{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume784","volumeNumber":9511,"name":"Dagstuhl Seminar Proceedings, Volume 9511","dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume784"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article2641","name":"09511 Abstracts Collection \u2013 Parameterized complexity and approximation algorithms","abstract":"From 14. 12. 2009 to 17. 12. 2009., the Dagstuhl Seminar 09511 \r\n``Parameterized complexity and approximation algorithms '' was held\r\nin Schloss Dagstuhl~--~Leibniz Center for Informatics.\r\nDuring the seminar, several participants presented their current\r\nresearch, and ongoing work and open problems were discussed. Abstracts of\r\nthe presentations given during the seminar as well as abstracts of\r\nseminar results and ideas are put together in this paper. The first section\r\ndescribes the seminar topics and goals in general.\r\nLinks to extended abstracts or full papers are provided, if available.","keywords":["Parameterized complexity","Approximation algorithms"],"author":[{"@type":"Person","name":"Demaine, Erik D.","givenName":"Erik D.","familyName":"Demaine"},{"@type":"Person","name":"Hajiaghayi, MohammadTaghi","givenName":"MohammadTaghi","familyName":"Hajiaghayi"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"position":1,"pageStart":1,"pageEnd":14,"dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Demaine, Erik D.","givenName":"Erik D.","familyName":"Demaine"},{"@type":"Person","name":"Hajiaghayi, MohammadTaghi","givenName":"MohammadTaghi","familyName":"Hajiaghayi"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume784"},{"@type":"ScholarlyArticle","@id":"#article2642","name":"09511 Executive Summary \u2013 Parameterized complexity and approximation algorithms","abstract":"Many of the computational problems that arise in practice are optimization\r\nproblems: the task is to find a solution where the cost, quality, size,\r\nprofit, or some other measure is as large or small as possible. The\r\nNP-hardness of an optimization problem implies that, unless P = NP, there is\r\nno polynomial-time algorithm that finds the exact value of the optimum.\r\nVarious approaches have been proposed in the literature to cope with NP-hard\r\nproblems. When designing approximation algorithms, we relax the requirement\r\nthat the algorithm produces an optimum solution, and our aim is to devise a\r\npolynomial-time algorithm such that the solution it produces is not\r\nnecessarily optimal, but there is some worst-case bound on the solution\r\nquality.","keywords":["Parameterized complexity","Approximation algorithms"],"author":[{"@type":"Person","name":"Demaine, Erik D.","givenName":"Erik D.","familyName":"Demaine"},{"@type":"Person","name":"Hajiaghayi, MohammadTaghi","givenName":"MohammadTaghi","familyName":"Hajiaghayi"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"position":2,"pageStart":1,"pageEnd":0,"dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Demaine, Erik D.","givenName":"Erik D.","familyName":"Demaine"},{"@type":"Person","name":"Hajiaghayi, MohammadTaghi","givenName":"MohammadTaghi","familyName":"Hajiaghayi"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume784"},{"@type":"ScholarlyArticle","@id":"#article2643","name":"09511 Open Problems \u2013 Parameterized complexity and approximation algorithms","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.","keywords":["Parameterized complexity","approximation algorithms","open problems"],"author":[{"@type":"Person","name":"Demaine, Erik D.","givenName":"Erik D.","familyName":"Demaine"},{"@type":"Person","name":"Hajiaghayi, MohammadTaghi","givenName":"MohammadTaghi","familyName":"Hajiaghayi"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"position":3,"pageStart":1,"pageEnd":10,"dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Demaine, Erik D.","givenName":"Erik D.","familyName":"Demaine"},{"@type":"Person","name":"Hajiaghayi, MohammadTaghi","givenName":"MohammadTaghi","familyName":"Hajiaghayi"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume784"},{"@type":"ScholarlyArticle","@id":"#article2644","name":"Approximating minimum cost connectivity problems","abstract":"We survey approximation algorithms of connectivity problems.\r\nThe survey presented describing various techniques. In the talk the following techniques and results are presented. \r\n\r\n1)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] . \r\nWe show how to use this to obtain a ratio 2 approximation for the min cost edge k-connectivity \r\nproblem. \r\n\r\n2)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.\r\nWe also show results for the min power vertex k-connected problem using this lemma.\r\nWe show that the min power is equivalent to the min-cost case with respect to approximation.