Beyond Max-Cut: λ-extendible properties parameterized above the Poljak–Turzík bound

We define strong λ-extendibility as a variant of the notion of λ-extendible properties of graphs (Poljak and Turzík, Discrete Mathematics, 1986). We show that the parameterized APT(Π) problem — given a connected graph G on n vertices and m edges and an integer parameter k, does there exist a spannin...

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Vydáno v:Journal of computer and system sciences Ročník 80; číslo 7; s. 1384 - 1403
Hlavní autoři: Mnich, Matthias, Philip, Geevarghese, Saurabh, Saket, Suchý, Ondřej
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.11.2014
Témata:
Above-guarantee parameterization
Algorithms
Algorithms and data structures
Blocking
Fixed-parameter tractable algorithms
Graphs
Integers
Labels
Lower bounds
Mathematical analysis
Mathematical models
Max-Cut
λ-extendible properties
Algorithms and data structures
λ-extendible properties
Above-guarantee parameterization
Fixed-parameter tractable algorithms
Max-Cut
ISSN:0022-0000, 1090-2724
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Shrnutí:We define strong λ-extendibility as a variant of the notion of λ-extendible properties of graphs (Poljak and Turzík, Discrete Mathematics, 1986). We show that the parameterized APT(Π) problem — given a connected graph G on n vertices and m edges and an integer parameter k, does there exist a spanning subgraph H of G such that H∈Π and H has at least λm+1−λ2(n−1)+k edges — is fixed-parameter tractable (FPT) for all 0<λ<1, for all strongly λ-extendible graph properties Π for which the APT(Π) problem is FPT on graphs which are O(k) vertices away from being a graph in which each block is a clique. Our results hold for properties of oriented graphs and graphs with edge labels, generalize the recent result of Crowston et al. (ICALP 2012) on Max-Cut parameterized above the Edwards–Erdős bound, and yield FPT algorithms for several graph problems parameterized above lower bounds. •We derive fixed-parameter algorithms for a generalization of above-guarantee Max-Cut.•The generalization also captures properties of oriented/edge-labelled graphs.•Our results build on and generalize the work of Crowston et al. (ICALP 2012) on Max-Cut.•As a corollary we solve an open question of Raman and Saurabh (Theor. Comput. Sci. 2006).
Bibliografie:ObjectType-Article-2
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ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2014.04.011