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Dagstuhl Seminar Proceedings, Volume 7281

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  • published at: 2007-11-28
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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Document
DOI: 10.4230/DagSemProc.07281.1
07281 Abstracts Collection – Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs

Authors: Erik Demaine, Gregory Z. Gutin, Daniel Marx, and Ulrike Stege

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. 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 Demaine, Gregory Z. Gutin, Daniel Marx, and Ulrike Stege. 07281 Abstracts Collection – Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{demaine_et_al:DagSemProc.07281.1,
  author =	{Demaine, Erik and Gutin, Gregory Z. and Marx, Daniel and Stege, Ulrike},
  title =	{{07281 Abstracts Collection – Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.1},
  URN =		{urn:nbn:de:0030-drops-12450},
  doi =		{10.4230/DagSemProc.07281.1},
  annote =	{Keywords: Parameterized complexity, fixed-parameter tractability, graph structure theory}
}
Document
DOI: 10.4230/DagSemProc.07281.2
07281 Open Problems – Structure Theory and FPT Algorithmcs for Graphs, Digraphs and Hypergraphs

Authors: Erik Demaine, Gregory Z. Gutin, Daniel Marx, and Ulrike Stege

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.
Cite as

Erik Demaine, Gregory Z. Gutin, Daniel Marx, and Ulrike Stege. 07281 Open Problems – Structure Theory and FPT Algorithmcs for Graphs, Digraphs and Hypergraphs. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{demaine_et_al:DagSemProc.07281.2,
  author =	{Demaine, Erik and Gutin, Gregory Z. and Marx, Daniel and Stege, Ulrike},
  title =	{{07281 Open Problems – Structure Theory and FPT Algorithmcs for Graphs, Digraphs and Hypergraphs}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.2},
  URN =		{urn:nbn:de:0030-drops-12542},
  doi =		{10.4230/DagSemProc.07281.2},
  annote =	{Keywords: }
}
Document
DOI: 10.4230/DagSemProc.07281.3
Approximating Solution Structure

Authors: Iris van Rooij, Matthew Hamilton, Moritz Müller, and Todd Wareham

Abstract
hen it is hard to compute an optimal solution $y in optsol(x)$ to an instance $x$ of a problem, one may be willing to settle for an efficient algorithm $A$ that computes an approximate solution $A(x)$. The most popular type of approximation algorithm in Computer Science (and indeed many other applications) computes solutions whose value is within some multiplicative factor of the optimal solution value, {em e.g.}, $max(frac{val(A(x))}{optval(x)}, frac{optval(x)}{val(A(x))}) leq h(|x|)$ for some function $h()$. However, an algorithm might also produce a solution whose structure is ``close'' to the structure of an optimal solution relative to a specified solution-distance function $d$, {em i.e.}, $d(A(x), y) leq h(|x|)$ for some $y in optsol(x)$. Such structure-approximation algorithms have applications within Cognitive Science and other areas. Though there is an extensive literature dating back over 30 years on value-approximation, there is to our knowledge no work on general techniques for assessing the structure-(in)approximability of a given problem. In this talk, we describe a framework for investigating the polynomial-time and fixed-parameter structure-(in)approximability of combinatorial optimization problems relative to metric solution-distance functions, {em e.g.}, Hamming distance. We motivate this framework by (1) describing a particular application within Cognitive Science and (2) showing that value-approximability does not necessarily imply structure-approximability (and vice versa). This framework includes definitions of several types of structure approximation algorithms analogous to those studied in value-approximation, as well as structure-approximation problem classes and a structure-approximability-preserving reducibility. We describe a set of techniques for proving the degree of structure-(in)approximability of a given problem, and summarize all known results derived using these techniques. We also list 11 open questions summarizing particularly promising directions for future research within this framework. vspace*{0.15in} oindent (co-presented with Todd Wareham) vspace*{0.15in} jointwork{Hamilton, Matthew; M"{u}ller, Moritz; van Rooij, Iris; Wareham, Todd}
Cite as

