

9:23 9:31

trip t1 9:00 9:05 9:08 9:17 9:23 9:31

Ankunftszeiten



Wdh. Begriffe

stop = Haltestelle

trip t1 9:00 9:05 9:08 9:17 9:23 9:31

Ankunftszeiten



Wdh. Begriffe

stop = Haltestelle

trip t1 9:00 9:05 9:08 9:17 9:23 9:31

trip t2 10:00 10:05 10:08 10:17 10:23 10:31

Ankunftszeiten



Wdh. Begriffe

stop = Haltestelle

trip t1 9:00 9:05 9:08 9:17 9:23 9:31

trip t2 10:00 10:05 10:08 10:17 10:23 10:31

trip t3 10:30 10:35 10:38 - - 10:53

Ankunftszeiten



Wdh. Begriffe

stop = Haltestelle

trip t1 9:00 9:05 9:08 9:17 9:23 9:31

trip t2 10:00 10:05 10:08 10:17 10:23 10:31

trip t3 10:30 10:35 10:38 - - 10:53

Route R1

Route R2

Ankunftszeiten



Wdh. Begriffe

trip t1 9:00 9:05 9:08 9:17 9:23 9:31

trip t2 10:00 10:05 10:08 10:17 10:23 10:31

trip t3 10:30 10:35 10:38 - - 10:53

Route R1

Route R2

Ankunftszeiten

Journey



Wdh. Problemstellung

Gesucht: „Gute“ Routen für Ankunftszeit und Anzahl Umstiege.

Ankunft 11:08 Uhr, 2 Umstiege Ankunft 11:09 Uhr, 0 Umstiege

Problem:Dijkstra basierter Multi-Label-Correcting Ansatz zu langsam



Graph-Modelle?Bis jetzt:

Modelliere Fahrplan als gerichteten GraphenZeitexpandiert vs zeitabhängigVerschiedene Varianten von Dijkstra’s AlgorithmusEarliest Arrival, Profil-, Multi-Criteria Suchen

ProblemeViele Knoten und KantenOverhead von Priority QueueWenig explizites Ausnutzen der FahrplanstrukturDynamische Szenarien erfordern Updates der Graph-TopologieAußerdem: Beschleunigungstechniken funktionieren nicht gut

Sind Graphen die beste Art Fahrpläne zu modellieren?



RAPTOR

Anforderungen:

Berechnen von Pareto-sets,mindestens Ankunftszeit und # Umstiege

Nutzt die Struktur der Fahrpläne aus,benutzt Routen und Trips explizit?

Funktioniert in dynamischen Szenarien,Verspätungen, Zugausfälle, Routenänderungen; keine Vorberechnung

Kann auf zusätzliche Kriterien erweitert werden, ...z.B. Tarifzonen, Umstiegssicherheit, etc

... und ist hinreichend schnellfür interaktive Szenarien

RAPTOR: Round-bAsed Public Transit Optimized Router



RAPTOR

Anforderungen:Berechnen von Pareto-sets,mindestens Ankunftszeit und # Umstiege

Nutzt die Struktur der Fahrpläne aus,benutzt Routen und Trips explizit?

Funktioniert in dynamischen Szenarien,Verspätungen, Zugausfälle, Routenänderungen; keine Vorberechnung

Kann auf zusätzliche Kriterien erweitert werden, ...z.B. Tarifzonen, Umstiegssicherheit, etc

... und ist hinreichend schnellfür interaktive Szenarien

RAPTOR: Round-bAsed Public Transit Optimized Router



Runden

Beobachtung: Wechseln zw. Trips führt immer zu einem Umstieg.

Idee: Eine Runde für jeden genommenen Trip.

s

t

Dep: 10:30

Ansatz: In Runde k werden Ankunftszeiten für k Trips berechnet.

Scanne jede Route höchstens einmal pro Runde.



Runden

Beobachtung: Wechseln zw. Trips führt immer zu einem Umstieg.Idee: Eine Runde für jeden genommenen Trip.

s

t

Dep: 10:30





Runden


t

s

Dep: 10:30

k = 1





Runden


t

s

10:50

11:00

Dep: 10:30

. . .

. . .

. . .

. . .

. . .

. . .





Runden


t

s

10:50

11:00

Dep: 10:30

. . .

. . .

. . .

. . .

. . .

. . .

13:00 (1 transfer)

11:45

k = 2





Runden


t

s

10:50

11:00

Dep: 10:30

. . .

. . .

. . .

. . .

. . .

. . .

13:00 (1 transfer)

11:4511:45 11:15

k = 2





Runden


t

s

10:50

11:00

Dep: 10:30

. . .

. . .

. . .

. . .

. . .

. . .

t13:00 (1 transfer)

11:45 11:15

k = 2





Runden


t

s

10:50

11:00 13:00 (1 transfer)

Dep: 10:30

. . .

. . .

. . .

. . .

. . .. . .

. . .

. . .

. . . . . .

. . .

. . .

. . .

. . .

11:45 11:15

k = 2





Runden


t

s

10:50

11:00

11:45 11:15

13:00 (1 transfer)

Dep: 10:30

. . .

. . .

. . .

. . .

. . .. . .

. . .

. . .

. . . . . .

. . .

. . .

. . .

. . .

k = 3





Runden


t

s

10:50

11:00

11:45 11:15

13:00 (1 transfer)

Dep: 10:30

12:30 (2 transfers)

. . .

. . .

. . .

. . .

. . .. . .

. . .

. . .

. . . . . .

. . .

. . .

. . .

. . .

. . .

. . .





RAPTOR: Übersicht

Für jede Runde k ← 1,2, . . .1 Scanne jede Route2 Relaxiere Fußwege s

t

Terminiere, wenn ... ?



Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: ⊥

∞

k-1

k ∞9:16

∞9:58 8:43

8:19

7:25

7:12

∞ 9:07

3min 6min 2min 5min 5min 4min

∞ ∞ ∞

Jeder Stop hat ein Label (Ankunftszeit) pro RundeAktiver Trip entlang der Route wird stets verbessert.

In Runde k :Update Labels von Runde k mit Labels aus Runde k − 1.

Dynamischer Programmierungsansatz.



Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: ⊥

∞

k-1

k ∞9:16

∞9:58 8:43

8:19

7:25

7:12

∞ 9:07

?


∞ ∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 13

∞

k-1

k ∞9:16

∞9:58 8:43

8:19

7:25

7:12

∞ 9:07

9:20


∞ ∞∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 13

∞

k-1

k ∞9:16

∞9:58 8:43

8:19

7:25

7:12

∞ 9:07

9:26


∞∞ ∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 13

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞ 9:07

9:26


∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 13

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞ 9:07

9:28


∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 11

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞ 9:07

8:58


∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 11

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞ 9:07

9:03


∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 3

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞ 9:07

7:33


∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 3

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞ 9:07

7:38


∞ ∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 3

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞7:38

9:07

7:38


∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 3

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞7:38

9:07

7:42


∞






Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 3

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞7:38

9:07

7:42

7:42







Scannen von Routen

Some route

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Current Trip: 3

∞

k-1

k ∞9:16

∞9:58

9:26

8:43

8:19

7:25

7:12

∞7:38

9:07

7:42







Markieren und PruningBeobachtung: Nicht alle Routen werden in jeder Runde erreicht.

s

t

Markieren und PruningRoute scannen: Markiere Stop falls Ankunftszeit verbessert.Nächste Runde: Nur Routen von markierten Stops scannen.Scanne jede Route ab ihrem ersten markierten Stop.

Markiere nur Stops wenn sie die beste Ankunftszeit am Zielverbessern.



Markieren und PruningBeobachtung: Nicht alle Routen werden in jeder Runde erreicht.

s

t

Markieren und PruningRoute scannen: Markiere Stop falls Ankunftszeit verbessert.Nächste Runde: Nur Routen von markierten Stops scannen.Scanne jede Route ab ihrem ersten markierten Stop.Markiere nur Stops wenn sie die beste Ankunftszeit am Zielverbessern.



RAPTOR: Übersicht

Relaxiere FußwegeFür jede Runde k ← 1,2, . . .

1 Wähle erreichte Routen aus letzter Runde2 Scanne diese Routen3 Relaxiere Fußwege

s

t

Terminiere, wenn kein Stop markiert wurde.



Parallelisierung

Beobachtung: Routen werden in bel. Reihenfolge gescannt.

Verteile Routen auf verschiedene CPU Kerne; Scanne parallel.

Vermeiden von Race-Conditions:Lock auf Schreiben von Labels (teuer).Synchronisiere Labels nach jeder Runde.Sicherstellen dass nur „unabhängige“Routen gleichzeitig gescannt werden.

(Reduktion auf Färbeproblem)



Parallelisierung

Beobachtung: Routen werden in bel. Reihenfolge gescannt.

Verteile Routen auf verschiedene CPU Kerne; Scanne parallel.

Vermeiden von Race-Conditions:Lock auf Schreiben von Labels (teuer).Synchronisiere Labels nach jeder Runde.Sicherstellen dass nur „unabhängige“Routen gleichzeitig gescannt werden.(Reduktion auf Färbeproblem)



Andere Kriterien: Übersicht

Mögliche ErweiterungenProfil-Anfragen (Intervallanfragen),Flexible Abfahrtszeiten.

Tarifzonen,Längere Routen könnten billiger sein.

Umstiegssicherheit,Routen könnten knappe Umstiege haben.

. . .

2 3 4 5 6

7 889

112

2

3

4

56

2

3

4

56

3456

River Thames

River Thames

Station outsidethe zones

Station in Zone 5

Station in Zone 4

Station in Zone 3

Station in Zone 2Station in both zones

Station in Zone 1

Revised September 2009

Travelcard Zones

6

5

4

3

2

1




Station in Zone 6

Station in Zone 77

Station in Zone 88

Station in Zone 99

Bakerloo

Central

Circle

District

InterchangeStationStationKey to lines

Replacement bus services

London Overground

Hammersmith & City

Metropolitan

Northern

Victoria

DLR

Jubilee

National Rail

London Tramlink

Piccadilly

Waterloo & City

Smitham

Southwark


North HarrowHarrow-on-the-Hill Northwick

Park

Harrow & Wealdstone

Watford Junction

Bushey

Headstone Lane

Pinner

Stanmore

Canons Park

Queensbury

Preston Road

Edgware

Burnt Oak

ColindaleKingsbury

WembleyPark Hendon

NeasdenDollis Hill

WillesdenGreen

Kilburn

Hatch End

Elstree & Borehamwood

Mill Hill Broadway Mill Hill East

Hendon Central

Brent CrossGolders Green

HampsteadCricklewoodHampstead Heath

Gospel Oak

Kentish Town West

West Ruislip

RuislipGardens

South Ruislip

RaynersLane

South Harrow

NortholtPark

West Harrow

Northolt

South Kenton

North Wembley WembleyStadium

StonebridgePark

Harlesden

SouthGreenford

Castle BarPark

DraytonGreen

WestDrayton

Hayes &Harlington

Southall

Hanwell WestEaling

EalingBroadway

North Ealing

Boston ManorHounslow

East

HounslowWest Hounslow

Central

NorthfieldsChiswick

Park

ActonTown

SouthActon

ActonMain Line

WestActon

St. Margarets

KewGardens

Feltham

StrawberryHill

Hampton Wick

HamptonCourt

ThamesDitton

Surbiton

ChessingtonSouth

ChessingtonNorth

Brondesbury Park

Kensal Rise

Queen’sPark

WembleyCentral

EdgwareRoad

Kilburn ParkMaida Vale

Warwick Avenue

WestbournePark

Ladbroke Grove

EdgwareRoad

NorthActon

EastActon

Latimer RoadPark Royal

HangerLane

EalingCommon

WhiteCity

Shepherd’sBush Market

Goldhawk Road

ActonCentral

BaronsCourt

Kensington(Olympia)

