Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics

Komusiewicz, Christian; Nichterlein, André; Niedermeier, Rolf

doi:10.1007/978-3-662-53174-7_1

Cited by 4 publications

(3 citation statements)

References 39 publications

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“…While these lower bounds and data reduction rules give a significant speedup in practice as shown in Section 6 (also cf. Komusiewicz et al [21]), we could not show an improved theoretical worst-case bound.…”

Section: Branchandbound Algorithmcontrasting

confidence: 58%

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On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering

Figiel¹,

Himmel²,

Nichterlein³

et al. 2020

Preprint

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Editing a graph into a disjoint union of clusters is a standard optimization task in graph-based data clustering. Here, complementing classic work where the clusters shall be cliques, we focus on clusters that shall be 2-clubs, that is, subgraphs of diameter two. This naturally leads to the two NP-hard problems 2-Club Cluster Editing (the allowed editing operations are edge insertion and edge deletion) and 2-Club Cluster Vertex Deletion (the allowed editing operations are vertex deletions).Answering an open question from the literature, we show that 2-Club Cluster Editing is W[2]-hard with respect to the number of edge modifications, thus contrasting the fixed-parameter tractability result for the classic Cluster Editing problem (considering cliques instead of 2-clubs). Then focusing on 2-Club Cluster Vertex Deletion, which is easily seen to be fixed-parameter tractable, we show that under standard complexity-theoretic assumptions it does not have a polynomial-size problem kernel when parameterized by the number of vertex deletions. Nevertheless, we develop several effective data reduction and pruning rules, resulting in a competitive solver, clearly outperforming a standard CPLEX solver in most instances of an established biological test data set.

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Section: Branchandbound Algorithmcontrasting

confidence: 58%

“…Data reduction rules may be considered the most valuable contribution of parameterized algorithmics to algorithm engineering [21]. In this section, we will introduce polynomial-time data reduction rules that can be applied in each step of our search tree algorithm.…”

Section: Data Reduction Rulesmentioning

confidence: 99%

On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering

Figiel¹,

Himmel²,

Nichterlein³

et al. 2020

Preprint

Self Cite

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show abstract

“…Most considered modification operations include adding/deleting a limited number of vertices/edges. Graph modification problems have a wide range of applications and have been extensively studied in the literature, see, e.g., [1,2,3,7,8,9,12]. In particular, as the number of added/deleted vertices/edges is expected to be small in many real-world applications, it is very natural to investigate graph modification problems from the parameterized complexity perspective.…”

Section: Introductionmentioning

confidence: 99%

Improved Kernels and Algorithms for Claw and Diamond Free Edge Deletion Based on Refined Observations

Wang²,

Yang³

2017

Preprint

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In the {Claw, Diamond}-Free Edge Deletion problem, we are given a graph G and an integer k > 0, the question is whether there are at most k edges whose deletion results in a graph without claws and diamonds as induced graphs. Based on some refined observations, we propose a kernel of O(k 3 ) vertices and O(k 4 ) edges, significantly improving the previous kernel of O(k 12 ) vertices and O(k 24 ) edges. In addition, we derive an O * (3.792 k )-time algorithm for the {Claw, Diamond}-Free Edge Deletion problem.

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