Iris van Rooij, Matthew Hamilton, Moritz Müller, and Todd Wareham. Approximating Solution Structure. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{vanrooij_et_al:DagSemProc.07281.3,
  author =	{van Rooij, Iris and Hamilton, Matthew and M\"{u}ller, Moritz and Wareham, Todd},
  title =	{{Approximating Solution Structure}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--24},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.3},
  URN =		{urn:nbn:de:0030-drops-12345},
  doi =		{10.4230/DagSemProc.07281.3},
  annote =	{Keywords: Approximation Algorithms, Solution Structure}
}
Document
DOI: 10.4230/DagSemProc.07281.4
Directed Feedback Vertex Set is Fixed-Parameter Tractable

Authors: Igor Razgon and Barry O'Sullivan

Abstract
We resolve positively a long standing open question regarding the fixed-parameter tractability of the parameterized Directed Feedback Vertex Set problem. In particular, we propose an algorithm which solves this problem in $O(8^kk!*poly(n))$.
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Igor Razgon and Barry O'Sullivan. Directed Feedback Vertex Set is Fixed-Parameter Tractable. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{razgon_et_al:DagSemProc.07281.4,
  author =	{Razgon, Igor and O'Sullivan, Barry},
  title =	{{Directed Feedback Vertex Set is Fixed-Parameter Tractable}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.4},
  URN =		{urn:nbn:de:0030-drops-12363},
  doi =		{10.4230/DagSemProc.07281.4},
  annote =	{Keywords: Directed FVS, Multicut, Directed Acyclic Graph (DAG)}
}
Document
DOI: 10.4230/DagSemProc.07281.5
Directed Feedback Vertex Set Problem is FPT

Authors: Jianer Chen, Yang Liu, and Songiian Lu

Abstract
To decide if the {sc parameterized feedback vertex set} problem in directed graph is fixed-parameter tractable is a long standing open problem. In this paper, we prove that the {sc parameterized feedback vertex set} in directed graph is fixed-parameter tractable and give the first FPT algorithm of running time $O((1.48k)^kn^{O(1)})$ for it. As the {sc feedback arc set} problem in directed graph can be transformed to a {sc feedback vertex set} problem in directed graph, hence we also show that the {sc parameterized feedback arc set} problem can be solved in time of $O((1.48k)^kn^{O(1)})$.
Cite as

Jianer Chen, Yang Liu, and Songiian Lu. Directed Feedback Vertex Set Problem is FPT. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{chen_et_al:DagSemProc.07281.5,
  author =	{Chen, Jianer and Liu, Yang and Lu, Songiian},
  title =	{{Directed Feedback Vertex Set Problem is FPT}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.5},
  URN =		{urn:nbn:de:0030-drops-12333},
  doi =		{10.4230/DagSemProc.07281.5},
  annote =	{Keywords: Directed feedback vertex set problem, parameterized algorithm,}
}
Document
DOI: 10.4230/DagSemProc.07281.6
Exact Elimination of Cycles in Graphs

Authors: Daniel Raible and Henning Fernau

Abstract
One of the standard basic steps in drawing hierarchical graphs is to invert some arcs of the given graph to make the graph acyclic. We 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.
Cite as

Daniel Raible and Henning Fernau. Exact Elimination of Cycles in Graphs. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{raible_et_al:DagSemProc.07281.6,
  author =	{Raible, Daniel and Fernau, Henning},
  title =	{{Exact Elimination of Cycles in Graphs}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.6},
  URN =		{urn:nbn:de:0030-drops-12353},
  doi =		{10.4230/DagSemProc.07281.6},
  annote =	{Keywords: Maximum Acyclic Subgraph, Feedback Arc Set, Amortized Analysis, Exact exponential algorthms}
}

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  • Authors
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  • Chen, Jianer
  • D
  • Demaine, Erik
  • F
  • Fernau, Henning
  • G
  • Gutin, Gregory Z.
  • H
  • Hamilton, Matthew
  • L
  • Liu, Yang
  • Lu, Songiian
  • M
  • Marx, Daniel
  • Müller, Moritz
  • O
  • O'Sullivan, Barry
  • R
  • Raible, Daniel
  • Razgon, Igor
  • S
  • Stege, Ulrike
  • V
  • van Rooij, Iris
  • W
  • Wareham, Todd

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