WestKensington

RavenscourtPark

StamfordBrook

TurnhamGreen

NorthSheen

Parsons Green

Putney Bridge

East PutneyPutney

Wimbledon Park

Southfields

Wimbledon

Raynes Park

New MaldenNorbiton

CheamBelmont

Sutton

West Sutton

Sutton Common

St. Helier

WorcesterPark

MaldenManor

SouthMerton

MordenSouth

Morden

MotspurPark

WimbledonChase

South Wimbledon

ColliersWood

Earlsfield

WandsworthTown

TootingBec

Tooting Broadway

BalhamClapham South

ClaphamCommon

Clapham North

ClaphamHigh Street

WandsworthRoadClapham Junction

QueenstownRoad

BatterseaPark

Fulham Broadway

WestBrompton

Pimlico

SouthKensington

Earl’sCourt

SloaneSquare

GloucesterRoad

Knightsbridge


Hyde ParkCorner

GreenPark

High Barnet


Belsize Park

West HampsteadChalk Farm

Camden Town

Finchley Road

Kentish Town

Swiss Cottage

St. John’s Wood

MorningtonCrescent

CamdenRoad

ImperialWharf

BakerStreet

GreatPortland

StreetEuston

WarrenStreetRegent’s

Park

OxfordCircus

BondStreet

TottenhamCourt Road

EustonSquare

GoodgeStreet

Holborn

RussellSquare

ChanceryLane

PiccadillyCircus

CityThameslinkCovent

Garden

LeicesterSquareCharingCross

St. James’sPark

LambethNorth

Vauxhall

Borough

LondonBridge

Elephant& Castle

South Bermondsey

LoughboroughJunction Denmark Hill Nunhead

East Dulwich

Peckham Rye

Herne Hill

Tulse Hill

North Dulwich

West Dulwich

MitchamJunction

West Croydon

CarshaltonBeeches

Waddon

ReedhamCoulsdon South

Purley Oaks

SouthCroydon

EastCroydon

WestNorwood

GipsyHill

CrystalPalace

Birkbeck

PengeWest

Kent HousePenge East

Lower Sydenham

Forest HillHonor Oak Park

Crofton Park

New Cross Gate

Sydenham Hill

New CrossQueens RoadPeckham

St. Johns

Surrey Quays

Rotherhithe

Cannon Street

FenchurchStreet

TowerGateway

TowerHill

Monument

AldgateEast

St. Paul’s

Shadwell

StepneyGreen

Old Street

Essex Road


International

LiverpoolStreet

CaledonianRoad &

Barnsbury

CaledonianRoad

HollowayRoad

Upper Holloway

DraytonPark

Tufnell Park

Archway

Highgate

Totteridge &Whetstone

OakleighPark

Woodside Park

West Finchley

Finchley Central

NewSouthgate

East FinchleyAlexandra Palace

Hornsey

Crouch Hill

Palmers Green

Cockfosters

Arnos Grove

Bowes Park

Wood Green

Turnpike Lane


ManorHouse

New Barnet

Hadley Wood Crews Hill

Gordon Hill

EnfieldChase

Grange Park

Winchmore Hill

Bush HillPark

EnfieldTown

Turkey Street

Southbury

Enfield Lock

Ponders End

Angel Road

EdmontonGreen

White HartLane

Bruce Grove

SouthTottenham

NorthumberlandPark

TottenhamHale

SevenSisters

StamfordHillFinsbury Park

Silver Street

BlackhorseRoad

Stoke NewingtonSt. JamesStreet

ClaptonRectory Road

Highbury & IslingtonHackney

DownsHackneyCentral

DalstonKingsland

London FieldsCambridge Heath

Bethnal Green

BethnalGreen

MileEnd

Bow Road

HackneyWick

Limehouse

PuddingMillLane

Bromley-by-Bow

Catford Bridge

BeckenhamHill

New BeckenhamRavensbourne

Sundridge Park

BromleyNorth

BeckenhamJunction

Elmers End

Eden ParkWestWickham

BromleySouth

Petts Wood

ChelsfieldKnockholt

St. Mary Cray

Sidcup

ElmsteadWoods

Grove Park

NewEltham

Lee

Hither Green

AlbanyPark

Slade Green

WoolwichDockyard

AbbeyWood

MazeHill

WestcombePark

Charlton WoolwichArsenal

Plumstead

DagenhamDock

WestHam East Ham

ForestGate

WoodgrangePark

Manor Park


WansteadPark

DagenhamHeathway

Dagenham East

ElmPark

SevenKings

HornchurchLeytonMidlandRoad

WalthamstowQueen’s Road Leytonstone

Wanstead GantsHill

Newbury Park

WalthamstowCentral

South Woodford

ChadwellHeath Upminster

Bridge

EmersonPark

Gidea Park

Harold Wood

GrangeHill

RodingValley

Wood Street

Highams Park

Buckhurst Hill

NottingHill Gate

Denham

HighWycombe

Moor Park

Carpenders Park

Watford High Street

Luton

Radlett

Slough

Staines

Hinchley Wood

WokingGuildford

Ewell West

EwellEast

Dorking

Banstead

Gatwick Airport

Caterham

East Grinstead

Upper Warlingham

Potters Bar

WelwynGardenCity

Cheshunt

Theobalds Grove

Stansted Airport

Waltham Cross

Dunton Green

Medway TownsSevenoaks

GravesendMedway Towns

Grays

Purfleet

Shoeburyness

WestHorndon

Shenfield

Debden

DevonsRoad

EastIndia

MarbleArch

Queensway

Theydon BoisLoughton

