Dagstuhl Seminar Proceedings, Volume 9511



Publication Details

  • published at: 2010-03-02
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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09511 Abstracts Collection – Parameterized complexity and approximation algorithms

Authors: Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx


Abstract
From 14. 12. 2009 to 17. 12. 2009., the Dagstuhl Seminar 09511 ``Parameterized complexity and approximation algorithms '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

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Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx. 09511 Abstracts Collection – Parameterized complexity and approximation algorithms. In Parameterized complexity and approximation algorithms. Dagstuhl Seminar Proceedings, Volume 9511, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{demaine_et_al:DagSemProc.09511.1,
  author =	{Demaine, Erik D. and Hajiaghayi, MohammadTaghi and Marx, D\'{a}niel},
  title =	{{09511 Abstracts Collection – Parameterized complexity and approximation algorithms}},
  booktitle =	{Parameterized complexity and approximation algorithms},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9511},
  editor =	{Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.1},
  URN =		{urn:nbn:de:0030-drops-25025},
  doi =		{10.4230/DagSemProc.09511.1},
  annote =	{Keywords: Parameterized complexity, Approximation algorithms}
}
Document
09511 Executive Summary – Parameterized complexity and approximation algorithms

Authors: Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx


Abstract
Many of the computational problems that arise in practice are optimization problems: the task is to find a solution where the cost, quality, size, profit, or some other measure is as large or small as possible. The NP-hardness of an optimization problem implies that, unless P = NP, there is no polynomial-time algorithm that finds the exact value of the optimum. Various approaches have been proposed in the literature to cope with NP-hard problems. When designing approximation algorithms, we relax the requirement that the algorithm produces an optimum solution, and our aim is to devise a polynomial-time algorithm such that the solution it produces is not necessarily optimal, but there is some worst-case bound on the solution quality.

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Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx. 09511 Executive Summary – Parameterized complexity and approximation algorithms. In Parameterized complexity and approximation algorithms. Dagstuhl Seminar Proceedings, Volume 9511, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{demaine_et_al:DagSemProc.09511.2,
  author =	{Demaine, Erik D. and Hajiaghayi, MohammadTaghi and Marx, D\'{a}niel},
  title =	{{09511 Executive Summary – Parameterized complexity and approximation algorithms}},
  booktitle =	{Parameterized complexity and approximation algorithms},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9511},
  editor =	{Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.2},
  URN =		{urn:nbn:de:0030-drops-25011},
  doi =		{10.4230/DagSemProc.09511.2},
  annote =	{Keywords: Parameterized complexity, Approximation algorithms}
}
Document
09511 Open Problems – Parameterized complexity and approximation algorithms

Authors: Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx


Abstract
The paper contains a list of the problems presented on Monday, December 14, 2009 at the open problem session of the Seminar on Parameterized Complexity and Approximation Algorithms, held at Schloss Dagstuhl in Wadern, Germany.

Cite as

Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx. 09511 Open Problems – Parameterized complexity and approximation algorithms. In Parameterized complexity and approximation algorithms. Dagstuhl Seminar Proceedings, Volume 9511, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{demaine_et_al:DagSemProc.09511.3,
  author =	{Demaine, Erik D. and Hajiaghayi, MohammadTaghi and Marx, D\'{a}niel},
  title =	{{09511 Open Problems – Parameterized complexity and approximation algorithms}},
  booktitle =	{Parameterized complexity and approximation algorithms},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9511},
  editor =	{Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.3},
  URN =		{urn:nbn:de:0030-drops-24992},
  doi =		{10.4230/DagSemProc.09511.3},
  annote =	{Keywords: Parameterized complexity, approximation algorithms, open problems}
}
Document
Approximating minimum cost connectivity problems

Authors: Guy Kortsarz and Zeev Nutov


Abstract
We survey approximation algorithms of connectivity problems. The survey presented describing various techniques. In the talk the following techniques and results are presented. 1)Outconnectivity: Its well known that there exists a polynomial time algorithm to solve the problems of finding an edge k-outconnected from r subgraph [EDMONDS] and a vertex k-outconnectivity subgraph from r [Frank-Tardos] . We show how to use this to obtain a ratio 2 approximation for the min cost edge k-connectivity problem. 2)The critical cycle theorem of Mader: We state a fundamental theorem of Mader and use it to provide a 1+(k-1)/n ratio approximation for the min cost vertex k-connected subgraph, in the metric case. We also show results for the min power vertex k-connected problem using this lemma. We show that the min power is equivalent to the min-cost case with respect to approximation. 3)Laminarity and uncrossing: We use the well known laminarity of a BFS solution and show a simple new proof due to Ravi et al for Jain's 2 approximation for Steiner network.

Cite as

Guy Kortsarz and Zeev Nutov. Approximating minimum cost connectivity problems. In Parameterized complexity and approximation algorithms. Dagstuhl Seminar Proceedings, Volume 9511, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{kortsarz_et_al:DagSemProc.09511.4,
  author =	{Kortsarz, Guy and Nutov, Zeev},
  title =	{{Approximating minimum cost connectivity problems}},
  booktitle =	{Parameterized complexity and approximation algorithms},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9511},
  editor =	{Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.4},
  URN =		{urn:nbn:de:0030-drops-24975},
  doi =		{10.4230/DagSemProc.09511.4},
  annote =	{Keywords: Connectivity, laminar, uncrossing, Mader's Theorem, power problems}
}
Document
Contraction Bidimensionality: the Accurate Picture

Authors: Fedor V. Fomin, Petr Golovach, and Dimitrios M. Thilikos


Abstract
We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory – the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters.

