Fixed-Parameter Algorithms for Kemeny Scores

Betzler, Nadja; Fellows, Michael R.; Guo, Jiong; Niedermeier, Rolf; Rosamond, Frances A.

doi:10.1007/978-3-540-68880-8_8

Cited by 22 publications

(29 citation statements)

References 10 publications

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“…We develop algorithms of running times O * (1.403 kt ), O * (5.823 kt/m ) ≤ O * (5.823 kavg ) and O * (4.829 kmax ) for the problem, ignoring the polynomial factors in the O * notation, where k t is the optimum total τ -distance, m is the number of votes, and k avg (resp, k max ) is the average (resp, maximum) over pairwise τ -distances of votes. Our algorithms improve the best previously known running times of O * (1.53 kt ) and O * (16 kavg ) ≤ O * (16 kmax ) [4,5], which also implies an O * (16 4kt/m ) running time. We also show how to enumerate all optimal solutions in O * (36 kt/m ) ≤ O * (36 kavg ) time.…”

Section: Introductionsupporting

confidence: 61%

“…We can also use Lemma 2 to improve the O * (1.53 kt ) running time by Betzler et al [4] to O * (1.403 kt ). Since m ≥ 3, Lemma 2 proves the following relationship between d and k:…”

Section: Theorem 1 An Optimal Aggregation Can Be Found In Timementioning

confidence: 99%

“…Compared to the search tree algorithm of Betzler et al [4], we incorporate a tournament majority graph into our search algorithm, and branch on triples of dirty pairs that form a C 3 in T M , instead of all triples of dirty pairs. Using the ideas in the search tree algorithm of Raman and Saurabh [12], designed to find a minimum feedback arc set, we go one step further, and consider C 4 's whenever possible.…”

Section: Algorithm 1: Findaggregation1mentioning

confidence: 99%

“…Given a set of m total orders, called votes, over a set of n alternatives, called candidates, the Kemeny-optimal aggregation problem asks for a total order over candidates, called an optimal aggregation, that minimizes the sum of τ -distances from the votes, where the τ -distance between total orders π 1 , π 2 is the number of pairs of candidates that are ordered differently in the two total orders. [4] 16 kavg [5] 16 kmax [5] Figure 1: A summary of the running times proved in this paper and the best previous running times. Only the exponential terms are listed.…”

Section: Introductionmentioning

confidence: 99%

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Improved Parameterized Algorithms for the Kemeny Aggregation Problem

Simjour

2009

Parameterized and Exact Computation

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We give improvements over fixed parameter tractable (FPT) algorithms to solve the Kemeny aggregation problem, where the task is to summarize a multi-set of preference lists, called votes, over a set of alternatives, called candidates, into a single preference list that has the minimum total τ -distance from the votes. The τ -distance between two preference lists is the number of pairs of candidates that are ordered differently in the two lists. We study the problem for preference lists that are total orders. We develop algorithms of running times O * (1.403 kt ), O * (5.823 kt/m ) ≤ O * (5.823 kavg ) and O * (4.829 kmax ) for the problem, ignoring the polynomial factors in the O * notation, where k t is the optimum total τ -distance, m is the number of votes, and k avg (resp, k max ) is the average (resp, maximum) over pairwise τ -distances of votes. Our algorithms improve the best previously known running times of O * (1.53 kt ) and O * (16 kavg ) ≤ O * (16 kmax ) [4,5], which also implies an O * (16 4kt/m ) running time. We also show how to enumerate all optimal solutions in O * (36 kt/m ) ≤ O * (36 kavg ) time.

show abstract

Section: Introductionsupporting

confidence: 61%

“…We can also use Lemma 2 to improve the O * (1.53 kt ) running time by Betzler et al [4] to O * (1.403 kt ). Since m ≥ 3, Lemma 2 proves the following relationship between d and k:…”

Section: Theorem 1 An Optimal Aggregation Can Be Found In Timementioning

confidence: 99%

Section: Algorithm 1: Findaggregation1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved Parameterized Algorithms for the Kemeny Aggregation Problem

Simjour

2009

Parameterized and Exact Computation

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“…, n} under the Kendall-τ distance is a NP-hard problem when m ≥ 4. However, this problem has been well-studied in recent years, and several good heuristics are known to exist [1,5,6,13,20,28].…”

Section: And ((π[I] < π[J] and σ[I] > σ[J]) Or(π[i] > π[J] And σ[I]mentioning

confidence: 99%

Using Kendall-τ Meta-Bagging to Improve Protein-Protein Docking Predictions

Azé

Bourquard

Hamel

et al. 2011

Lecture Notes in Computer Science

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Abstract. Predicting the three-dimensional (3D) structures of macromolecular protein-protein complexes from the structures of individual partners (docking), is a major challenge for computational biology. Most docking algorithms use two largely independent stages. First, a fast sampling stage generates a large number (millions or even billions) of candidate conformations, then a scoring stage evaluates these conformations and extracts a small ensemble amongst which a good solution is assumed to exist. Several strategies have been proposed for this stage. However, correctly distinguishing and discarding false positives from the native biological interfaces remains a difficult task. Here, we introduce a new scoring algorithm based on learnt bootstrap aggregation ("bagging") models of protein shape complementarity. 3D Voronoi diagrams are used to describe and encode the surface shapes and physico-chemical properties of proteins. A bagging method based on Kendall-τ distances is then used to minimise the pairwise disagreements between the ranks of the elements obtained from several different bagging approaches. We apply this method to the protein docking problem using 51 protein complexes from the standard Protein Docking Benchmark. Overall, our approach improves in the ranks of near-native conformation and results in more biologically relevant predictions.

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Parameterized Computational Complexity of Dodgson and Young Elections

Betzler

Guo

Niedermeier

2008

Algorithm Theory – SWAT 2008

Self Cite

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Abstract. We show that, other than for standard complexity theory with known NP-completeness results, the computational complexity of the Dodgson and Young election systems is completely different from a parameterized complexity point of view. That is, on the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]-complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixed-parameter tractability as well as W[2]-hardness results depending on the cost model for switching ties.

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Fixed-Parameter Algorithms for Kemeny Scores

Cited by 22 publications

References 10 publications

Improved Parameterized Algorithms for the Kemeny Aggregation Problem

Improved Parameterized Algorithms for the Kemeny Aggregation Problem

Using Kendall-τ Meta-Bagging to Improve Protein-Protein Docking Predictions

Parameterized Computational Complexity of Dodgson and Young Elections

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