WoodLane

Plaistow

Upton Park

RuislipManor

Eastcote

Ruislip

Hemel Hempstead

Sevenoaks

West India Quay

CanadaWater

SouthEaling

Hillingdon

Uxbridge Ickenham

NorwoodJunction

Bow Church

Oakwood

Southgate

BoundsGreen

HertfordNorth

Cuffley

Brimsdown Chingford

Epping

Chigwell

AlpertonGreenford

Perivale

Brondesbury

Harringay

Arsenal

Canonbury

Homerton Leyton

Stratford

Woodford

Snaresbrook

Goodmayes

Redbridge

Becontree

Hainault

Fairlop

Barkingside

Romford

Upminster

Brentwood

Ockendon

Tilbury

Iver

Hammersmith

Royal OakMarylebone

Paddington

Bayswater

LancasterGate

HollandPark

Victoria Westminster

Embankment

Blackfriars

Temple

Farringdon

Barbican

Moorgate

Bank Aldgate

Angel

Shoreditch

Wapping

Westferry Blackwall

Poplar

All SaintsLangdon

Park

MarylandIlford

Upney

Barking

Rainham

Ashford

Shepperton

KemptonPark

Hampton

Fulwell

Whitton

Teddington

Twickenham

Osterley

Richmond Mortlake

Barnes

Waterloo

Oval Kennington

Stockwell

Brixton Brockley

Deptford

Blackheath Kidbrooke Falconwood

Eltham Welling

Belvedere

Bexleyheath

Barnehurst

Erith

KingstonBerrylands

Esher

Guildford

Haydons Road

Tooting

NorburyStreatham Common

Carshalton

Hackbridge

Sydenham

Anerley

Catford

Ladywell

Bellingham

Shortlands

Bickley

Mottingham

Chislehurst

Orpington

Bexley

Crayford

Dartford

Swanley

Tolworth

Stoneleigh

Woodmansterne KenleyWhyteleafe

Riddlesdown

Sanderstead

Coombe Lane

Hayes

MansionHouse

Chesham

Chalfont& Latimer

Amersham

Aylesbury Rickmansworth

Watford

CroxleyChorleywood

Bermondsey

Deptford Bridge

Elverson Road

Lewisham


Greenwich

Bus 285 toHeathrow Terminals 1, 2 & 3

Bus 490 toHeathrow Terminals 4 & 5

MertonPark

TherapiaLane

AmpereWay

GeorgeStreet

ChurchStreet

BeddingtonLane

WaddonMarsh Wandle

ParkReevesCorner

WellesleyRoad

Mitcham

LebanonRoad

Lloyd Park

Addiscombe

AvenueRoad

Belgrave Walk

Phipps Bridge

Morden Road

Sandilands

WoodsideArena

HarringtonRoad

BlackhorseLane

BeckenhamRoad

Addington VillageKing Henry’s Drive

New Addington

Gravel HillFieldway

Purley

Clock House

DundonaldRoad

KewBridge

Gunnersbury

Epsom

HattonCross

TramlinkTravelcards valid in

Zones 3, or 4, or 5, or 6 (orcombination of these Zones)

and Bus & Tram Passes areavailable on Tramlink

throughout the grey area

Isleworth

Syon Lane

Brentford

Streatham

StreathamHill

Kenton

Barnes Bridge

WandsworthCommon

Sudbury &Harrow Road

KensalGreen

Sudbury HillHarrow

Sudbury Hill

SudburyTown

KilburnHigh Road

SouthHampstead

Beckton

CanningTown

WestSilvertown

PontoonDock

London CityAirport

King George V

Prince RegentRoyal Albert

Beckton Park

Royal Victoria

Cyprus


Gallions Reach

Travelcards are notvalid on HeathrowConnect between

Hayes & Harlingtonand Heathrow

and on HeathrowExpress

Centrale

Woldingham

WhyteleafeSouth

Merstham

TattenhamCorner

ChipsteadKingswood

Tadworth

EpsomDowns

Whitechapel

Willesden Junction

ThorntonHeath

Selhurst

Wallington

Chiswick

Hounslow

MitchamEastfields

ELW

ELW

225

Terminal 4

Terminals1, 2, 3

Terminal 5

Underground station closed until late 2011

Shepherd’sBush

381/N381

The routes shown on this map are a guide toweekday, off-peak services but do not guaranteedirect trains between the stations shown.

Some stations and lines have restricted opening times.

South QuayCrossharbour

MudchuteIsland Gardens

Canary Wharf

Heron Quays

Improvement works may affect your journey,particularly at weekends.Check before you travel; look for publicityat stations, visit tfl.gov.uk/checkor call 020 7222 1234

Watford Junction is outside Transport for London zonalarea. Special fares apply.

East London line is closedfor major line extension work to become part of the London Overground network.

HeathrowAirport

NorthGreenwich

Performance hängt von Anzahl nichtdominierter Routen ab.



More Criteria: McRAPTOR

Ziel: Erweitern von RAPTOR auf zusätzliche Kriterien.

Arrive 10:00, £ 5

Arrive 10:15, £ 2s t

Ansatz

Labels haben Wert für jedes zusätzliche Kriterium.Mehrere nichtdominierte Labels pro Stop und Runde.Mehrere aktive Trips beim Scannen von Routen.Lösche dominierte Labels on-the-fly.



