Show simple item record

dc.contributor.authorWheatley, David
dc.date.accessioned2007-09-26 16:49:30 (GMT)
dc.date.available2007-09-26 16:49:30 (GMT)
dc.date.issued2007-09-26T16:49:30Z
dc.date.submitted2007
dc.identifier.urihttp://hdl.handle.net/10012/3317
dc.description.abstractIn this thesis we consider some network design games that arise from common network design problems. A network design game involves multiple players who control nodes in a network, each of which has a personal interest in seeing their nodes connected in some manner. To this end, the players will submit bids to a mechanism whose task will be to select which of the players to connect, how to connect their nodes, and how much to charge each player for the connection. We rely on many fundamental results from mechanism design (from [8], [9] & [5]) in this thesis and focus our efforts on designing and analyzing cost-sharing methods. That is, for a given set of players and their connection requirements, our algorithms compute a solution that satisfies all the players’ requirements and calculates ’fair’ prices to charge each of them for the connection. Our cost-sharing methods use a primal-dual framework developed by Agrawal, Klein and Ravi in [1] and generalized by Goemans &Williamson in [3]. We modify the algorithms by using the concept of death-time introduced by K¨onemann, Leonardi & Sch¨afer in [6]. Our main result is a 2-budget balanced and cross-monotonic cost sharing method for the downwards monotone set cover game, which arises naturally from any downwards monotone 0, 1-function. We have also designed a 2-budget balanced and cross-monotonic cost sharing method for two versions of the edge cover game arising from the edge cover problem. These games are special cases of the downwards monotone set cover game. By a result by Immorlica, Mahdian & Mirrokni in [4] our result is best possible for the edge cover game. We also designed a cross-monotonic cost sharing method for a network design game we call the Even Parity Connection game arising from the T-Join problem that generalizes proper cut requirement functions. We can show our algorithm returns cost shares that recover at least half the cost of the solution. We conjecture that our cost sharing method for the even parity connection game is competitive and thus 2-budget balance.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectGame Theoryen
dc.subjectNetwork Designen
dc.subjectCost-Sharing Methodsen
dc.titleCross-monotonic Cost-Sharing Methods for Network Design Gamesen
dc.typeMaster Thesisen
dc.pendingfalseen
dc.subject.programCombinatorics and Optimizationen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record


UWSpace

University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages