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39
Faster fixed parameter tractable algorithms for undirected feedback vertex set
 In Proc. 13th ISAAC, volume 2518 of LNCS
, 2002
"... Abstract. A feedback vertex set (fvs) of a graph is a set of vertices whose removal results in an acyclic graph. We show that if an undirected graph on n vertices with minimum degree at least 3 has a fvs on at most 1 3 n1−ɛ vertices, then there is a cycle of length at most 6 (for ɛ ≥ 1/2, we can eve ..."
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Cited by 26 (3 self)
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Abstract. A feedback vertex set (fvs) of a graph is a set of vertices whose removal results in an acyclic graph. We show that if an undirected graph on n vertices with minimum degree at least 3 has a fvs on at most 1 3 n1−ɛ vertices, then there is a cycle of length at most 6 (for ɛ ≥ 1/2, we can even improve ɛ this to just 6). 12 log k Using this, we obtain a O(( log log k + 6)knω) algorithm for testing whether an undirected graph on n vertices has a fvs of size at most k. Here nω is the complexity of the best matrix multiplication algorithm. The previous best parameterized algorithm for this problem took O((2k + 1) k n2) time. We also investigate the fixed parameter complexity of weighted feedback vertex set problem in weighted undirected graphs.
Approximation Algorithms for Classes of Graphs Excluding SingleCrossing Graphs as Minors
"... Many problems that are intractable for general graphs allow polynomialtime solutions for structured classes of graphs, such as planar graphs and graphs of bounded treewidth. ..."
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Cited by 26 (18 self)
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Many problems that are intractable for general graphs allow polynomialtime solutions for structured classes of graphs, such as planar graphs and graphs of bounded treewidth.
A Structural View on Parameterizing Problems: Distance from Triviality
 In First International Workshop on Parameterized and Exact Computation, IWPEC 2004, LNCS Proceedings
, 2004
"... Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters in analyzing computationally hard problems. The underlying idea is to consid ..."
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Cited by 25 (12 self)
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Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters in analyzing computationally hard problems. The underlying idea is to consider tractable special cases of generally hard problems and to introduce parameters that measure the distance from these special cases. In this paper we present several case studies of distance from triviality parameterizations (concerning Clique, Power Dominating Set, Set Cover, and Longest Common Subsequence) that exhibit the versatility of this approach to develop important new views for computational complexity analysis.
Techniques For Practical FixedParameter Algorithms
, 2007
"... The fixedparameter approach is an algorithm design technique for solving combinatorially hard (mostly NPhard) problems. For some of these problems, it can lead to algorithms that are both efficient and yet at the same time guaranteed to find optimal solutions. Focusing on their application to solv ..."
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Cited by 23 (8 self)
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The fixedparameter approach is an algorithm design technique for solving combinatorially hard (mostly NPhard) problems. For some of these problems, it can lead to algorithms that are both efficient and yet at the same time guaranteed to find optimal solutions. Focusing on their application to solving NPhard problems in practice, we survey three main techniques to develop fixedparameter algorithms, namely: kernelization (data reduction with provable performance guarantee), depthbounded search trees and a new technique called iterative compression. Our discussion is circumstantiated by several concrete case studies and provides pointers to various current challenges in the field.
Efficient Data Reduction for Dominating Set: A Linear Problem Kernel for the Planar Case (Extended Abstract)
 Lecture Notes in Computer Science (LNCS
, 2002
"... Dealing with the NPcomplete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set on planar graphs has a socalled problem kernel of linear size, achieved ..."
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Cited by 21 (8 self)
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Dealing with the NPcomplete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set on planar graphs has a socalled problem kernel of linear size, achieved by two simple and easy to implement reduction rules. This answers an open question from previous work on the parameterized complexity of Dominating Set on planar graphs.
Experiments on Data Reduction for Optimal Domination in Networks
 in Proceedings International Network Optimization Conference (INOC 2003), Evry/Paris
, 2003
"... We present empirical results on computing optimal dominating sets in networks by means of data reduction through preprocessing rules. Thus, we demonstrate the usefulness of so far only theoretically considered reduction techniques for practically solving one of the most important network problems ..."
