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Ailon, Nir; Charikar, Moses; Newman, Alantha

doi:10.1145/1060590.1060692

Cited by 330 publications

(670 citation statements)

References 20 publications

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“…Bang-Jensen and Thomassen [5] conjectured that FAS is N P-complete even for tournaments. This conjecture was proved independently by at least four groups of researchers [1,2,8,9]. Interestingly, FAS is polynomial time solvable for planar digraphs [4,35] and trivially polynomial time solvable for undirected graphs.…”

Section: Feedback Arc and Vertex Set Problemsmentioning

confidence: 97%

“…Using this lemma it is not difficult to prove that the length of a shortest cycle C in a digraph D of S h is at most n g(n) for some function g(n) = o (1). By Part (ii) of Proposition 3.2, D has a FAS of size at most k if and only if (D+yx)−xy has a FAS of size at most k−1 for at least one arc xy of C. This observation implies an…”

Section: The Minimum Number Of Backward Arcs In An Ordering Of D;mentioning

confidence: 99%

“…The following problem was posed in [32], a paper on data-mining the internet to identify online communities. The problem seems to be an obvious and perhaps easy candidate for W [1]-hardness, but in fact has resisted much effort. …”

Section: Other Parameterized Problems On Digraphsmentioning

confidence: 99%

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Some Parameterized Problems On Digraphs

Gutin

Yeo

2007

The Computer Journal

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Section: Feedback Arc and Vertex Set Problemsmentioning

confidence: 97%

Section: The Minimum Number Of Backward Arcs In An Ordering Of D;mentioning

confidence: 99%

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Some Parameterized Problems On Digraphs

Gutin

Yeo

2007

The Computer Journal

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“…One of our main results is an elegant iterative compression algorithm for weighted Cluster Vertex Deletion using matching techniques, running in O(2 k k 9 + nm) time. 4 We extend our studies to the (also NP-hard) case where the number of clusters to be generated is limited by a second parameter d. Such studies have also been undertaken for Cluster Editing [19,22,36], but note that for Cluster Editing clearly d ≤ 2k. By way of contrast, since vertex deletion is a stronger operation than edge deletion, in the case of Cluster Vertex Deletion also d > 2k is possible.…”

Section: Introductionmentioning

confidence: 90%

“…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%

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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A novel ranking distance measure combining Cayley and Spearman footrule metrics

Sípos

Gere

Popp

et al. 2018

Journal of Chemometrics

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Defining the appropriate ranking distance measures among rankings is a classic area of study. The goal of our work is to identify a combination of methodologies, which is proven to be capable for the determination of a proper ranking system. In our study, we used 3 well-established metrics: Kendall tau, Spearman footrule, and Cayley distance and a novel metric created by the combination of Cayley and Spearman footrule metrics. The results of the newly introduced metric depend on how fast we can trade a permutation of items to the reference permutation according to the Spearman footrule. On the other hand, the distance also depends on the number of cycles and the inversions in the cycle. Two case studies-chemometric data of phytonutrients of tomato varieties and sensometric data of orange juices-were used to test the performance of the studied ranking distance metrics. The properties of the new metric were compared to the traditional metrics regarding the normality of their distributions, significant number of differences between the rating objects, and the quality of the rankings. Results were validated by leave-oneout cross-validation and significant differences by Wilcoxon matched pairs test.

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Aggregating inconsistent information

Cited by 330 publications

References 20 publications

Some Parameterized Problems On Digraphs

Some Parameterized Problems On Digraphs

Fixed-Parameter Algorithms for Cluster Vertex Deletion

A novel ranking distance measure combining Cayley and Spearman footrule metrics

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