\r\n\r\n3)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.","keywords":["Connectivity","laminar","uncrossing","Mader's Theorem","power problems"],"author":[{"@type":"Person","name":"Kortsarz, Guy","givenName":"Guy","familyName":"Kortsarz"},{"@type":"Person","name":"Nutov, Zeev","givenName":"Zeev","familyName":"Nutov"}],"position":4,"pageStart":1,"pageEnd":0,"dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kortsarz, Guy","givenName":"Guy","familyName":"Kortsarz"},{"@type":"Person","name":"Nutov, Zeev","givenName":"Zeev","familyName":"Nutov"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume784"},{"@type":"ScholarlyArticle","@id":"#article2645","name":"Contraction Bidimensionality: the Accurate Picture","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 \u2013 the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters.","keywords":["Paramerterized Algorithms","Bidimensionality","Graph Minors"],"author":[{"@type":"Person","name":"Fomin, Fedor V.","givenName":"Fedor V.","familyName":"Fomin"},{"@type":"Person","name":"Golovach, Petr","givenName":"Petr","familyName":"Golovach"},{"@type":"Person","name":"Thilikos, Dimitrios M.","givenName":"Dimitrios M.","familyName":"Thilikos"}],"position":5,"pageStart":1,"pageEnd":12,"dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Fomin, Fedor V.","givenName":"Fedor V.","familyName":"Fomin"},{"@type":"Person","name":"Golovach, Petr","givenName":"Petr","familyName":"Golovach"},{"@type":"Person","name":"Thilikos, Dimitrios M.","givenName":"Dimitrios M.","familyName":"Thilikos"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.5","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume784"},{"@type":"ScholarlyArticle","@id":"#article2646","name":"Differentially Private Combinatorial Optimization","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?}\r\n\r\nIn 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.\r\n\r\nApart 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.\r\n\r\nJoint work with Anupam Gupta, Katrina Ligett, Frank McSherry and Aaron Roth.","keywords":["Differential Privacy","Approximation Algorithms"],"author":[{"@type":"Person","name":"Talwar, Kunal","givenName":"Kunal","familyName":"Talwar"},{"@type":"Person","name":"Gupta, Anupam","givenName":"Anupam","familyName":"Gupta"},{"@type":"Person","name":"Ligett, Katrina","givenName":"Katrina","familyName":"Ligett"},{"@type":"Person","name":"McSherry, Frank","givenName":"Frank","familyName":"McSherry"},{"@type":"Person","name":"Roth, Aaron","givenName":"Aaron","familyName":"Roth"}],"position":6,"pageStart":1,"pageEnd":31,"dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Talwar, Kunal","givenName":"Kunal","familyName":"Talwar"},{"@type":"Person","name":"Gupta, Anupam","givenName":"Anupam","familyName":"Gupta"},{"@type":"Person","name":"Ligett, Katrina","givenName":"Katrina","familyName":"Ligett"},{"@type":"Person","name":"McSherry, Frank","givenName":"Frank","familyName":"McSherry"},{"@type":"Person","name":"Roth, Aaron","givenName":"Aaron","familyName":"Roth"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.6","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume784"},{"@type":"ScholarlyArticle","@id":"#article2647","name":"Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses","abstract":"Consider the following two-player communication process to decide a\r\nlanguage $L$: The first player holds the entire input $x$ but is\r\npolynomially bounded; the second player is computationally unbounded\r\nbut does not know any part of $x$; their goal is to cooperatively\r\ndecide whether $x$ belongs to $L$ at small cost, where the cost\r\nmeasure is the number of bits of communication from the first player\r\nto the second player.\r\n\r\nFor any integer $d geq 3$ and positive real $epsilon$ we show that\r\nif satisfiability for $n$-variable $d$-CNF formulas has a protocol of\r\ncost $O(n^{d-epsilon})$ then coNP is in NP\/poly, which implies that\r\nthe polynomial-time hierarchy collapses to its third level. The result\r\neven holds when the first player is conondeterministic, and is tight as\r\nthere exists a trivial protocol for $epsilon = 0$. Under the\r\nhypothesis that coNP is not in NP\/poly, our result implies tight lower\r\nbounds for parameters of interest in several areas, namely\r\nsparsification, kernelization in parameterized complexity, lossy\r\ncompression, and probabilistically checkable proofs.\r\n\r\nBy reduction, similar results hold for other NP-complete problems.\r\nFor the vertex cover problem on $n$-vertex $d$-uniform hypergraphs,\r\nthe above statement holds for any integer $d geq 2$. The case $d=2$\r\nimplies that no NP-hard vertex deletion problem based on a graph\r\nproperty that is inherited by subgraphs can have kernels consisting of\r\n$O(k^{2-epsilon})$ edges unless coNP is in NP\/poly, where $k$ denotes\r\nthe size of the deletion set. Kernels consisting of $O(k^2)$ edges are\r\nknown for several problems in the class, including vertex cover,\r\nfeedback vertex set, and bounded-degree deletion.","keywords":["Sparsification","Kernelization","Parameterized Complexity","Probabilistically Checkable Proofs","Satisfiability","Vertex Cover"],"author":[{"@type":"Person","name":"Dell, Holger","givenName":"Holger","familyName":"Dell"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"}],"position":7,"pageStart":1,"pageEnd":29,"dateCreated":"2010-03-11","datePublished":"2010-03-11","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Dell, Holger","givenName":"Holger","familyName":"Dell"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.7","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume784"}]}