msc projects at bt innovate - keith briggs: :...
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BT Research Wireless networks Projects
MSc projects at BT Innovate
Keith Briggs [email protected]
Mobility Research Centre, BT Innovatehttp://keithbriggs.info
University of York MSc talk 2009-02-11 1515
BT Research Wireless networks Projects
BT Research - Adastral Park
BT Research Wireless networks Projects
BT Research centres
• Broadband Centre
• Foresight Centre
• IT futures research Centre
• Intelligent systems Centre
• Mobility Centre
• Networks Centre
• Pervasive ICT Centre
• Security Centre
• Asian Research Centre
• Disruptive lab at MIT
BT Research Wireless networks Projects
Wireless networks
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BT Research Wireless networks Projects
BT Research Wireless networks Projects
BT Research Wireless networks Projects
BT Research Wireless networks Projects
BT Research Wireless networks Projects
Graph concepts
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0
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4
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• clique - a complete subgraph
• clique number ω - the number of nodes ina largest clique
• coloring - an assignment of colors tonodes in which no neighbours have thesame color
• chromatic number χ - the number ofcolors in a coloring with a minimalnumber of colors
• edge coloring - an assignment of colors toedges in which no edges with a commonendpoint have the same color
BT Research Wireless networks Projects
Graph concepts
1
0
2
3
4
5
• clique - a complete subgraph• clique number ω - the number of nodes in
a largest clique
• coloring - an assignment of colors tonodes in which no neighbours have thesame color
• chromatic number χ - the number ofcolors in a coloring with a minimalnumber of colors
• edge coloring - an assignment of colors toedges in which no edges with a commonendpoint have the same color
BT Research Wireless networks Projects
Graph concepts
1
0
2
3
4
5
• clique - a complete subgraph• clique number ω - the number of nodes in
a largest clique• coloring - an assignment of colors to
nodes in which no neighbours have thesame color
• chromatic number χ - the number ofcolors in a coloring with a minimalnumber of colors
• edge coloring - an assignment of colors toedges in which no edges with a commonendpoint have the same color
BT Research Wireless networks Projects
Graph concepts
1
0
2
3
4
5
• clique - a complete subgraph• clique number ω - the number of nodes in
a largest clique• coloring - an assignment of colors to
nodes in which no neighbours have thesame color
• chromatic number χ - the number ofcolors in a coloring with a minimalnumber of colors
• edge coloring - an assignment of colors toedges in which no edges with a commonendpoint have the same color
BT Research Wireless networks Projects
Graph concepts
1
0
2
3
4
5
• clique - a complete subgraph• clique number ω - the number of nodes in
a largest clique• coloring - an assignment of colors to
nodes in which no neighbours have thesame color
• chromatic number χ - the number ofcolors in a coloring with a minimalnumber of colors
• edge coloring - an assignment of colors toedges in which no edges with a commonendpoint have the same color
BT Research Wireless networks Projects
Bridge design by Costas Skarakis from 2008
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BT Research Wireless networks Projects
Quantifying TV whitespace for cognitive radio operation
Cognitive radio is being intensively studied for opportunistic accessto the so-called TV whitespace: large portions of the VHF/UHFTV bands will become available after the digital switchover. Usingaccurate digital TV (DTV) coverage maps together with adatabase of DTV transmitters, we would like to develop anaccurate methodology for identifying TVWS frequencies at anygiven location in the United Kingdom.A preliminary study has already proved the worth of this approach;we wish to take it further and make the results much more precise.The project largely involves computational geometry: such ideas asconvex hulls and point-in-polygon tests. These ideas are well worthknowing about for other applications. This is a project with directapplicability to a currently hot topic in telecoms, as well as usingfundamental geometric algorithms that need to be well-designed tomake the whole computation feasible.
BT Research Wireless networks Projects
The maths of MIMO
MIMO refers to multiple antenna systems currently beinginvestigated for use in wireless data networks. There is a lot of nicemaths used in this topic, especially for the decoding - maximumlikelihood estimation, singular-value decomposition, etc.I think a good project would be to study the basics and write anexposition emphasizing the mathematics that the method dependsupon. There is plenty of engineering expertise in my research labwhich we could draw on. An open-ended research question wouldbe to what extent exact maximum likelihood estimation can beused, or is its computational complexity too high?
BT Research Wireless networks Projects
SAT
The SAT (satisfiability) problem is a very basic problem in logic: todetermine whether a given Boolean function has an input whichmakes the output true. There are many good algorithms nowavailable to solve SAT problems, and many practical problems areequivalent to, and can be translated into SAT.This project would make a comparison of available solvers, andstudy their application to some practical problems in optimization,scheduling, and graph coloring. The fun part would be writingprograms to translate these into SAT!
