Parameterized computational complexity of finding small-diameter subgraphs

Schäfer, Alexander; Komusiewicz, Christian; Moser, Hannes; Niedermeier, Rolf

doi:10.1007/s11590-011-0311-5

Cited by 64 publications

(63 citation statements)

References 18 publications

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“…1-Club is equivalent to Clique and thus W [1]-hard with respect to . In contrast, for s ≥ 2, s-Club is fixed-parameter tractable with respect to [8,22,23]. s-Club can be solved in O * (2 n− ) time by a search tree algorithm [8,22,23] 1 .…”

Section: S-clubmentioning

confidence: 99%

Parameterized Algorithmics and Computational Experiments for Finding 2-Clubs

Hartung¹,

Komusiewicz²,

Nichterlein³

2015

JGAA

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Abstract. Given an undirected graph G = (V, E) and an integer ≥ 1, the NP-hard 2-Club problem asks for a vertex set S ⊆ V of size at least such that the subgraph induced by S has diameter at most two. In this work, we extend previous parameterized complexity studies for 2-Club. On the positive side, we give polynomial kernels for the parameters "feedback edge set size of G" and "size of a cluster editing set of G" and present a direct combinatorial algorithm for the parameter "treewidth of G". On the negative side, we first show that unless NP ⊆ coNP/poly, 2-Club does not admit a polynomial kernel with respect to the "size of a vertex cover of G". Next, we show that, under the strong exponential time hypothesis, a previous O * (2 |V |− ) search tree algorithm [Schäfer et al., Optim. Lett. 2012] cannot be improved and that, unless NP ⊆ coNP/poly, there is no polynomial kernel for the dual parameter |V | − . Finally, we show that, in spite of this lower bound, the search tree algorithm for the dual parameter |V | − can be tuned into an efficient exact algorithm for 2-Club that substantially outperforms previous implementations.

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Section: S-clubmentioning

confidence: 99%

Parameterized Algorithmics and Computational Experiments for Finding 2-Clubs

Hartung¹,

Komusiewicz²,

Nichterlein³

2015

JGAA

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“…We mention that this kind of kernelization is called Turing kernelization. See the works of BinkeleRaible, Fernau, Fomin, Lokshtanov, Saurabh, and Villanger (2012) and Schäfer, Komusiewicz, Moser, and Niedermeier (2012) for examples of this concept in the context of graph problems. Now, observe that for a given choice of p, adding exactly t candidates with the same {d, p}-signature has the same effect on the relative scores of p and d as adding more than t such candidates.…”

Section: Destructive Control By Adding Candidatesmentioning

confidence: 99%

Elections with Few Voters: Candidate Control Can Be Easy

Faliszewski¹,

Niedermeier²,

Talmon³

2017

jair

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We study the computational complexity of candidate control in elections with few voters, that is, we consider the parameterized complexity of candidate control in elections with respect to the number of voters as a parameter. We consider both the standard scenario of adding and deleting candidates, where one asks whether a given candidate can become a winner (or, in the destructive case, can be precluded from winning) by adding or deleting few candidates, as well as a combinatorial scenario where adding/deleting a candidate automatically means adding or deleting a whole group of candidates. Considering several fundamental voting rules, our results show that the parameterized complexity of candidate control, with the number of voters as the parameter, is much more varied than in the setting with many voters.

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“…Despite these theoretical limits, in the last decade resources and algorithm theory have made significant progress toward workaround, heuristic and practical detection algorithms to detect k-clubs (Bourjolly et al 2000(Bourjolly et al , 2002Pasupuleti 2008;Asahiro et al 2010;Yang et al 2010;Carvalho and Almeida 2011;Schäfer et al 2012;Chang et al 2012;Veremyev and Boginski 2012;Hartung et al 2012Hartung et al , 2013Pajouh and Balasundaram 2012;Shahinpour and Butenko 2012). Most of these algorithms find either kclubs of at least a given minimum size in a given graph G, or the maximum (i.e.…”

Section: Finding Boroughs and 2-clubsmentioning

confidence: 99%

Close communities in social networks: boroughs and 2-clubs

Laan

Marx

Mokken

2016

Soc. Netw. Anal. Min.

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The structure of close communication, contacts and association in social networks is studied in the form of maximal subgraphs of diameter 2 (2-clubs), corresponding to three types of close communities: hamlets, social circles and coteries. The concept of borough of a graph is defined and introduced. Each borough is a chained union of 2-clubs of the network and any 2-club of the network belongs to one borough. Thus the set of boroughs of a network, together with the 2-clubs held by them, are shown to contain the structure of close communication in a network. Applications are given with examples from real world network data.

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Parameterized computational complexity of finding small-diameter subgraphs

Abstract: Finding subgraphs of small diameter in undirected graphs has been seemingly unexplored from a parameterized complexity perspective. We perform the first parameterized complexity study on the corresponding NP-hard s-Club problem. We consider two parameters: the solution size and its dual.

Cited by 64 publications

References 18 publications

Parameterized Algorithmics and Computational Experiments for Finding 2-Clubs

Parameterized Algorithmics and Computational Experiments for Finding 2-Clubs

Elections with Few Voters: Candidate Control Can Be Easy

Close communities in social networks: boroughs and 2-clubs

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