Results 1 - 10 of 252

Feedback Vertex Sets in Tournaments

by Serge Gaspers, Matthias Mnich , 2010
"... We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices ..."
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We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices

Feedback Vertex set and longest . . .

by Dieter Kratsch , Haiko Müller, Ioan Todinca
"... We present a polynomial time algorithm to compute a minimum (weight) feedback vertex setfor AT-free graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.We also present an O(nm²) algorithm to ..."
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We present a polynomial time algorithm to compute a minimum (weight) feedback vertex setfor AT-free graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.We also present an O(nm²) algorithm to

Parameterized algorithms for feedback vertex set

by Iyad Kanj, Michael Pelsmajer, Marcus Schaefer - in Proc. 1st Int. Workshop on Parameterized and Exact Computation, IWPEC 2004
"... Abstract. We present an algorithm for the parameterized feedback vertex set problem that runs in time O((2 lg k + 2 lg lg k + 18) k n 2). This improves the previous O(max{12 k, (4 lg k) k}n ω) algorithm by Raman et al. by roughly a 2 k factor (n w ∈ O(n 2.376) is the time needed to multiply two n × ..."
Abstract - Cited by 15 (0 self) - Add to MetaCart
Abstract. We present an algorithm for the parameterized feedback vertex set problem that runs in time O((2 lg k + 2 lg lg k + 18) k n 2). This improves the previous O(max{12 k, (4 lg k) k}n ω) algorithm by Raman et al. by roughly a 2 k factor (n w ∈ O(n 2.376) is the time needed to multiply two n

Feedback Vertex Set in Mixed Graphs

by Paul Bonsma, Daniel Lokshtanov
"... Abstract. A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph onnvertices contains a feedback vertex set (FVS) of size at mostk, in time47.5 k ·k!·O(n 4). This is the first fixed parameter tractable algorithm for FVS that ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
Abstract. A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph onnvertices contains a feedback vertex set (FVS) of size at mostk, in time47.5 k ·k!·O(n 4). This is the first fixed parameter tractable algorithm for FVS

Improved algorithms for feedback vertex set problems

by Jianer Chen , Fedor V Fomin , Yang Liu , Songjian Lu , Yngve Villanger - J. Comput. Syst. Sci
"... Abstract. We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5 k kn 2 ). The algorithms construct a feedback vertex set of size bounded by k (in the weighted case this set is of minimum weight among ..."
Abstract - Cited by 42 (9 self) - Add to MetaCart
Abstract. We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5 k kn 2 ). The algorithms construct a feedback vertex set of size bounded by k (in the weighted case this set is of minimum weight among

A cubic kernel for feedback vertex set

by Hans L. Bodlaender , 2006
"... Abstract. In this paper, it is shown that the Feedback Vertex Set problem on unweighted, undirected graphs has a kernel of cubic size. I.e., a polynomial time algorithm is described, that, when given a graph G andanintegerk, finds a graph H and integer k ′ ≤ k, such that H has a feedback vertex set ..."
Abstract - Cited by 27 (6 self) - Add to MetaCart
Abstract. In this paper, it is shown that the Feedback Vertex Set problem on unweighted, undirected graphs has a kernel of cubic size. I.e., a polynomial time algorithm is described, that, when given a graph G andanintegerk, finds a graph H and integer k ′ ≤ k, such that H has a feedback vertex

A quadratic kernel for feedback vertex set

by Stéphan Thomassé - in Proc. 20th SODA, ACM/SIAM, 2009
"... We prove that given an undirected graph G on n vertices and an integer k, one can compute in polynomial time in n a graph G ′ with at most 5k 2 +k vertices and an integer k ′ such that G has a feedback vertex set of size at most k iff G ′ has a feedback vertex set of size at most k ′. This result im ..."
Abstract - Cited by 35 (3 self) - Add to MetaCart
We prove that given an undirected graph G on n vertices and an integer k, one can compute in polynomial time in n a graph G ′ with at most 5k 2 +k vertices and an integer k ′ such that G has a feedback vertex set of size at most k iff G ′ has a feedback vertex set of size at most k ′. This result

Isomorphism for graphs of bounded feedback vertex set number

by Stefan Kratsch, Pascal Schweitzer , 2009
"... This paper presents an O(n 2) algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex deletions required to obtain a forest. Our result implies that Graph Isomorphism is fixed-parameter tractable with respect t ..."
Abstract - Cited by 12 (3 self) - Add to MetaCart
This paper presents an O(n 2) algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex deletions required to obtain a forest. Our result implies that Graph Isomorphism is fixed-parameter tractable with respect

Directed Feedback Vertex Set problem is FPT

by Jianer Chen, Yang Liu, Songjian Lu - DAGSTUHL SEMINAR SERIES, SEMINAR 07281 (2007), AVAILABLE ELECTORNICALLY AT HTTP://KATHRIN.DAGSTUHL.DE/FILES/MATERIALS/07/07281/ 07281.CHENJIANER.PAPER.PDF , 2007
"... To decide if the 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 parameterized feedback vertex set in directed graph is fixed-parameter tractable and give the first FPT algorithm of running ti ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
To decide if the 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 parameterized feedback vertex set in directed graph is fixed-parameter tractable and give the first FPT algorithm of running

Faster deterministic feedback vertex set

by Tomasz Kociumaka, Marcin Pilipczuk - CoRR
"... ar ..."
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Results 1 - 10 of 252