McRAPTOR Beispiel: Tarifzonen

2 3 4 5 6

7 889

112

2

3

4

56

2

3

4

56

3456

River Thames

River Thames


Station in Zone 5

Station in Zone 4

Station in Zone 3


Station in Zone 1


Travelcard Zones

6

5

4

3

2

1




Station in Zone 6

Station in Zone 77

Station in Zone 88

Station in Zone 99

Bakerloo

Central

Circle

District



London Overground

Hammersmith & City

Metropolitan

Northern

Victoria

DLR

Jubilee

National Rail

London Tramlink

Piccadilly

Waterloo & City

Smitham

Southwark



Park

Harrow & Wealdstone

Watford Junction

Bushey

Headstone Lane

Pinner

Stanmore

Canons Park

Queensbury

Preston Road

Edgware

Burnt Oak

ColindaleKingsbury

WembleyPark Hendon

NeasdenDollis Hill

WillesdenGreen

Kilburn

Hatch End



Hendon Central



Gospel Oak

Kentish Town West

West Ruislip

RuislipGardens

South Ruislip

RaynersLane

South Harrow

NortholtPark

West Harrow

Northolt

South Kenton


StonebridgePark

Harlesden

SouthGreenford

Castle BarPark

DraytonGreen

WestDrayton

Hayes &Harlington

Southall

Hanwell WestEaling

EalingBroadway

North Ealing


East


Central

NorthfieldsChiswick

Park

ActonTown

SouthActon

ActonMain Line

WestActon

St. Margarets

KewGardens

Feltham

StrawberryHill

Hampton Wick

HamptonCourt

ThamesDitton

Surbiton

ChessingtonSouth

ChessingtonNorth

Brondesbury Park

Kensal Rise

Queen’sPark

WembleyCentral

EdgwareRoad


Warwick Avenue

WestbournePark

Ladbroke Grove

EdgwareRoad

NorthActon

EastActon


HangerLane

EalingCommon

WhiteCity


Goldhawk Road

ActonCentral

BaronsCourt

Kensington(Olympia)

