2 Search Results for "Gordon, Andrew D."

Document
DOI: 10.4230/LIPIcs.ESA.2019.37
Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Authors: Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, and Andrew van der Poel

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world networks) while still guaranteeing approximation ratios. The idea is to edit a given graph via vertex- or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution to apply to the original graph. We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as Independent Set, Vertex Cover, Feedback Vertex Set, Minimum Maximal Matching, Chromatic Number, (l-)Dominating Set, Edge (l-)Dominating Set, and Connected Dominating Set. To enable this framework, we develop new editing algorithms that find the approximately-fewest edits required to bring a given graph into one of a few important graph classes (in some cases these are bicriteria algorithms which simultaneously approximate both the number of editing operations and the target parameter of the family). For bounded degeneracy, we obtain an O(r log{n})-approximation and a bicriteria (4,4)-approximation which also extends to a smoother bicriteria trade-off. For bounded treewidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w}))-approximation, and for bounded pathwidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w} * log n))-approximation. For treedepth 2 (related to bounded expansion), we obtain a 4-approximation. We also prove complementary hardness-of-approximation results assuming P != NP: in particular, these problems are all log-factor inapproximable, except the last which is not approximable below some constant factor 2 (assuming UGC).
Cite as

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, and Andrew van der Poel. Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{demaine_et_al:LIPIcs.ESA.2019.37,
  author =	{Demaine, Erik D. and Goodrich, Timothy D. and Kloster, Kyle and Lavallee, Brian and Liu, Quanquan C. and Sullivan, Blair D. and Vakilian, Ali and van der Poel, Andrew},
  title =	{{Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.37},
  URN =		{urn:nbn:de:0030-drops-111583},
  doi =		{10.4230/LIPIcs.ESA.2019.37},
  annote =	{Keywords: structural rounding, graph editing, approximation algorithms}
}
Document
DOI: 10.4230/DagRep.5.4.123
Challenges and Trends in Probabilistic Programming (Dagstuhl Seminar 15181)

Authors: Gilles Barthe, Andrew D. Gordon, Joost-Pieter Katoen, and Annabelle McIver

Published in: Dagstuhl Reports, Volume 5, Issue 4 (2015)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 15181 "Challenges and Trends in Probabilistic Programming". Probabilistic programming is at the heart of machine learning for describing distribution functions; Bayesian inference is pivotal in their analysis. Probabilistic programs are used in security for describing both cryptographic constructions (such as randomised encryption) and security experiments. In addition, probabilistic models are an active research topic in quantitative information now. Quantum programs are inherently probabilistic due to the random outcomes of quantum measurements. Finally, there is a rapidly growing interest in program analysis of probabilistic programs, whether it be using model checking, theorem proving, static analysis, or similar. Dagstuhl Seminar 15181 brought researchers from these various research communities together so as to exploit synergies and realize cross-fertilisation.
Cite as

Gilles Barthe, Andrew D. Gordon, Joost-Pieter Katoen, and Annabelle McIver. Challenges and Trends in Probabilistic Programming (Dagstuhl Seminar 15181). In Dagstuhl Reports, Volume 5, Issue 4, pp. 123-141, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@Article{barthe_et_al:DagRep.5.4.123,
  author =	{Barthe, Gilles and Gordon, Andrew D. and Katoen, Joost-Pieter and McIver, Annabelle},
  title =	{{Challenges and Trends in Probabilistic Programming (Dagstuhl Seminar 15181)}},
  pages =	{123--141},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2015},
  volume =	{5},
  number =	{4},
  editor =	{Barthe, Gilles and Gordon, Andrew D. and Katoen, Joost-Pieter and McIver, Annabelle},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.5.4.123},
  URN =		{urn:nbn:de:0030-drops-53536},
  doi =		{10.4230/DagRep.5.4.123},
  annote =	{Keywords: Bayesian networks, differential privacy, machine learning, probabilistic programs, security, semantics, static analysis, verification}
}
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