The Cluster Editing Problem: Implementations and Experiments

Dehne, Frank; Langston, Michael A.; Luo, Xiaohua; Pitre, Sylvain; Shaw, Peter; Zhang, Yun

doi:10.1007/11847250_2

Cited by 60 publications

(73 citation statements)

References 6 publications

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“…Several drawbacks of this model have been pointed out (see e.g. [4,6]): for low values of the parameter k, it does not capture instances with a high number of false positives and negatives, nor does it allow overlap between clusters. As it has been observed that clusters do not always represent an equivalence relation (see [8,17]), overlapping clusters have been considered [5,7].…”

Section: Introductionmentioning

confidence: 99%

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

Heggernes

Lokshtanov

Nederlof

et al. 2010

Graph Theoretic Concepts in Computer Science

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Cluster Editing is a classical graph theoretic approach to tackle the problem of data set clustering: it consists of modifying a similarity graph into a disjoint union of cliques, i.e, clusters. As pointed out in a number of recent papers, the cluster editing model is too rigid to capture common features of real data sets. Several generalizations have thereby been proposed. In this paper, we introduce (p, q)-cluster graphs, where each cluster misses at most p edges to be a clique, and there are at most q edges between a cluster and other clusters. Our generalization is the first one that allows a large number of false positives and negatives in total, while bounding the number of these locally for each cluster by p and q. We show that recognizing (p, q)-cluster graphs is NP-complete when p and q are input. On the positive side, we show that (0, q)-cluster, (p, 1)-cluster, (p, 2)-cluster, and (1, 3)-cluster graphs can be recognized in polynomial time.

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Section: Introductionmentioning

confidence: 99%

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

Heggernes

Lokshtanov

Nederlof

et al. 2010

Graph Theoretic Concepts in Computer Science

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“…Graph modification problems ask whether a given graph G can be transformed to have a certain property using a small number of edits (such as deleting/adding vertices or edges), and have been the subject of significant previous work [29,7,8,9,25].…”

Section: Introductionmentioning

confidence: 99%

On the Threshold of Intractability

Drange

Dregi

Lokshtanov

et al. 2015

Algorithms - ESA 2015

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We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-hard, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics, 113(1): [109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124][125][126][127][128] 2001). On the positive side, we show the problem admits a quadratic vertex kernel. Furthermore, we give a subexponential time parameterized algorithm solving Threshold Editing in 2 O( √ k log k) + poly(n) time, making it one of relatively few natural problems in this complexity class on general graphs. These results are of broader interest to the field of social network analysis, where recent work of Brandes (ISAAC, 2014) posits that the minimum edit distance to a threshold graph gives a good measure of consistency for node centralities. Finally, we show that all our positive results extend to the related problem of Chain Editing, as well as the completion and deletion variants of both problems.

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“…Cluster Editing is NP-complete; it recently has shown particularly useful for clustering biological data [10,33]. Whereas also a factor-2.5 polynomialtime approximation for Cluster Editing is known [3,4,38], in practical applications fixed-parameter algorithms (combined with some heuristics) providing optimal solutions seem to dominate [5,6,10,33]. For a background on fixed-parameter algorithmics we refer to [12,15,29].…”

Section: Introductionmentioning

confidence: 99%

“…For a background on fixed-parameter algorithmics we refer to [12,15,29]. Parameterized complexity studies for Cluster Editing were initiated by Gramm et al [21] and have been further pursued in a series of papers [5,6,10,13,20,22,32,33]. A previously shown bound of O(1.92 k + n 3 ) for an n-vertex graph [20] can be improved by combining a linear-time problem kernelization algorithm [13] that yields an instance with O(k 2 ) vertices with the currently best claimed running time of O(1.82 k +n 3 ) [6] to get an algorithm with running time O(1.82 k +n+m), where m is the number of edges in the graph.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Parameter Algorithms for Cluster Vertex Deletion

Hüffner

Komusiewicz

Moser

et al.

Lecture Notes in Computer Science

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We initiate the first systematic study of the NP-hard Cluster Vertex Deletion (CVD) problem (unweighted and weighted) in terms of fixed-parameter algorithmics. In the unweighted case, one searches for a minimum number of vertex deletions to transform a graph into a collection of disjoint cliques. The parameter is the number of vertex deletions. We present efficient fixed-parameter algorithms for CVD applying the fairly new iterative compression technique. Moreover, we study the variant of CVD where the maximum number of cliques to be generated is prespecified. Here, we exploit connections to fixed-parameter algorithms for (weighted) Vertex Cover.

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The Cluster Editing Problem: Implementations and Experiments

Cited by 60 publications

References 6 publications

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

On the Threshold of Intractability

Fixed-Parameter Algorithms for Cluster Vertex Deletion

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