WestKensington

RavenscourtPark

StamfordBrook

TurnhamGreen

NorthSheen

Parsons Green

Putney Bridge

East PutneyPutney

Wimbledon Park

Southfields

Wimbledon

Raynes Park

New MaldenNorbiton

CheamBelmont

Sutton

West Sutton

Sutton Common

St. Helier

WorcesterPark

MaldenManor

SouthMerton

MordenSouth

Morden

MotspurPark

WimbledonChase

South Wimbledon

ColliersWood

Earlsfield

WandsworthTown

TootingBec

Tooting Broadway

BalhamClapham South

ClaphamCommon

Clapham North

ClaphamHigh Street


QueenstownRoad

BatterseaPark

Fulham Broadway

WestBrompton

Pimlico

SouthKensington

Earl’sCourt

SloaneSquare

GloucesterRoad

Knightsbridge


Hyde ParkCorner

GreenPark

High Barnet


Belsize Park


Camden Town

Finchley Road

Kentish Town

Swiss Cottage

St. John’s Wood

MorningtonCrescent

CamdenRoad

ImperialWharf

BakerStreet

GreatPortland

StreetEuston


Park

OxfordCircus

BondStreet

TottenhamCourt Road

EustonSquare

GoodgeStreet

Holborn

RussellSquare

ChanceryLane

PiccadillyCircus


Garden


St. James’sPark

LambethNorth

Vauxhall

Borough

LondonBridge

Elephant& Castle

South Bermondsey


East Dulwich

Peckham Rye

Herne Hill

Tulse Hill

North Dulwich

West Dulwich

MitchamJunction

West Croydon

CarshaltonBeeches

Waddon


Purley Oaks

SouthCroydon

EastCroydon

WestNorwood

GipsyHill

CrystalPalace

Birkbeck

PengeWest


Lower Sydenham


Crofton Park

New Cross Gate

Sydenham Hill


St. Johns

Surrey Quays

Rotherhithe

Cannon Street

FenchurchStreet

TowerGateway

TowerHill

Monument

AldgateEast

St. Paul’s

Shadwell

StepneyGreen

Old Street

Essex Road


International

LiverpoolStreet

CaledonianRoad &

Barnsbury

CaledonianRoad

HollowayRoad

Upper Holloway

DraytonPark

Tufnell Park

Archway

Highgate


OakleighPark

Woodside Park

West Finchley

Finchley Central

NewSouthgate


Hornsey

Crouch Hill

Palmers Green

Cockfosters

Arnos Grove

Bowes Park

Wood Green

Turnpike Lane


ManorHouse

New Barnet


Gordon Hill

EnfieldChase

Grange Park

Winchmore Hill

Bush HillPark

EnfieldTown

Turkey Street

Southbury

Enfield Lock

Ponders End

Angel Road

EdmontonGreen

White HartLane

Bruce Grove

SouthTottenham

NorthumberlandPark

TottenhamHale

SevenSisters


Silver Street

BlackhorseRoad


ClaptonRectory Road


DownsHackneyCentral

DalstonKingsland


Bethnal Green

BethnalGreen

MileEnd

Bow Road

HackneyWick

Limehouse

PuddingMillLane

Bromley-by-Bow

Catford Bridge

BeckenhamHill


Sundridge Park

BromleyNorth

BeckenhamJunction

Elmers End


BromleySouth

Petts Wood

ChelsfieldKnockholt

St. Mary Cray

Sidcup

ElmsteadWoods

Grove Park

NewEltham

Lee

Hither Green

AlbanyPark

Slade Green

WoolwichDockyard

AbbeyWood

MazeHill

WestcombePark


Plumstead

DagenhamDock

WestHam East Ham

ForestGate

WoodgrangePark

Manor Park


WansteadPark

DagenhamHeathway

Dagenham East

ElmPark

SevenKings



Wanstead GantsHill

Newbury Park

WalthamstowCentral

South Woodford


Bridge

EmersonPark

Gidea Park

Harold Wood

GrangeHill

RodingValley

Wood Street

Highams Park

Buckhurst Hill

NottingHill Gate

Denham

HighWycombe

Moor Park

Carpenders Park

Watford High Street

Luton

Radlett

Slough

Staines

Hinchley Wood

WokingGuildford

Ewell West

EwellEast

Dorking

Banstead

Gatwick Airport

Caterham

East Grinstead

Upper Warlingham

Potters Bar

WelwynGardenCity

Cheshunt

Theobalds Grove

Stansted Airport

Waltham Cross

Dunton Green



Grays

Purfleet

Shoeburyness

WestHorndon

Shenfield

Debden

DevonsRoad

EastIndia

MarbleArch

Queensway


WoodLane

Plaistow

Upton Park

RuislipManor

Eastcote

Ruislip

Hemel Hempstead

Sevenoaks

West India Quay

CanadaWater

SouthEaling

Hillingdon

Uxbridge Ickenham

NorwoodJunction

Bow Church

Oakwood

Southgate

BoundsGreen

HertfordNorth

Cuffley

Brimsdown Chingford

Epping

Chigwell

AlpertonGreenford

Perivale

Brondesbury

Harringay

Arsenal

Canonbury

Homerton Leyton

Stratford

Woodford

Snaresbrook

Goodmayes

Redbridge

Becontree

Hainault

Fairlop

BarkingsideRomford

Upminster

Brentwood

Ockendon

Tilbury

Iver

Hammersmith

Royal OakMarylebone

Paddington

Bayswater

LancasterGate

HollandPark


Embankment

Blackfriars

Temple

Farringdon

Barbican

Moorgate

Bank Aldgate

Angel

Shoreditch

Wapping

Westferry Blackwall

Poplar

All SaintsLangdon

Park

MarylandIlford

Upney

Barking

Rainham

Ashford

Shepperton

KemptonPark

Hampton

Fulwell

Whitton

Teddington

Twickenham

Osterley

Richmond Mortlake

Barnes

Waterloo

Oval Kennington

Stockwell

Brixton Brockley

Deptford


Eltham Welling

Belvedere

Bexleyheath

Barnehurst

Erith

KingstonBerrylands

Esher

Guildford

Haydons Road

Tooting


Carshalton

Hackbridge

Sydenham

Anerley

Catford

Ladywell

Bellingham

Shortlands

Bickley

Mottingham

Chislehurst

Orpington

Bexley

Crayford

Dartford

Swanley

Tolworth

Stoneleigh


Riddlesdown

Sanderstead

Coombe Lane

Hayes

MansionHouse

Chesham

Chalfont& Latimer

Amersham


Watford

CroxleyChorleywood

Bermondsey

Deptford Bridge

Elverson Road

Lewisham


Greenwich



MertonPark

TherapiaLane

AmpereWay

GeorgeStreet

ChurchStreet

BeddingtonLane

WaddonMarsh Wandle

ParkReevesCorner

WellesleyRoad

Mitcham

LebanonRoad

Lloyd Park

Addiscombe

AvenueRoad

Belgrave Walk

Phipps Bridge

Morden Road

Sandilands

WoodsideArena

HarringtonRoad

BlackhorseLane

BeckenhamRoad


New Addington

Gravel HillFieldway

Purley

Clock House

DundonaldRoad

KewBridge

Gunnersbury

Epsom

HattonCross





Isleworth

Syon Lane

Brentford

Streatham

StreathamHill

Kenton

Barnes Bridge

WandsworthCommon


KensalGreen

Sudbury HillHarrow

Sudbury Hill

SudburyTown

KilburnHigh Road

SouthHampstead

Beckton

CanningTown

WestSilvertown

PontoonDock

London CityAirport

King George V


Beckton Park

Royal Victoria

Cyprus


Gallions Reach




Centrale

Woldingham

WhyteleafeSouth

Merstham

TattenhamCorner

ChipsteadKingswood

Tadworth

EpsomDowns

Whitechapel

Willesden Junction

ThorntonHeath

Selhurst

Wallington

Chiswick

Hounslow

MitchamEastfields

ELW

ELW

225

Terminal 4

Terminals1, 2, 3

Terminal 5


Shepherd’sBush

381/N381





Canary Wharf

Heron Quays




HeathrowAirport

NorthGreenwich



McRAPTOR Beispiel: Tarifzonen

Tarifzonen einbauenDirekte Preise (£) nicht handhabbar.

⇒ Berechne alle Kombinationen vonTarifzonen,und filtere im Postprocessing.

2 3 4 5 6

7 889

112

2

3

4

56

2

3

4

56

3456

River Thames

River Thames


Station in Zone 5

Station in Zone 4

Station in Zone 3


Station in Zone 1


Travelcard Zones

6

5

4

3

2

1




Station in Zone 6

Station in Zone 77

Station in Zone 88

Station in Zone 99

Bakerloo

Central

Circle

District



London Overground

Hammersmith & City

Metropolitan

Northern

Victoria

DLR

Jubilee

National Rail

London Tramlink

Piccadilly

Waterloo & City

Smitham

Southwark



Park

Harrow & Wealdstone

Watford Junction

Bushey

Headstone Lane

Pinner

Stanmore

Canons Park

Queensbury

Preston Road

Edgware

Burnt Oak

ColindaleKingsbury

WembleyPark Hendon

NeasdenDollis Hill

WillesdenGreen

Kilburn

Hatch End



Hendon Central



Gospel Oak

Kentish Town West

West Ruislip

RuislipGardens

South Ruislip

RaynersLane

South Harrow

NortholtPark

West Harrow

Northolt

South Kenton


StonebridgePark

Harlesden

SouthGreenford

Castle BarPark

DraytonGreen

WestDrayton

Hayes &Harlington

Southall

Hanwell WestEaling

EalingBroadway

North Ealing


East


Central

NorthfieldsChiswick

Park

ActonTown

SouthActon

ActonMain Line

WestActon

St. Margarets

KewGardens

Feltham

StrawberryHill

Hampton Wick

HamptonCourt

ThamesDitton

Surbiton

ChessingtonSouth

ChessingtonNorth

Brondesbury Park

Kensal Rise

Queen’sPark

WembleyCentral

EdgwareRoad


Warwick Avenue

WestbournePark

Ladbroke Grove

EdgwareRoad

NorthActon

EastActon


HangerLane

EalingCommon

WhiteCity


Goldhawk Road

ActonCentral

BaronsCourt

Kensington(Olympia)

