{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume660","volumeNumber":7281,"name":"Dagstuhl Seminar Proceedings, Volume 7281","dateCreated":"2007-11-28","datePublished":"2007-11-28","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":"#volume660"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article1874","name":"07281 Abstracts Collection \u2013 Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs","abstract":"From 8th to 13th July 2007, the Dagstuhl Seminar ``Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.\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","fixed-parameter tractability","graph structure theory"],"author":[{"@type":"Person","name":"Demaine, Erik","givenName":"Erik","familyName":"Demaine"},{"@type":"Person","name":"Gutin, Gregory Z.","givenName":"Gregory Z.","familyName":"Gutin"},{"@type":"Person","name":"Marx, Daniel","givenName":"Daniel","familyName":"Marx"},{"@type":"Person","name":"Stege, Ulrike","givenName":"Ulrike","familyName":"Stege"}],"position":1,"pageStart":1,"pageEnd":14,"dateCreated":"2007-11-28","datePublished":"2007-11-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Demaine, Erik","givenName":"Erik","familyName":"Demaine"},{"@type":"Person","name":"Gutin, Gregory Z.","givenName":"Gregory Z.","familyName":"Gutin"},{"@type":"Person","name":"Marx, Daniel","givenName":"Daniel","familyName":"Marx"},{"@type":"Person","name":"Stege, Ulrike","givenName":"Ulrike","familyName":"Stege"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07281.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume660"},{"@type":"ScholarlyArticle","@id":"#article1875","name":"07281 Open Problems \u2013 Structure Theory and FPT Algorithmcs for Graphs, Digraphs and Hypergraphs","abstract":"The following is a list of the problems presented on Monday, July 9, 2007 at the open-problem session of the Seminar on Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs, held at Schloss Dagstuhl in Wadern, Germany.","author":[{"@type":"Person","name":"Demaine, Erik","givenName":"Erik","familyName":"Demaine"},{"@type":"Person","name":"Gutin, Gregory Z.","givenName":"Gregory Z.","familyName":"Gutin"},{"@type":"Person","name":"Marx, Daniel","givenName":"Daniel","familyName":"Marx"},{"@type":"Person","name":"Stege, Ulrike","givenName":"Ulrike","familyName":"Stege"}],"position":2,"pageStart":1,"pageEnd":6,"dateCreated":"2007-12-05","datePublished":"2007-12-05","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Demaine, Erik","givenName":"Erik","familyName":"Demaine"},{"@type":"Person","name":"Gutin, Gregory Z.","givenName":"Gregory Z.","familyName":"Gutin"},{"@type":"Person","name":"Marx, Daniel","givenName":"Daniel","familyName":"Marx"},{"@type":"Person","name":"Stege, Ulrike","givenName":"Ulrike","familyName":"Stege"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07281.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume660"},{"@type":"ScholarlyArticle","@id":"#article1876","name":"Approximating Solution Structure","abstract":"hen it is hard to compute an optimal solution $y in optsol(x)$ to an\r\ninstance $x$ of a problem, one may be willing to settle for an efficient\r\nalgorithm $A$ that computes an approximate solution $A(x)$. The most\r\npopular type of approximation algorithm in Computer Science (and indeed\r\nmany other applications) computes solutions whose value is within some multiplicative factor of the optimal solution value, {em e.g.},\r\n$max(frac{val(A(x))}{optval(x)}, frac{optval(x)}{val(A(x))}) leq\r\nh(|x|)$ for some function $h()$. However, an algorithm might also\r\nproduce a solution whose structure is ``close'' to the structure of an\r\noptimal solution relative to a specified solution-distance function $d$,\r\n{em i.e.}, $d(A(x), y) leq h(|x|)$ for some $y in optsol(x)$. Such\r\nstructure-approximation algorithms have applications within Cognitive\r\nScience and other areas. Though there is an\r\nextensive literature dating back over 30 years on value-approximation,\r\nthere is to our knowledge no work on general techniques for assessing\r\nthe structure-(in)approximability of a given problem.\r\n\r\nIn this talk, we describe a framework for investigating the\r\npolynomial-time and fixed-parameter structure-(in)approximability of\r\ncombinatorial optimization problems relative to metric solution-distance\r\nfunctions, {em e.g.}, Hamming distance. We motivate this framework by\r\n(1) describing a particular application within Cognitive Science and (2)\r\nshowing that value-approximability does not necessarily imply\r\nstructure-approximability (and vice versa). This framework includes\r\ndefinitions of several types of structure approximation algorithms\r\nanalogous to those studied in value-approximation, as well as\r\nstructure-approximation problem classes and a\r\nstructure-approximability-preserving reducibility. We describe a set of techniques for proving the degree of\r\nstructure-(in)approximability of a given problem, and summarize all\r\nknown results derived using these techniques. We also list 11 open\r\nquestions summarizing particularly promising directions for future\r\nresearch within this framework.