Approximating the Minimum Chain Completion problem

Feder, Tomás; Mannila, Heikki; Terzi, Evimaria

doi:10.1016/j.ipl.2009.05.006

Cited by 8 publications

(9 citation statements)

References 8 publications

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“…al. [11] give a 2-approximation. The total edge addition version of Chordal Completion has an O( √ ∆ log 4 (n))-approximation algorithm [1] where ∆ is the maximum degree of the input graph.…”

Section: Related Workmentioning

confidence: 99%

“…al. [11] claim an 8d + 2-approximation, where d is the smallest number such that every vertex-induced subgraph of the original graph has some vertex of degree at most d. Natanzon et. al.…”

Section: Related Workmentioning

confidence: 99%

“…Table 1 summarizes the known results for the aforementioned graph modification problems. Unknown approximation, FPT [9] Addition 8OP T -approx [21], FPT [9] 8OP T -approx [21], 8d + 2-approx [11], FPT [9] Total Addition O( √ ∆ log 4 (n))-approx [1], FPT [9] 2-approx [11], FPT [9] For the k-near problems, we show that the Unconstrained k-near Editing problem is NP-hard by adapting the NP-hardness proof for Threshold Editing from Drange et. al.…”

Section: Related Workmentioning

confidence: 99%

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Algorithms for Automatic Ranking of Participants and Tasks in an Anonymized Contest

Jiao

Ravi

Gatterbauer

2017

WALCOM: Algorithms and Computation

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We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task pair, we know whether the participant has succeeded at the task or not. We assume that participants vary in their ability to solve tasks, and that tasks vary in their difficulty to be solved. In an ideal world, stronger participants should succeed at a superset of tasks that weaker participants succeed at. Similarly, easier tasks should be completed successfully by a superset of participants who succeed at harder tasks. In reality, it can happen that a stronger participant fails at a task that a weaker participants succeeds at. Our goal is to find a perfect nesting of the participant-task relations by flipping a minimum number of participant-task relations, implying such a "nearest perfect ordering" to be the one that is closest to the truth of participant strengths and task difficulties. Many variants of the problem are known to be NP-hard. We propose six natural k-near versions of the Chain Editing problem and classify their complexity. The input to a k-near Chain Editing problem includes an initial ordering of the participants (or tasks) that we are required to respect by moving each participant (or task) at most k positions from the initial ordering. We obtain surprising results on the complexity of the six k-near problems: Five of the problems are polynomial-time solvable using dynamic programming, but one of them is NP-hard.

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Section: Related Workmentioning

confidence: 99%

“…al. [11] claim an 8d + 2-approximation, where d is the smallest number such that every vertex-induced subgraph of the original graph has some vertex of degree at most d. Natanzon et. al.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Algorithms for Automatic Ranking of Participants and Tasks in an Anonymized Contest

Jiao

Ravi

Gatterbauer

2017

WALCOM: Algorithms and Computation

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“…The relation to threshold graphs is obvious, see Figure 3 for a comparison. The problem of completing edges to obtain a chain graph was introduced by Golumbic [16] and later studied by Yannakakis [31], Feder, Mannila and Terzi [12] and finally by Fomin and Villanger [14] who showed that Chain Completion when given a bipartite graph whose bipartition must be respected is solvable in subexponential time.…”

Section: Proposition 24 (Threshold Decomposition)mentioning

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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“…The concept of chain graph has surprising applications in ecology [42,47]. Feder et al in [20] gave approximation algorithms for this problem. As an almost direct corollary of our results, it follows that Minimum Chain Completion is solvable in O(2 O( √ k log k) +k 2 nm) time.…”

Section: Question: Is There F ⊆ [V ]mentioning

confidence: 99%