Dagstuhl Seminar Proceedings, Volume 7281
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
7281
2007
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-7281
07281 Abstracts Collection – Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs
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.
Parameterized complexity
fixed-parameter tractability
graph structure theory
1-14
Regular Paper
Erik
Demaine
Erik Demaine
Gregory Z.
Gutin
Gregory Z. Gutin
Daniel
Marx
Daniel Marx
Ulrike
Stege
Ulrike Stege
10.4230/DagSemProc.07281.1
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07281 Open Problems – Structure Theory and FPT Algorithmcs for Graphs, Digraphs and Hypergraphs
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.
1-6
Regular Paper
Erik
Demaine
Erik Demaine
Gregory Z.
Gutin
Gregory Z. Gutin
Daniel
Marx
Daniel Marx
Ulrike
Stege
Ulrike Stege
10.4230/DagSemProc.07281.2
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Approximating Solution Structure
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}
Approximation Algorithms
Solution Structure
1-24
Regular Paper
Iris
van Rooij
Iris van Rooij
Matthew
Hamilton
Matthew Hamilton
Moritz
Müller
Moritz Müller
Todd
Wareham
Todd Wareham
10.4230/DagSemProc.07281.3
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Directed Feedback Vertex Set is Fixed-Parameter Tractable
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 $O(8^kk!*poly(n))$.
Directed FVS
Multicut
Directed Acyclic Graph (DAG)
1-14
Regular Paper
Igor
Razgon
Igor Razgon
Barry
O'Sullivan
Barry O'Sullivan
10.4230/DagSemProc.07281.4
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Directed Feedback Vertex Set Problem is FPT
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 $O((1.48k)^kn^{O(1)})$.
Directed feedback vertex set problem
parameterized algorithm,
1-17
Regular Paper
Jianer
Chen
Jianer Chen
Yang
Liu
Yang Liu
Songiian
Lu
Songiian Lu
10.4230/DagSemProc.07281.5
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Exact Elimination of Cycles in Graphs
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.
Maximum Acyclic Subgraph
Feedback Arc Set
Amortized Analysis
Exact exponential algorthms
1-25
Regular Paper
Daniel
Raible
Daniel Raible
Henning
Fernau
Henning Fernau
10.4230/DagSemProc.07281.6
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