WestKensington

RavenscourtPark

StamfordBrook

TurnhamGreen

NorthSheen

Parsons Green

Putney Bridge

East PutneyPutney

Wimbledon Park

Southfields

Wimbledon

Raynes Park

New MaldenNorbiton

CheamBelmont

Sutton

West Sutton

Sutton Common

St. Helier

WorcesterPark

MaldenManor

SouthMerton

MordenSouth

Morden

MotspurPark

WimbledonChase

South Wimbledon

ColliersWood

Earlsfield

WandsworthTown

TootingBec

Tooting Broadway

BalhamClapham South

ClaphamCommon

Clapham North

ClaphamHigh Street


QueenstownRoad

BatterseaPark

Fulham Broadway

WestBrompton

Pimlico

SouthKensington

Earl’sCourt

SloaneSquare

GloucesterRoad

Knightsbridge


Hyde ParkCorner

GreenPark

High Barnet


Belsize Park


Camden Town

Finchley Road

Kentish Town

Swiss Cottage

St. John’s Wood

MorningtonCrescent

CamdenRoad

ImperialWharf

BakerStreet

GreatPortland

StreetEuston


Park

OxfordCircus

BondStreet

TottenhamCourt Road

EustonSquare

GoodgeStreet

Holborn

RussellSquare

ChanceryLane

PiccadillyCircus


Garden


St. James’sPark

LambethNorth

Vauxhall

Borough

LondonBridge

Elephant& Castle

South Bermondsey


East Dulwich

Peckham Rye

Herne Hill

Tulse Hill

North Dulwich

West Dulwich

MitchamJunction

West Croydon

CarshaltonBeeches

Waddon


Purley Oaks

SouthCroydon

EastCroydon

WestNorwood

GipsyHill

CrystalPalace

Birkbeck

PengeWest


Lower Sydenham


Crofton Park

New Cross Gate

Sydenham Hill


St. Johns

Surrey Quays

Rotherhithe

Cannon Street

FenchurchStreet

TowerGateway

TowerHill

Monument

AldgateEast

St. Paul’s

Shadwell

StepneyGreen

Old Street

Essex Road


International

LiverpoolStreet

CaledonianRoad &

Barnsbury

CaledonianRoad

HollowayRoad

Upper Holloway

DraytonPark

Tufnell Park

Archway

Highgate


OakleighPark

Woodside Park

West Finchley

Finchley Central

NewSouthgate


Hornsey

Crouch Hill

Palmers Green

Cockfosters

Arnos Grove

Bowes Park

Wood Green

Turnpike Lane


ManorHouse

New Barnet


Gordon Hill

EnfieldChase

Grange Park

Winchmore Hill

Bush HillPark

EnfieldTown

Turkey Street

Southbury

Enfield Lock

Ponders End

Angel Road

EdmontonGreen

White HartLane

Bruce Grove

SouthTottenham

NorthumberlandPark

TottenhamHale

SevenSisters


Silver Street

BlackhorseRoad


ClaptonRectory Road


DownsHackneyCentral

DalstonKingsland


Bethnal Green

BethnalGreen

MileEnd

Bow Road

HackneyWick

Limehouse

PuddingMillLane

Bromley-by-Bow

Catford Bridge

BeckenhamHill


Sundridge Park

BromleyNorth

BeckenhamJunction

Elmers End


BromleySouth

Petts Wood

ChelsfieldKnockholt

St. Mary Cray

Sidcup

ElmsteadWoods

Grove Park

NewEltham

Lee

Hither Green

AlbanyPark

Slade Green

WoolwichDockyard

AbbeyWood

MazeHill

WestcombePark


Plumstead

DagenhamDock

WestHam East Ham

ForestGate

WoodgrangePark

Manor Park


WansteadPark

DagenhamHeathway

Dagenham East

ElmPark

SevenKings



Wanstead GantsHill

Newbury Park

WalthamstowCentral

South Woodford


Bridge

EmersonPark

Gidea Park

Harold Wood

GrangeHill

RodingValley

Wood Street

Highams Park

Buckhurst Hill

NottingHill Gate

Denham

HighWycombe

Moor Park

Carpenders Park

Watford High Street

Luton

Radlett

Slough

Staines

Hinchley Wood

WokingGuildford

Ewell West

EwellEast

Dorking

Banstead

Gatwick Airport

Caterham

East Grinstead

Upper Warlingham

Potters Bar

WelwynGardenCity

Cheshunt

Theobalds Grove

Stansted Airport

Waltham Cross

Dunton Green



Grays

Purfleet

Shoeburyness

WestHorndon

Shenfield

Debden

DevonsRoad

EastIndia

MarbleArch

Queensway


WoodLane

Plaistow

Upton Park

RuislipManor

Eastcote

Ruislip

Hemel Hempstead

Sevenoaks

West India Quay

CanadaWater

SouthEaling

Hillingdon

Uxbridge Ickenham

NorwoodJunction

Bow Church

Oakwood

Southgate

BoundsGreen

HertfordNorth

Cuffley

Brimsdown Chingford

Epping

Chigwell

AlpertonGreenford

Perivale

Brondesbury

Harringay

Arsenal

Canonbury

Homerton Leyton

Stratford

Woodford

Snaresbrook

Goodmayes

Redbridge

Becontree

Hainault

Fairlop

Barkingside

Romford

Upminster

Brentwood

Ockendon

Tilbury

Iver

