An improved FPT algorithm for Almost Forest Deletion problem

Almost Forest Deletion problem (AFD) is a generalization of the Feedback Vertex Set problem, which decides whether there exist at most k vertices in a given graph G whose removal from G results in an l-forest, where k and l are two given non-negative integers, and an l-forest is a graph which can be...

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Veröffentlicht in:Information processing letters Jg. 136; S. 30 - 36
Hauptverfasser: Lin, Mugang, Feng, Qilong, Wang, Jianxin, Chen, Jianer, Fu, Bin, Li, Wenjun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.08.2018
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ISSN:0020-0190, 1872-6119
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Abstract Almost Forest Deletion problem (AFD) is a generalization of the Feedback Vertex Set problem, which decides whether there exist at most k vertices in a given graph G whose removal from G results in an l-forest, where k and l are two given non-negative integers, and an l-forest is a graph which can be transformed into a forest by deleting at most l edges. Based on the iterative compression technique, we study the iterative version of the AFD problem, called Almost Forest Deletion Disjoint Compression problem (AFDDC), which asks for a new l-forest deletion set X′ of size at most k for a given graph G that is disjoint with a given l-forest deletion set X of graph G for two given non-negative integers k and l. For the AFDDC problem, we develop some reduction rules to simplify a given instance, and give a new branching algorithm for the problem. A new branching measure is presented to evaluate the efficiency of the algorithm, which results in an algorithm of running time O⁎(4k+l). Based on the proposed algorithm for the AFDDC problem, a parameterized algorithm for the AFD problem with running time O⁎(5k4l) is presented, improving the previous result O⁎(5.0024(k+l)). •Studying a generalization of the FVS problem, called Almost Forest Deletion problem.•Presenting some reduction rules and branching rules to deal with the problem.•Introducing a measure with uniform coefficient to analyze the branching algorithm.•Developing a new parameterized algorithm with running time O⁎(5k4l) for the problem.
AbstractList Almost Forest Deletion problem (AFD) is a generalization of the Feedback Vertex Set problem, which decides whether there exist at most k vertices in a given graph G whose removal from G results in an l-forest, where k and l are two given non-negative integers, and an l-forest is a graph which can be transformed into a forest by deleting at most l edges. Based on the iterative compression technique, we study the iterative version of the AFD problem, called Almost Forest Deletion Disjoint Compression problem (AFDDC), which asks for a new l-forest deletion set X′ of size at most k for a given graph G that is disjoint with a given l-forest deletion set X of graph G for two given non-negative integers k and l. For the AFDDC problem, we develop some reduction rules to simplify a given instance, and give a new branching algorithm for the problem. A new branching measure is presented to evaluate the efficiency of the algorithm, which results in an algorithm of running time O⁎(4k+l). Based on the proposed algorithm for the AFDDC problem, a parameterized algorithm for the AFD problem with running time O⁎(5k4l) is presented, improving the previous result O⁎(5.0024(k+l)). •Studying a generalization of the FVS problem, called Almost Forest Deletion problem.•Presenting some reduction rules and branching rules to deal with the problem.•Introducing a measure with uniform coefficient to analyze the branching algorithm.•Developing a new parameterized algorithm with running time O⁎(5k4l) for the problem.
Author Fu, Bin
Feng, Qilong
Chen, Jianer
Lin, Mugang
Li, Wenjun
Wang, Jianxin
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Keywords Iterative compression
Almost forest deletion
Graph algorithms
Feedback vertex set
Fixed-parameter algorithm
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Snippet Almost Forest Deletion problem (AFD) is a generalization of the Feedback Vertex Set problem, which decides whether there exist at most k vertices in a given...
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StartPage 30
SubjectTerms Almost forest deletion
Feedback vertex set
Fixed-parameter algorithm
Graph algorithms
Iterative compression
Title An improved FPT algorithm for Almost Forest Deletion problem
URI https://dx.doi.org/10.1016/j.ipl.2018.03.016
Volume 136
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