Cite as

Fedor V. Fomin, Petr Golovach, and Dimitrios M. Thilikos. Contraction Bidimensionality: the Accurate Picture. In Parameterized complexity and approximation algorithms. Dagstuhl Seminar Proceedings, Volume 9511, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{fomin_et_al:DagSemProc.09511.5,
  author =	{Fomin, Fedor V. and Golovach, Petr and Thilikos, Dimitrios M.},
  title =	{{Contraction Bidimensionality: the Accurate Picture}},
  booktitle =	{Parameterized complexity and approximation algorithms},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9511},
  editor =	{Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.5},
  URN =		{urn:nbn:de:0030-drops-25009},
  doi =		{10.4230/DagSemProc.09511.5},
  annote =	{Keywords: Paramerterized Algorithms, Bidimensionality, Graph Minors}
}
Document
Differentially Private Combinatorial Optimization

Authors: Kunal Talwar, Anupam Gupta, Katrina Ligett, Frank McSherry, and Aaron Roth


Abstract
Consider the following problem: given a metric space, some of whose points are ``clients,'' select a set of at most $k$ facility locations to minimize the average distance from the clients to their nearest facility. This is just the well-studied $k$-median problem, for which many approximation algorithms and hardness results are known. Note that the objective function encourages opening facilities in areas where there are many clients, and given a solution, it is often possible to get a good idea of where the clients are located. This raises the following quandary: what if the locations of the clients are sensitive information that we would like to keep private? emph{Is it even possible to design good algorithms for this problem that preserve the privacy of the clients?} In this paper, we initiate a systematic study of algorithms for discrete optimization problems in the framework of differential privacy (which formalizes the idea of protecting the privacy of individual input elements). We show that many such problems indeed have good approximation algorithms that preserve differential privacy; this is even in cases where it is impossible to preserve cryptographic definitions of privacy while computing any non-trivial approximation to even the emph{value} of an optimal solution, let alone the entire solution. Apart from the $k$-median problem, we consider the problems of vertex and set cover, min-cut, facility location, and Steiner tree, and give approximation algorithms and lower bounds for these problems. We also consider the recently introduced submodular maximization problem, ``Combinatorial Public Projects'' (CPP), shown by Papadimitriou et al. cite{PSS08} to be inapproximable to subpolynomial multiplicative factors by any efficient and emph{truthful} algorithm. We give a differentially private (and hence approximately truthful) algorithm that achieves a logarithmic additive approximation. Joint work with Anupam Gupta, Katrina Ligett, Frank McSherry and Aaron Roth.

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Kunal Talwar, Anupam Gupta, Katrina Ligett, Frank McSherry, and Aaron Roth. Differentially Private Combinatorial Optimization. In Parameterized complexity and approximation algorithms. Dagstuhl Seminar Proceedings, Volume 9511, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{talwar_et_al:DagSemProc.09511.6,
  author =	{Talwar, Kunal and Gupta, Anupam and Ligett, Katrina and McSherry, Frank and Roth, Aaron},
  title =	{{Differentially Private Combinatorial Optimization}},
  booktitle =	{Parameterized complexity and approximation algorithms},
  pages =	{1--31},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9511},
  editor =	{Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.6},
  URN =		{urn:nbn:de:0030-drops-24986},
  doi =		{10.4230/DagSemProc.09511.6},
  annote =	{Keywords: Differential Privacy, Approximation Algorithms}
}
Document
Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses

Authors: Holger Dell and Dieter van Melkebeek


Abstract
Consider the following two-player communication process to decide a language $L$: The first player holds the entire input $x$ but is polynomially bounded; the second player is computationally unbounded but does not know any part of $x$; their goal is to cooperatively decide whether $x$ belongs to $L$ at small cost, where the cost measure is the number of bits of communication from the first player to the second player. For any integer $d geq 3$ and positive real $epsilon$ we show that if satisfiability for $n$-variable $d$-CNF formulas has a protocol of cost $O(n^{d-epsilon})$ then coNP is in NP/poly, which implies that the polynomial-time hierarchy collapses to its third level. The result even holds when the first player is conondeterministic, and is tight as there exists a trivial protocol for $epsilon = 0$. Under the hypothesis that coNP is not in NP/poly, our result implies tight lower bounds for parameters of interest in several areas, namely sparsification, kernelization in parameterized complexity, lossy compression, and probabilistically checkable proofs. By reduction, similar results hold for other NP-complete problems. For the vertex cover problem on $n$-vertex $d$-uniform hypergraphs, the above statement holds for any integer $d geq 2$. The case $d=2$ implies that no NP-hard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of $O(k^{2-epsilon})$ edges unless coNP is in NP/poly, where $k$ denotes the size of the deletion set. Kernels consisting of $O(k^2)$ edges are known for several problems in the class, including vertex cover, feedback vertex set, and bounded-degree deletion.

Cite as

Holger Dell and Dieter van Melkebeek. Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses. In Parameterized complexity and approximation algorithms. Dagstuhl Seminar Proceedings, Volume 9511, pp. 1-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{dell_et_al:DagSemProc.09511.7,
  author =	{Dell, Holger and van Melkebeek, Dieter},
  title =	{{Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses}},
  booktitle =	{Parameterized complexity and approximation algorithms},
  pages =	{1--29},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9511},
  editor =	{Erik D. Demaine and MohammadTaghi Hajiaghayi and D\'{a}niel Marx},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.7},
  URN =		{urn:nbn:de:0030-drops-25043},
  doi =		{10.4230/DagSemProc.09511.7},
  annote =	{Keywords: Sparsification, Kernelization, Parameterized Complexity, Probabilistically Checkable Proofs, Satisfiability, Vertex Cover}
}

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