2 Search Results for "Khodabande, Hadi"


Document
Rapid Mixing for the Hardcore Glauber Dynamics and Other Markov Chains in Bounded-Treewidth Graphs

Authors: David Eppstein and Daniel Frishberg

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)


Abstract
We give a new rapid mixing result for a natural random walk on the independent sets of a graph G. We show that when G has bounded treewidth, this random walk - known as the Glauber dynamics for the hardcore model - mixes rapidly for all fixed values of the standard parameter λ > 0, giving a simple alternative to existing sampling algorithms for these structures. We also show rapid mixing for analogous Markov chains on dominating sets, b-edge covers, b-matchings, maximal independent sets, and maximal b-matchings. (For b-matchings, maximal independent sets, and maximal b-matchings we also require bounded degree.) Our results imply simpler alternatives to known algorithms for the sampling and approximate counting problems in these graphs. We prove our results by applying a divide-and-conquer framework we developed in a previous paper, as an alternative to the projection-restriction technique introduced by Jerrum, Son, Tetali, and Vigoda. We extend this prior framework to handle chains for which the application of that framework is not straightforward, strengthening existing results by Dyer, Goldberg, and Jerrum and by Heinrich for the Glauber dynamics on q-colorings of graphs of bounded treewidth and bounded degree.

Cite as

David Eppstein and Daniel Frishberg. Rapid Mixing for the Hardcore Glauber Dynamics and Other Markov Chains in Bounded-Treewidth Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 30:1-30:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{eppstein_et_al:LIPIcs.ISAAC.2023.30,
  author =	{Eppstein, David and Frishberg, Daniel},
  title =	{{Rapid Mixing for the Hardcore Glauber Dynamics and Other Markov Chains in Bounded-Treewidth Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{30:1--30:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.30},
  URN =		{urn:nbn:de:0030-drops-193324},
  doi =		{10.4230/LIPIcs.ISAAC.2023.30},
  annote =	{Keywords: Glauber dynamics, mixing time, projection-restriction, multicommodity flow}
}
Document
Non-approximability and Polylogarithmic Approximations of the Single-Sink Unsplittable and Confluent Dynamic Flow Problems

Authors: Mordecai J. Golin, Hadi Khodabande, and Bo Qin

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)


Abstract
Dynamic Flows were introduced by Ford and Fulkerson in 1958 to model flows over time. They define edge capacities to be the total amount of flow that can enter an edge in one time unit. Each edge also has a length, representing the time needed to traverse it. Dynamic Flows have been used to model many problems including traffic congestion, hop-routing of packets and evacuation protocols in buildings. While the basic problem of moving the maximal amount of supplies from sources to sinks is polynomial time solvable, natural minor modifications can make it NP-hard. One such modification is that flows be confluent, i.e., all flows leaving a vertex must leave along the same edge. This corresponds to natural conditions in, e.g., evacuation planning and hop routing. We investigate the single-sink Confluent Quickest Flow problem. The input is a graph with edge capacities and lengths, sources with supplies and a sink. The problem is to find a confluent flow minimizing the time required to send supplies to the sink. Our main results include: a) Logarithmic Non-Approximability: Directed Confluent Quickest Flows cannot be approximated in polynomial time with an O(\log n) approximation factor, unless P=NP. b) Polylogarithmic Bicriteria Approximations: Polynomial time (O(\log^8 n), O(\log^2 \kappa)) bicritera approximation algorithms for the Confluent Quickest Flow problem where \kappa is the number of sinks, in both directed and undirected graphs. Corresponding results are also developed for the Confluent Maximum Flow over time problem. The techniques developed also improve recent approximation algorithms for static confluent flows.

Cite as

Mordecai J. Golin, Hadi Khodabande, and Bo Qin. Non-approximability and Polylogarithmic Approximations of the Single-Sink Unsplittable and Confluent Dynamic Flow Problems. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 41:1-41:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{golin_et_al:LIPIcs.ISAAC.2017.41,
  author =	{Golin, Mordecai J. and Khodabande, Hadi and Qin, Bo},
  title =	{{Non-approximability and Polylogarithmic Approximations of the Single-Sink Unsplittable and Confluent Dynamic Flow Problems}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{41:1--41:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.41},
  URN =		{urn:nbn:de:0030-drops-82435},
  doi =		{10.4230/LIPIcs.ISAAC.2017.41},
  annote =	{Keywords: Optimization, Approximation, Dynamic Flow, Confluent Flow}
}
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