\r\n\r\nvspace*{0.15in}\r\n\r\noindent\r\n(co-presented with Todd Wareham)\r\nvspace*{0.15in}\r\n\r\njointwork{Hamilton, Matthew; M\"{u}ller, Moritz; van Rooij, Iris; Wareham, Todd}","keywords":["Approximation Algorithms","Solution Structure"],"author":[{"@type":"Person","name":"van Rooij, Iris","givenName":"Iris","familyName":"van Rooij"},{"@type":"Person","name":"Hamilton, Matthew","givenName":"Matthew","familyName":"Hamilton"},{"@type":"Person","name":"M\u00fcller, Moritz","givenName":"Moritz","familyName":"M\u00fcller"},{"@type":"Person","name":"Wareham, Todd","givenName":"Todd","familyName":"Wareham"}],"position":3,"pageStart":1,"pageEnd":24,"dateCreated":"2007-11-28","datePublished":"2007-11-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"van Rooij, Iris","givenName":"Iris","familyName":"van Rooij"},{"@type":"Person","name":"Hamilton, Matthew","givenName":"Matthew","familyName":"Hamilton"},{"@type":"Person","name":"M\u00fcller, Moritz","givenName":"Moritz","familyName":"M\u00fcller"},{"@type":"Person","name":"Wareham, Todd","givenName":"Todd","familyName":"Wareham"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07281.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume660"},{"@type":"ScholarlyArticle","@id":"#article1877","name":"Directed Feedback Vertex Set is Fixed-Parameter Tractable","abstract":"We resolve positively a long standing open question regarding the\r\nfixed-parameter tractability of the parameterized Directed Feedback\r\nVertex Set problem. In particular, we propose an algorithm which\r\nsolves this problem in $O(8^kk!*poly(n))$.","keywords":["Directed FVS","Multicut","Directed Acyclic Graph (DAG)"],"author":[{"@type":"Person","name":"Razgon, Igor","givenName":"Igor","familyName":"Razgon"},{"@type":"Person","name":"O'Sullivan, Barry","givenName":"Barry","familyName":"O'Sullivan"}],"position":4,"pageStart":1,"pageEnd":14,"dateCreated":"2007-11-28","datePublished":"2007-11-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Razgon, Igor","givenName":"Igor","familyName":"Razgon"},{"@type":"Person","name":"O'Sullivan, Barry","givenName":"Barry","familyName":"O'Sullivan"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07281.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume660"},{"@type":"ScholarlyArticle","@id":"#article1878","name":"Directed Feedback Vertex Set Problem is FPT","abstract":"To decide if the {sc parameterized feedback vertex set} problem\r\nin directed graph is fixed-parameter tractable is a long standing\r\nopen problem. In this paper, we prove that the {sc parameterized\r\nfeedback vertex set} in directed graph is fixed-parameter\r\ntractable and give the first FPT algorithm of running time\r\n$O((1.48k)^kn^{O(1)})$ for it. As the {sc feedback arc set}\r\nproblem in directed graph can be transformed to a {sc\r\n feedback vertex set} problem in directed graph,\r\nhence we also show that the {sc parameterized feedback arc set}\r\nproblem can be solved in time of $O((1.48k)^kn^{O(1)})$.","keywords":["Directed feedback vertex set problem","parameterized algorithm,"],"author":[{"@type":"Person","name":"Chen, Jianer","givenName":"Jianer","familyName":"Chen"},{"@type":"Person","name":"Liu, Yang","givenName":"Yang","familyName":"Liu"},{"@type":"Person","name":"Lu, Songiian","givenName":"Songiian","familyName":"Lu"}],"position":5,"pageStart":1,"pageEnd":17,"dateCreated":"2007-11-28","datePublished":"2007-11-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Chen, Jianer","givenName":"Jianer","familyName":"Chen"},{"@type":"Person","name":"Liu, Yang","givenName":"Yang","familyName":"Liu"},{"@type":"Person","name":"Lu, Songiian","givenName":"Songiian","familyName":"Lu"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07281.5","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume660"},{"@type":"ScholarlyArticle","@id":"#article1879","name":"Exact Elimination of Cycles in Graphs","abstract":"One of the standard basic steps in drawing hierarchical graphs\r\nis to invert some arcs of the given graph to make the graph acyclic.\r\nWe discuss exact and parameterized algorithms for this problem. In particular we examine a graph class called $(1,n)$-graphs, which contains cubic graphs. For both exact and parameterized algorithms we use a non-standard measure approach for the analysis. The analysis of the parameterized algorithm is of special interest, as it is not an amortized analysis modelled by 'finite states' but rather a 'top-down' amortized analysis. For $(1,n)$-graphs we achieve a running time of $Oh^*(1.1871^m)$ and $Oh^*(1.212^k)$, for cubic graphs $Oh^*(1.1798^m)$ and $Oh^*(1.201^k)$, respectively. As a by-product the trivial bound of $2^n$ for {sc Feedback Vertex Set} on planar directed graphs is broken.","keywords":["Maximum Acyclic Subgraph","Feedback Arc Set","Amortized Analysis","Exact exponential algorthms"],"author":[{"@type":"Person","name":"Raible, Daniel","givenName":"Daniel","familyName":"Raible"},{"@type":"Person","name":"Fernau, Henning","givenName":"Henning","familyName":"Fernau"}],"position":6,"pageStart":1,"pageEnd":25,"dateCreated":"2007-11-28","datePublished":"2007-11-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Raible, Daniel","givenName":"Daniel","familyName":"Raible"},{"@type":"Person","name":"Fernau, Henning","givenName":"Henning","familyName":"Fernau"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07281.6","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume660"}]}