Integrated Logistics PROBE

Princeton University, 10/31-11/1

Presentation OutlineDefining LogisticsApplications and Key ProblemsFacility Location

Known Results Open Problems

Hierarchical Network Design Known Results Open Problems

Defining LogisticsGiven service demands, must satisfy “transporting products” from A to BGoal is to minimize service costAggregation problems

Facility Location Problems Open facilities Each demand near

to some facility Minimize sum or

max distances Some restriction on

facilities to open NP Hard (1.46)

Hierarchical Aggregation More than one level

of “cluster” Basically building a

tree or forest Solve FL over and

over… but don’t want to pay much!

App: Trucking Service

App: Trucking ServiceTalk by Ted Gifford

Schneider LogisticsMulti-Billion dollar industrySolve FL problems

Difficult to determine costs, constraints Often solve problems exactly (IP) Usually ~500-1000 nodes

Open Problems: TruckingOften multi-commodity FLHierarchical, but typically only 3-4 levelsNeed extremely accurate solutions

“average case” bounds?

App: Databases

App: DatabasesTalk by Sudipto Guha

U. Penn, AT&T researchDistributed databases

Determining data placement on networkDatabase Clustering

Many models, measures Many different heuristics!

Open Problems: DatabasesDatabases can be VERY large

“polynomial-time” not good enough Streaming/sampling based approaches

Data may change with time Need fast “update” algorithm

No clear measure of quality “quick and dirty” may be best

App: Genetics

App: GeneticsTalk by Kamesh Munagala

Stanford University, Strand GenomicsFinding patterns in DNA/proteins

Known DNA code, but proteins mysterious Can scan protein content of cells fast Scan is not very accurate though Find patterns in healthy vs. tumor cells

Open Problems: GeneticsHuge amounts of data!

Also, not very accurate, many “mistakes”Try to find separating dimension

Potentially many clusterings, find “best”Really two-step problem

Find best “dimension” of exp. combinations Cluster it, see if it separates

Results: Facility LocationTalk by David Shmoys

Cornell UniversityThree main

paradigms Linear Program

Rounding Primal-Dual Method Local Search

Results: Facility LocationTalk by Kamal Jain

Microsoft ResearchTalk by Mohammad Mahdian

MITBest approximation: 1.52

Primal-dual based “greedy” algorithm Solve LP to find “worst-case” approx

Results: Facility LocationTalk by Martin Pal

Cornell UniversityProblem of FL with hard capacitiesO(1) via local searchOpen: O(1) via primal-dual or LP?

What is LP gap? Often good to have “lower bound”

Results: Facility LocationTalk by Ramgopal Mettu

Dartmouth UniversityFAST approximations for k-median

O(nk) constant approx Repeated sampling approach

Compared to DB clustering heuristics Slightly slower, much more accurate

Open Problems: FLEliminate the gap!

1.52 vs. 1.46, VERY close Analysis of Mahdian is tight Maybe time to revisit lower bound?

K-Median Problem Local search gives 3, improve?

Load Balanced Problem Exact on the lower bounds?

Results: Network Design Talk by Adam Meyerson

CMU

O(log n) for single-sink O(log n log log n) for

one function O(1) for one sink, one

function

Results: Network DesignTalk by Kunal Talwar

UC Berkeley

Improved O(1) for one sink, function LP rounding

Results: Network DesignConnected Facility Location

Talks by Anupam Gupta Lucent Research, CMU

Chaitanya Swamy Cornell University

Give 9-approx for the problem Greedy, primal-dual approaches

Results: Network DesignTalk by Amitabh Sinha

CMUCombining Buy-at-bulk with FL

O(log n) immediate, but what about O(1)?O(1) for one cable type, small constantO(1) in generalWhat about capacitated? K-med?

Open Problems: NDMulti-commodity, multiple function

No nontrivial approximations known!O(1) for single sink?

LP gap not even known!O(1) for single function?

Cannot depend on tree embeddingMake the constants reasonable!Euclidean problem: easier?

ConclusionsMany applications and open problems!Must get in touch with DB community…Workshop was a success, but…

Need more OR participation Too short notice for faculty?

Plan another workshop, late March Hope to have some more solutions!

Thanks to Princeton

Local Arrangements by Moses Charikar + Mitra Kelly