BT Research Wireless networks Projects
Maximum-likelihood period estimation
This project would be to study the paper (only 4 pages!):Maximum-likelihood period estimation from sparse, noisy timingdata, by Robby McKilliam and I. Vaughan L. Clarksonand write a program to implement the method. This is animportant problem area with applications in telecoms.
BT Research Wireless networks Projects
Railway route planning allowing for delays
A previous project looked at statistical models in the delay todeparture time of trains. An interesting result was obtained - thatthe delays follow a q-exponential distribution.This project would develop algorithms and software for planningrail journeys, which takes account of the delay distribution. Theaim would be to be able to specify a specific set of trains to takefrom A to B, where the final arrival time has a probabilisticguarantee, such as “the probability of being more than 10 minuteslate is less than 3%”.
BT Research Wireless networks Projects
Chromatic number of geometric random graphs
Geometric random graphs are models of wireless communicationnetworks. The chromatic number tells us how many frequencychannels are needed to operate the network without interference.I am currently doing some work on how the chromatic number ofpurely random graphs (without the geometric structure) dependson the density (number of links per node). I find some veryinteresting results - namely, if the graph is big enough, thechromatic number is almost surely determined. This project wouldbe to examine the analogue of this behaviour for geometric randomgraphs. It will not be exactly true, but might be in someappropriate limiting cases. There is already quite a lot of work inthis area which wold have to be taken into account.
BT Research Wireless networks Projects
Semidefinite programming and graph theory
Semidefinite programming (SDP) is a kind of generalized linearprogramming. Many practical optimization problems can beformulated as SDPs. There has been rapid progress in the last 20years on understanding the theory of SDP, but the development ofSDP software that is convenient to use has lagged behind. Goodsoftware is now available. This project would use sdpsol for smalltest problems, and then move to DSDP for large problems. Theaim of the project is to see what performance one can achieve onreal graph theory problems of the types that come up in networkmodelling. Such problems include the Lovasz number (a lowerbound for the chromatic number), the maximal stable set problem,and the maximum cut problem. An important outcome of theproject would be a determination of how the computation timescales with problem size. Geometric optimization problems couldalso be studied.
BT Research Wireless networks Projects
Fast random selection
Consider the problem: a large number N of objects are presentedto us one by one, and we wish to either: Select exactly somespecified number n6N of them Select each with some specifiedprobability p.The problem becomes hard to solve efficiently when p is small,because to generate a random number which usually results in arejection is inefficient. It would be better to skip over a block ofitems. Ways to do these were proposed by Vitter in ACM TransMath Soft 13, 58 (1987).This project would investigate these methods and check theirefficiency in practice. There are applications to the generation oflarge random graphs.
BT Research Wireless networks Projects
Random sampling of set partitions
A partition of [n]=0, 1, ..., n−1 is an assignment each element to asubset called a block, without regard to the labelling of the block, ororder of elements within a block. The block structure of a partition maybe indicated by listing the elements and separating blocks with a symbolsuch as —. Thus for [5], 01—2—34 and 2—10—43 are the samepartition. If there are k blocks, we speak of a k-partition. The number ofk-partitions of [n] is given by the Stirling number of the second kindS(n, k), which can be computed from the recursionsS(n, k)=S(n−1, k−1)+kS(n−1, k), S(n, 1)=S(n, n)=1. The totalnumber of partitions of [n] is given by the sum over k of S(n, k), andthis is called a Bell number B(k).There are algorithms for generating all partitions in a Gray code order,due to Ehrlich and Ruskey. In such a sequence, only one element movesto a new block on each step. Beyond about n=15, there are too manypartitions to allow us to construct all of them in reasonable time.
Thus, for large sets, simulations must rely on a uniform random sampling
procedure. This project would investigate such methods and produce a
well-designed C library for use in other projects.
BT Research Wireless networks Projects
Fast counting
This project is inspired by the paper HyperLoglog: the analysis of anear-optimal cardinality estimation algorithm of Flajolet et al. Howdo we estimate (rapidly, and with minimal storage) the number ofdistinct items in a very large set (or data stream)? In other words,the problem concerns estimating the cardinality of a multiset.Flajolet et al. previously developed their loglog algorithm, and Iworked on an efficient C implementation of this. They have nowimproved this with the hyperloglog algorithm, and this projectwould be to implement this and compare its performance inpractice with alternatives.The algorithm should have practical applications in informatics; forexample, counting the number of different packet types in anetwork.