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25
Parameterized complexity and approximation algorithms
 Comput. J
, 2006
"... Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems. In this paper, our aim is to investigate how these two fields can be combined to achieve better algorithms than what any of the two theories could offer. We ..."
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Cited by 58 (2 self)
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Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems. In this paper, our aim is to investigate how these two fields can be combined to achieve better algorithms than what any of the two theories could offer. We discuss the different ways parameterized complexity can be extended to approximation algorithms, survey results of this type and propose directions for future research. 1.
Reflections on multivariate algorithmics and problem parameterization
 PROC. 27TH STACS
, 2010
"... Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and e ..."
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Cited by 36 (21 self)
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Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and exploitation of the “parameter space” of computationally hard problems.
Parameterized coloring problems on chordal graphs
 Theor. Comput. Sci
, 2006
"... In the precoloring extension problem (PrExt) a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper coloring of the graph with the given number of colors. Two parameterized versions of the problem are studied in ..."
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Cited by 16 (4 self)
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In the precoloring extension problem (PrExt) a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper coloring of the graph with the given number of colors. Two parameterized versions of the problem are studied in the paper: either the number of precolored vertices or the number of colors used in the precoloring is restricted to be at most k. We show that for chordal graphs these problems are polynomialtime solvable for every fixed k, but W[1]hard if k is the parameter. For a graph class F, let F + ke (resp., F +kv) denote those graphs that can be made to be a member of F by deleting at most k edges (resp., vertices). We investigate the connection between PrExt in F (with the two parameters defined above) and the coloring of F + ke, F + kv graphs (with k being the parameter). Answering an open question of Leizhen Cai [5], we show that coloring chordal+ke graphs is fixedparameter tractable. 1
Parameterized Complexity of Geometric Problems
, 2007
"... This paper surveys parameterized complexity results for hard geometric algorithmic problems. It includes fixedparameter tractable problems in graph drawing, geometric graphs, geometric covering and several other areas, together with an overview of the algorithmic techniques used. Fixedparameter in ..."
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Cited by 15 (5 self)
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This paper surveys parameterized complexity results for hard geometric algorithmic problems. It includes fixedparameter tractable problems in graph drawing, geometric graphs, geometric covering and several other areas, together with an overview of the algorithmic techniques used. Fixedparameter intractability results are surveyed as well. Finally, we give some directions for future research.
Improved algorithms and complexity results for power domination
 in graphs, Lecture Notes Comp. Sci. 3623
, 2005
"... Abstract. 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 ve ..."
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Cited by 15 (2 self)
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Abstract. 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. 1
Backdoors to satisfaction
 The Multivariate Algorithmic Revolution and Beyond  Essays Dedicated to Michael R. Fellows on the Occasion of His 60th Birthday, volume 7370 of Lecture
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The traveling salesman problem with few inner points
 In Proc. 10th COCOON, volume 3106 of LNCS
, 2004
"... We propose two algorithms for the planar Euclidean traveling salesman problem. The first runs in O(k!kn) time and O(k) space, and the second runs in O(2 k k 2 n) time and O(2 k kn) space, where n denotes the number of input points and k denotes the number of points interior to the convex hull. ..."
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Cited by 10 (1 self)
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We propose two algorithms for the planar Euclidean traveling salesman problem. The first runs in O(k!kn) time and O(k) space, and the second runs in O(2 k k 2 n) time and O(2 k kn) space, where n denotes the number of input points and k denotes the number of points interior to the convex hull.
Constant thresholds can make target set selection tractable
 In MedAlg
"... Abstract. Target Set Selection, which is a prominent NPhard problem occurring in social network analysis and distributed computing, is notoriously hard both in terms of achieving useful approximation as well as fixedparameter algorithms. The task is to select a minimum number of vertices into a “t ..."
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Cited by 10 (3 self)
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Abstract. Target Set Selection, which is a prominent NPhard problem occurring in social network analysis and distributed computing, is notoriously hard both in terms of achieving useful approximation as well as fixedparameter algorithms. The task is to select a minimum number of vertices into a “target set ” such that all other vertices will become active in course of a dynamic process (which may go through several activation rounds). A vertex, which is equipped with a threshold value t, becomes active once at least t of its neighbors are active; initially, only the target set vertices are active. We contribute further insights into islands of tractability for Target Set Selection by spotting new parameterizations characterizing some sparse graphs as well as some “cliquish ” graphs and developing corresponding fixedparameter tractability and (parameterized) hardness results. In particular, we demonstrate that upperbounding the thresholds by a constant may significantly alleviate the search for efficiently solvable, but still meaningful special cases of Target Set Selection. 1
Kemeny Elections with Bounded SinglePeaked or SingleCrossing Width
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... This paper is devoted to complexity results regarding specific measures of proximity to singlepeakedness and singlecrossingness, called “singlepeaked width” [Cornaz et al., 2012] and “singlecrossing width”. Thanks to the use of the PQtree data structure [Booth and Lueker, 1976], we show that bot ..."
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Cited by 9 (0 self)
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This paper is devoted to complexity results regarding specific measures of proximity to singlepeakedness and singlecrossingness, called “singlepeaked width” [Cornaz et al., 2012] and “singlecrossing width”. Thanks to the use of the PQtree data structure [Booth and Lueker, 1976], we show that both problems are polynomial time solvable in the general case (while it was only known for singlepeaked width and in the case of narcissistic preferences). Furthermore, we establish one of the first results (to our knowledge) concerning the effect of nearly singlepeaked electorates on the complexity of an NPhard voting system, namely we show the fixedparameter tractability of Kemeny elections with respect to the parameters “singlepeaked width ” and “singlecrossing width”.
Exploiting bounded signal flow for graph orientation based on causeeffect pairs
 In Proceedings of the 1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems (TAPAS 2011
"... Background: We consider the following problem: Given an undirected network and a set of sender–receiver pairs, direct all edges such that the maximum number of “signal flows ” defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein intera ..."
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Cited by 8 (0 self)
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Background: We consider the following problem: Given an undirected network and a set of sender–receiver pairs, direct all edges such that the maximum number of “signal flows ” defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein interaction based cell regulation mechanisms. Since this problem is NPhard, research so far concentrated on polynomialtime approximation algorithms and tractable special cases. Results: We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixedparameter tractability results, and in one case a sharp complexity dichotomy between a lineartime solvable case and a slightly more general NPhard case. We examine the value of these parameters for several realworld network instances. Conclusions: Several biologically relevant special cases of the NPhard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies. Background Current technologies [1] like twohybrid screening can