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Subexponential Parameterized Algorithms on BoundedGenus Graphs and HMinorFree Graphs
"... cfl 202005 ACM 00045411/202005/0100100001 $5.00 ..."
Subexponential parameterized algorithms on graphs of boundedgenus and Hminorfree Graphs
"... ... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, singlecrossing ..."
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Cited by 62 (21 self)
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... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, singlecrossingminorfree
The bidimensional theory of boundedgenus graphs
 SIAM Journal on Discrete Mathematics
, 2004
"... 1 Introduction The recent theory of fixedparameter algorithms and parameterized complexity [13] has attracted much attention in its less than 10 years of existence. In general the goal is to understand when NPhard problems have algorithms thatare exponential only in a parameter k of the problem i ..."
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Cited by 16 (8 self)
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1 Introduction The recent theory of fixedparameter algorithms and parameterized complexity [13] has attracted much attention in its less than 10 years of existence. In general the goal is to understand when NPhard problems have algorithms thatare exponential only in a parameter k of the problem
Subexponential parameterized . . .
 A PRELIMINARY VERSION OF THIS ARTICLE APPEARED IN PROCEEDINGS OF THE 15TH ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS, ACM, NEW YORK, 2004, PP. 823–832
, 2004
"... We introduce a new framework for designing fixedparameter algorithms with subexponential running time—2 O( √ k) n O(1). Our results apply to a broad family of graph problems, called bidimensional problems, which includes many domination and problems such as vertex cover, feedback vertex set, minimu ..."
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cases, all previously known problems to have such subexponential algorithms. Previously, these algorithms applied to planar graphs, singlecrossingminorfree graphs, and/or map graphs; we extend these results to apply to boundedgenus graphs as well. In a parallel development
Dynamic Programming for Hminorfree Graphs?
"... Abstract. We provide a framework for the design and analysis of dynamic programming algorithms for Hminorfree graphs with branchwidth at most k. Our technique applies to a wide family of problems where standard (deterministic) dynamic programming runs in 2O(k·log k) · nO(1) steps, with n being t ..."
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Cited by 1 (1 self)
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Abstract. We provide a framework for the design and analysis of dynamic programming algorithms for Hminorfree graphs with branchwidth at most k. Our technique applies to a wide family of problems where standard (deterministic) dynamic programming runs in 2O(k·log k) · nO(1) steps, with n being
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
Faster approximation schemes and parameterized algorithms on hminorfree and oddminorfree graphs
 In MFCS
, 2010
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Subexponential parameterized algorithms
 Computer Science Review
"... We give a review of a series of techniques and results on the design of subexponential parameterized algorithms for graph problems. The design of such algorithms usually consists of two main steps: first find a branch (or tree) decomposition of the input graph whose width is bounded by a sublinear ..."
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Cited by 36 (17 self)
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We give a review of a series of techniques and results on the design of subexponential parameterized algorithms for graph problems. The design of such algorithms usually consists of two main steps: first find a branch (or tree) decomposition of the input graph whose width is bounded by a
Linear Kernels for (Connected) Dominating Set on Hminorfree graphs
"... We give the first linear kernels for DOMINATING SET and CONNECTED DOMINATING SET problems on graphs excluding a fixed graph H as a minor. In other words, we give polynomial time algorithms that, for a given Hminor free graph G and positive integer k, output an Hminor free graph G ′ on O(k) vertice ..."
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Cited by 7 (3 self)
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results we obtain the first subexponential time algorithms for CONNECTED DOMINATING SET, a deterministic algorithm solving the problem on an nvertex Hminor free graph in time 2 O( √ k log k) + n O(1) and a Monte Carlo algorithm of running time 2 O ( √ k) + n
Results 1  10
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