Complexity of the cluster deletion problem on subclasses of chordal graphs

Bonomo, Flavia; Durán, Guillermo; Valencia-Pabon, Mario

doi:10.1016/j.tcs.2015.07.001

Cited by 17 publications

(36 citation statements)

References 19 publications

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“…This concludes the proof for inequalities (11) and (12). Next we consider a triplet of nodes {i, j, k} where (i, j) ∈ F + , (j, k ) ∈ F + but (i, k ) ∈ F − .…”

Section: -Approximation For Lambdaccmentioning

confidence: 52%

“…The latter studied the problem in conjunction with other related edgemodification problems, including cluster completion and cluster editing. Numerous fixed parameter tractability results are known for cluster deletion [8,14,23,24], as well many results regarding special graphs for which the problem can be solved in polynomial time [10,11,17,21]. Dessmark et al proved that recursively finding maximum cliques will return a clustering with a cluster deletion score within a factor 2 of optimal [17], though in general this procedure is NPhard.…”

Section: Cluster Deletionmentioning

confidence: 99%

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A Correlation Clustering Framework for Community Detection

Veldt

Gleich

Wirth

2018

Proceedings of the 2018 World Wide Web Conference on World Wide Web - WWW '18

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Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called Lamb-daCC that is based on a specially weighted version of correlation clustering. A key component in our methodology is a clustering resolution parameter, λ, which implicitly controls the size and structure of clusters formed by our framework. We show that, by increasing this parameter, our objective effectively interpolates between two different strategies in graph clustering: finding a sparse cut and forming dense subgraphs. Our methodology unifies and generalizes a number of other important clustering quality functions including modularity, sparsest cut, and cluster deletion, and places them all within the context of an optimization problem that has been well studied from the perspective of approximation algorithms. Our approach is particularly relevant in the regime of finding dense clusters, as it leads to a 2-approximation for the cluster deletion problem. We use our approach to cluster several graphs, including large collaboration networks and social networks.

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“…This concludes the proof for inequalities (11) and (12). Next we consider a triplet of nodes {i, j, k} where (i, j) ∈ F + , (j, k ) ∈ F + but (i, k ) ∈ F − .…”

Section: -Approximation For Lambdaccmentioning

confidence: 52%

Section: Cluster Deletionmentioning

confidence: 99%

A Correlation Clustering Framework for Community Detection

Veldt

Gleich

Wirth

2018

Proceedings of the 2018 World Wide Web Conference on World Wide Web - WWW '18

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“…Such parameters and graph-types would then guide the derivation of useful fp-(in)tractability results relative to (if necessary, reformulations of) the modularization and remodularization problems defined in Section 2. This derivation process may benefit from both the results listed above and results for closely related problems, e.g., fp-tractability results for Cluster Deletion [4,5] and Highly Connected Deletion [14] and algorithms for Graph Partition [3].…”

Section: Discussionmentioning

confidence: 99%

On the Computational Complexity of Software (Re)Modularization: Elaborations and Opportunities

Wareham

2016

Proceedings of the 9th EAI International Conference on Bio-Inspired Information and Communications Technologies (Formerly BIONE

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Software system modularization and remodularization are key challenges in software engineering. All previous research has assumed that these problems are computationally intractable and hence focused on heuristic methods such as hill-climbing, evolutionary algorithms, and simulated annealing that are fast but do not guarantee to produce solutions of optimal or even near-optimal quality. However, this intractability has never been formally established. In this paper, we give the first proofs of the N P-hardness of software modularization and remodularization relative to several models of module-internal connectivity. We also review three popular algorithmic approaches for producing provably optimal or near-optimal solutions efficiently and both discuss the applicability of these approaches in and list results in the literature relevant to practical software modularization and remodularization.

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“…This problem is known to be NPhard [7] for general graphs. However, it may become easier and polynomial-time solvable in specific graphs, for instance split graphs, block graph, proper interval graph, cographs [8], [9]. Graph classes on which CD is polynomial-time solvable can also be specified by forbidding the occurrence of certain (small) subgraphs in the input graph.…”

Section: Introductionmentioning

confidence: 99%

“…Those results were obtained for unweighted graphs. For weighted graphs, the cluster deletion problem can be solved in polynomial time on the class of K 3 -free graphs for which the CD equivalent to maximum weighted matching [8], [11].…”

Section: Introductionmentioning

confidence: 99%

A new polynomial class of cluster deletion problem

Malek

Naanaa

2016

Annals of Computer Science and Information Systems

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Abstract-Cluster Deletion (CD) problem asks to transform a given graph into a cluster graph by at most k edge deletions. CD is a combinatorial problem arising in the field of classification. In this paper, we introduce a graph transformation which enabled the identification of new polynomially solvable classes of CD problem. We show that if a graph is K3-free or (diamond, kite, house, xbanner)-free then cluster deletion problem can be solved in polynomial time on that graph.

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Complexity of the cluster deletion problem on subclasses of chordal graphs

Cited by 17 publications

References 19 publications

A Correlation Clustering Framework for Community Detection

A Correlation Clustering Framework for Community Detection

On the Computational Complexity of Software (Re)Modularization: Elaborations and Opportunities

A new polynomial class of cluster deletion problem

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