Open AccessProceedings Article
Static and Dynamic Path Selection on Expander Graphs: A Random Walk Approach (Preliminary Version).
Andrei Z. Broder,Alan Frieze,Eli Upfal +2 more
- pp 531-539
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TLDR
The random walk approach gives a simple and fully distributed solution for the problem of virtual circuit switching in bounded degree expander graphs and shows that if the injection to the network and the duration of connections are both controlled by Poisson processes then the algorithm achieves a steady state utilization of the network.Abstract:
This paper addresses the problem of virtual circuit switching in bounded degree expander graphs We study the static and dynamic versions of this problem Our solutions are baaed on the rapidly mixing properties of random walks on expander graphs In the static version of the problem an algorithm is required to route a path between each of K pairs of vertices so that no edge is used by more than g paths A natural approach to this problem is through a multicommodity flow reduction However, we show that the random walk approach leads to significantly stronger results than those recently obtained by Leighton and Rao [10] using the multi-commodity flow setup In the dynamic version of the problem connection requests are continuously injected into the network, Once a connection is established it utilizes a path (a virtual circuit) for a certain time until the communication terminates and the pat h is deleted Again each edge in the network should not be used by more than g paths at once The dynamic version is a better model for the practical use of communication networks Our random walk approach gives a simple and fully distributed solution for this problem We show that if the injection to the network and the duration of connections are both controlled by Poisson processes then our algorithm achieves ●Digital Systems Research Center, 130 Lytton Ave, Palo Alto, CA 943o1 t Department of Mathematics, Carnegie-Mellon University A portion of this work was done while the author was visiting Digital SRC Supported in part by NSF grants CCR-9225008 and CCR9530974 t IBM Almaden Research Center, San Jose, CA 95120, and Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel Pumission 10nmkc digllalflmd topics ofnll or pflll ot’thismxtcrinlfhr pemmal or clmsnmm usc is gr:mtcd ivilhoul k pro!fidcd 111:11 the copies arc not mode or distrihltcd t’orprolit or conmwrciu I adwmtagc, Ihe copyrighl notice Ihc Iitle ol”thc puldicoliol) :In(i ils tialc appcw and nolicc is gi\&ll that LX)pyrigh(i, b) pNllli\,iOll (>~tht :’!Vhi ill~ “[’0LOp\ Othtr\! ist to republish 10 post on wrvers or 10 rcdis!r}l>tjlc IO 1ists requires speci Iic penniwion andfor kc ,$770( ‘ 97 1:1 1’,,so ‘1’c\m 1 ‘s:\ Copyrighl 11)97 ,-\Ckl0-XtJ7’)I-XXX-(V97,05 ,$3 5[) a steady state utilization of the network which is similar to the utilization achieved in the static case situationread more
Citations
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Proceedings ArticleDOI
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
TL;DR: Improved approximation algorithms for a family of problems involving edge-disjoint paths and unsplittable flow, and for some related routing problems, and the central theme is the underlying multi-commodity flow relaxation.
Journal ArticleDOI
Approximating disjoint-path problems using packing integer programs
TL;DR: Improved approximation algorithms for column-restricted packing integer programs are developed that are simple to implement and achieve good performance when the input has a special structure and are motivated by the disjoint paths applications.
References
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Approximate counting, uniform generation and rapidly mixing Markov chains
Alistair Sinclair,Mark Jerrum +1 more
TL;DR: In this article, it was shown that for self-reducible structures, almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible.
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Throughput-competitive on-line routing
TL;DR: A framework that allows us to address the issues of admission control and routing in high-speed networks under the restriction that once a call is admitted and routed, it has to proceed to completion and no reroutings are allowed is developed.
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Short paths in expander graphs
Jon Kleinberg,Ronitt Rubinfeld +1 more
TL;DR: This work shows that a greedy algorithm for approximating the maximum disjoint paths problem achieves a polylogarithmic approximation ratio in bounded-degree expanders, and develops new routing algorithms and structural results for bounded- degree expander graphs.
Proceedings ArticleDOI
Routing and admission control in general topology networks with Poisson arrivals
TL;DR: A new routing and admission control algorithm for general topology networks that does not require advance knowledge of the traffic patterns and outperforms greedy admission control over a broad range of network environments is suggested.
Journal ArticleDOI
Existence and Construction of Edge-Disjoint Pathson Expander Graphs
TL;DR: The authors prove sufficient conditions for the existence of edge-disjoint paths connecting any set of $q\leq n/(\log n)^\kappa$ disjoint pairs of vertices on any $n$ vertex bounded degree expander, where $\ kappa$ depends only on the expansion properties of the input graph, and not on $n$.