Parameterized algorithms for min-max multiway cut and list digraph homomorphism

•We design FPT-algorithms for the following two parameterized problems:•List Digraph Homomorphism, which is a “list” version of the classical Digraph Homomorphism problem.•Min-Max Multiway Cut, which is a variant of Multiway Cut.•We introduce a general problem, List Allocation, and we present parame...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 86; pp. 191 - 206
Main Authors: Kim, Eun Jung, Paul, Christophe, Sau, Ignasi, Thilikos, Dimitrios M.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2017
Elsevier
Subjects:
Digraph homomorphism
Fixed-Parameter Tractable algorithm
Mathematics
Multiway Cut
Parameterized complexity
Multiway Cut
Digraph homomorphism
Parameterized complexity
Fixed-Parameter Tractable algorithm
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:•We design FPT-algorithms for the following two parameterized problems:•List Digraph Homomorphism, which is a “list” version of the classical Digraph Homomorphism problem.•Min-Max Multiway Cut, which is a variant of Multiway Cut.•We introduce a general problem, List Allocation, and we present parameterized reductions of both aforementioned problems to it.•We provide an FPT-algorithm for the List Allocation adapting of the randomized contractions technique introduced by Chitnis et al. (2012). We design FPT-algorithms for the following problems. The first is List Digraph Homomorphism: given two digraphs G and H, with order n and h, respectively, and a list of allowed vertices of H for every vertex of G, does there exist a homomorphism from G to H respecting the list constraints? Let ℓ be the number of edges of G mapped to non-loop edges of H. The second problem is Min-Max Multiway Cut: given a graph G, an integer ℓ≥0, and a set T of r terminals, can we partition V(G) into r parts such that each part contains one terminal and there are at most ℓ edges with only one endpoint in this part? We solve both problems in time 2O(ℓ⋅log⁡h+ℓ2⋅log⁡ℓ)⋅n4⋅log⁡n and 2O((ℓr)2log⁡ℓr)⋅n4⋅log⁡n, respectively, via a reduction to a new problem called List Allocation, which we solve adapting the randomized contractions technique of Chitnis et al. (2012) [4].
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2017.01.003