Hammersmith

Royal OakMarylebone

Paddington

Bayswater

LancasterGate

HollandPark


Embankment

Blackfriars

Temple

Farringdon

Barbican

Moorgate

Bank Aldgate

Angel

Shoreditch

Wapping

Westferry Blackwall

Poplar

All SaintsLangdon

Park

MarylandIlford

Upney

Barking

Rainham

Ashford

Shepperton

KemptonPark

Hampton

Fulwell

Whitton

Teddington

Twickenham

Osterley

Richmond Mortlake

Barnes

Waterloo

Oval Kennington

Stockwell

Brixton Brockley

Deptford


Eltham Welling

Belvedere

Bexleyheath

Barnehurst

Erith

KingstonBerrylands

Esher

Guildford

Haydons Road

Tooting


Carshalton

Hackbridge

Sydenham

Anerley

Catford

Ladywell

Bellingham

Shortlands

Bickley

Mottingham

Chislehurst

Orpington

Bexley

Crayford

Dartford

Swanley

Tolworth

Stoneleigh


Riddlesdown

Sanderstead

Coombe Lane

Hayes

MansionHouse

Chesham

Chalfont& Latimer

Amersham


Watford

CroxleyChorleywood

Bermondsey

Deptford Bridge

Elverson Road

Lewisham


Greenwich



MertonPark

TherapiaLane

AmpereWay

GeorgeStreet

ChurchStreet

BeddingtonLane

WaddonMarsh Wandle

ParkReevesCorner

WellesleyRoad

Mitcham

LebanonRoad

Lloyd Park

Addiscombe

AvenueRoad

Belgrave Walk

Phipps Bridge

Morden Road

Sandilands

WoodsideArena

HarringtonRoad

BlackhorseLane

BeckenhamRoad


New Addington

Gravel HillFieldway

Purley

Clock House

DundonaldRoad

KewBridge

Gunnersbury

Epsom

HattonCross





Isleworth

Syon Lane

Brentford

Streatham

StreathamHill

Kenton

Barnes Bridge

WandsworthCommon


KensalGreen

Sudbury HillHarrow

Sudbury Hill

SudburyTown

KilburnHigh Road

SouthHampstead

Beckton

CanningTown

WestSilvertown

PontoonDock

London CityAirport

King George V


Beckton Park

Royal Victoria

Cyprus


Gallions Reach




Centrale

Woldingham

WhyteleafeSouth

Merstham

TattenhamCorner

ChipsteadKingswood

Tadworth

EpsomDowns

Whitechapel

Willesden Junction

ThorntonHeath

Selhurst

Wallington

Chiswick

Hounslow

MitchamEastfields

ELW

ELW

225

Terminal 4

Terminals1, 2, 3

Terminal 5


Shepherd’sBush

381/N381





Canary Wharf

Heron Quays




HeathrowAirport

NorthGreenwich

≤

ImplementierungMengen von Tarifzonen als Kriterium.Dominieren =̂ Teilmengenrelation.Benutze Bits von int64 für Mengen.



Profil-Anfragen: rRAPTOR

Problem: Finde alle besten Verbindungendie in einem Zeitintervall ∆ abfahren.

Lösbar mit McRAPTOR. . .. . . mit Abfahrtszeit als Kriterium.

1. Depart 10:002. Depart 10:15

2. Arrive 11:021. Arrive 11:00

Effizienterer Ansatz: rRAPTOR (Self-Pruning)

Sammle alle Abfahrten aus Intervall ∆ in Menge D.Dann: RAPTOR für jedes τ ∈ D geordnet absteigend nach Zeit.Reinitialisiere keine Labels zwischen den Aufrufen!

Prunt implizit Routen die früher abfahren und später ankommen.



Experimente



Das Londoner Netzwerk

Das vollständige Londoner NetzwerkEin Dienstag.Beinhaltet Tube, Bus, DLR, Tram. . .20 843 Stops,2 225 Routen mit 133 011 Trips,5 132 672 einzelne Abfahrten pro Tag.

Experimente: 10 000 zufällige s–t-Anfragen.



Vergleich der Algorithmen

(Hardware: Intel Xeon X5680 mit 3.33 GHz und 96 GiB DDR3-1333 RAM)

Algorithm Ar R Tr Fz Rounds Journeys [ms]

Dijkstra • ◦ ◦ ◦ — 0.9 14.2

RAPTOR • ◦ • ◦ 8.4 1.9 7.3LD • ◦ • ◦ — 1.9 44.5MLC • ◦ • ◦ — 1.9 67.2

McRAPTOR • ◦ • • 10.8 9.0 107.4MLC • ◦ • • — 9.0 399.5

McRAPTOR • • • ◦ 9.5 16.3 259.8rRAPTOR • • • ◦ 138.5 16.3 87.0SPCS • • ◦ ◦ — 7.8 183.6

(Ar: Arrival Time, R: Range, Tr: Transfers, Fz: Fare Zones)



Parallelisierung

1 core 3 cores 6 cores 12 coresAlgorithm Ar R Tr Fz [ms] [ms] [ms] [ms]

RAPTOR • ◦ • ◦ 7.7 5.0 4.1 3.7McRAPTOR • ◦ • • 118.6 49.4 29.9 26.1rRAPTOR • • • ◦ 92.3 39.5 26.8 21.6

SPCS • • ◦ ◦ 183.6 69.1 44.9 38.9

(Ar: Arrival Time, R: Range, Tr: Transfers, Fz: Fare Zones)

Exzellente Speedups auf bis zu 6 Kernen.RAPTOR immer ≤ 30 ms.



Literatur I

Daniel Delling, Thomas Pajor, and Renato F. Werneck.Round-Based Public Transit Routing.In Proceedings of the 14th Meeting on Algorithm Engineering and Experiments(ALENEX’12), pages 130–140. SIAM, 2012.



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