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Cited by 18 (13 self)
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We present empirical results on computing optimal dominating sets in networks by means of data reduction through preprocessing rules. Thus, we demonstrate the usefulness of so far only theoretically considered reduction techniques for practically solving one of the most important network problems in combinatorial optimization.
Improved exact algorithms for MAXSAT
 Discrete Applied Mathematics
, 2002
"... In this paper we present improved exact and parameterized algorithms for the maximum satisfiability problem. In particular, we give an algorithm that computes a truth assignment for a boolean formula F satisfying the maximum number of clauses in time O(1.3247 m F ), where m is the number of clause ..."
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Cited by 17 (1 self)
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In this paper we present improved exact and parameterized algorithms for the maximum satisfiability problem. In particular, we give an algorithm that computes a truth assignment for a boolean formula F satisfying the maximum number of clauses in time O(1.3247 m F ), where m is the number of clauses in F, and F  is the sum of the number of literals appearing in each clause in F. Moreover, given a parameter k, we give an O(1.3695 k + F ) parameterized algorithm that decides whether a truth assignment for F satisfying at least k clauses exists. Both algorithms improve the previous best algorithms by Bansal and Raman for the problem. Key words. maximum satisfiability, exact algorithms, parameterized algorithms. 1
Kernels in planar digraphs
 In Optimization Online. Mathematical Programming Society
, 2001
"... A set S of vertices in a digraph D = (V, A) is a kernel if S is independent and every vertex in V − S has an outneighbor in S. We show that there exist O(n2 19.1 √ k + n 4)time and O(2 19.1 √ k k 9 + n 2)time algorithms for checking whether a planar digraph D of order n has a kernel with at most k ..."
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Cited by 17 (1 self)
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A set S of vertices in a digraph D = (V, A) is a kernel if S is independent and every vertex in V − S has an outneighbor in S. We show that there exist O(n2 19.1 √ k + n 4)time and O(2 19.1 √ k k 9 + n 2)time algorithms for checking whether a planar digraph D of order n has a kernel with at most k vertices. Moreover, if D has a kernel of size at most k, the algorithms find such a kernel of minimal size. 1
Improved algorithms and complexity results for power domination in graphs
 IN GRAPHS, LECTURE NOTES COMP. SCI. 3623
, 2005
"... The Power Dominating Set problem is a variant of the classical domination problem in graphs: Given an undirected graph G = (V, E), find a minimum P ⊆ V such that all vertices in V are “observed” by vertices in P. Herein, a vertex observes itself and all its neighbors, and if an observed vertex has ..."
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Cited by 16 (2 self)
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The Power Dominating Set problem is a variant of the classical domination problem in graphs: Given an undirected graph G = (V, E), find a minimum P ⊆ V such that all vertices in V are “observed” by vertices in P. Herein, a vertex observes itself and all its neighbors, and if an observed vertex has all but one of its neighbors observed, then the remaining neighbor becomes observed as well. We show that Power Dominating Set can be solved by “boundedtreewidth dynamic programs.” Moreover, we simplify and extend several NPcompleteness results, particularly showing that Power Dominating Set remains NPcomplete for planar graphs, for circle graphs, and for split graphs. Specifically, our improved reductions imply that Power Dominating Set parameterized by P is W[2]hard and cannot be better approximated than Dominating Set.
The parameterized complexity of the induced matching problem in planar graphs
 In Proceedings of the 2007 International Frontiers of Algorithmics Workshop, Lecture Notes in Comput. Sci
, 2007
"... Given a graph G and an integer k ≥ 0, the NPcomplete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted grap ..."
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Cited by 15 (1 self)
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Given a graph G and an integer k ≥ 0, the NPcomplete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted graph classes has been studied intensively. However, other than the fact that the problem is W[1]hard on general graphs little is known about the parameterized complexity of the problem in restricted graph classes. In this work, we provide firsttime fixedparameter tractability results for planar graphs, boundeddegree graphs, graphs with girth at least six, bipartite graphs, line graphs, and graphs of bounded treewidth. In particular, we give a linearsize problem kernel for planar graphs.