Parameterized exact and approximation algorithms for maximum<i>k</i>-set cover and related satisfiability problems

Bonnet, Édouard; Paschos, Vangélis Th.; Sikora, Florian

doi:10.1051/ita/2016022

Cited by 22 publications

(21 citation statements)

References 29 publications

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“…The variant of the problem where each element appears in at most f sets can be approximated with the ratio f [51]. Parameterized approximation algorithms for the problem were considered by Bonnet et al [4], Skowron and Faliszewski [50] and Skowron [49].…”

Section: Coveringmentioning

confidence: 99%

Mixed integer programming with convex/concave constraints: Fixed-parameter tractability and applications to multicovering and voting

Bredereck

Faliszewski

Niedermeier

et al. 2020

Theoretical Computer Science

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A classic result of Lenstra [Math. Oper. Res. 1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameterization by the number of variables. We extend this result by incorporating piecewise linear convex or concave functions to our (mixed) integer programs. This general technique allows us to analyze the parameterized complexity of a number of classic NP-hard computational problems. In particular, we prove that WEIGHTED SET MULTICOVER is in FPT when parameterized by the number of elements to cover, and that there exists an FPT-time approximation scheme for MULTISET MULTICOVER for the same parameter. Further, we use our general technique to prove that a number of problems from computational social choice (e.g., problems related to bribery and control in elections) are in FPT when parameterized by the number of candidates. For bribery, this resolves a nearly 10-year old family of open problems, and for weighted electoral control of Approval voting, this improves some previously known XP-memberships to FPT-memberships.

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Section: Coveringmentioning

confidence: 99%

Mixed integer programming with convex/concave constraints: Fixed-parameter tractability and applications to multicovering and voting

Bredereck

Faliszewski

Niedermeier

et al. 2020

Theoretical Computer Science

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“…The k-PC problem generalizes the well-known k-Dominating Set (k-DS) problem, defined as follows. Given a graph G = (V,E) and a parameter k ∈ N, find the smallest size of a set U ⊆ V such that the number of nodes that belong to U or are neighbors of nodes in U is at least k. If k-PC can be solved in time t(|U |,|S|,k), then k-DS can be solved in time t(|V |,|V |,k) (see, e.g., [3]). Note that the special cases of k-PC and k-DS in which k = n, are the classical NP-complete Set Cover and Dominating Set problems [11], respectively.…”

Section: Prior Workmentioning

confidence: 99%

“…Table 1 presents a summary of known parameterized algorithms for k-PC and k-DS. We note that the parameterized complexity of k-PC and k-DS has been studied also with respect to other parameters and for more restricted inputs (see, e.g., [3,9,25]).…”

Section: Prior Workmentioning

confidence: 99%

“…Deterministic\Randomized Variant Running Time Bonnet et al [3] det k-PC O * (4 k k 2k ) Bläser [1] rand k-PC O * (5.437 k ) Kneis et al [15] det k-DS O * ((16 + ) k ) rand k-DS O * ((4 + ) k ) Chen et al [4] det k-DS O * (5.437 k ) Kneis [14] det k-DS O * ((4 + ) k ) Koutis et al [16] rand…”

Section: Referencementioning

confidence: 99%

“…Given the results of Stage 1, construct an efficient (n, k, p)-separator. 3. Use the separator generated in Stage 2 to construct a representative family.…”

Section: A Tradeoff-based Approachmentioning

confidence: 99%

See 2 more Smart Citations

Representative families: A unified tradeoff-based approach

Shachnai

Zehavi

2016

Journal of Computer and System Sciences

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Abstract. Let M = (E, I) be a matroid, and let S be a family of subsets of size p of E. A subfamily S ⊆ S represents S if for every pair of sets X ∈ S and Y ⊆ E \X such that X ∪Y ∈ I, there is a set X ∈ S disjoint from Y such that X ∪ Y ∈ I. Fomin et al. (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2014) introduced a powerful technique for fast computation of representative families for uniform matroids. In this paper, we show that this technique leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems. This includes, among others, k-Partial Cover, k-Internal Out-Branching, and Long Directed Cycle. Our approach exploits an interesting tradeoff between running time and the size of the representative families.

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Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints

Bevern

Tsidulko

Zschoche

2019

Lecture Notes in Computer Science

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We consider a variant of the matroid median problem introduced by Krishnaswamy et al. [SODA 2011]: an uncapacitated discrete facility location problem where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids. We show that the problem is fixed-parameter tractable parameterized by the number of matroids and the minimum rank among the client-side matroids. To this end, we derive fixed-parameter algorithms for computing representative families for matroid intersections and maximum-weight set packings with multiple matroid constraints. To illustrate the modeling capabilities of the new problem, we use it to obtain algorithms for a problem in social network analysis. We complement our tractability results by lower bounds.Keywords: matroid set packing · matroid parity · matroid median · representative families · social network analysis · strong triadic closure 4 The State Register of Waste Disposal Facilities of the Russian Federation lists 18 dumps for municipal solid waste in Moscow region-the largest city of Europe.

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Parameterized exact and approximation algorithms for maximumk-set cover and related satisfiability problems

Cited by 22 publications

References 29 publications

Mixed integer programming with convex/concave constraints: Fixed-parameter tractability and applications to multicovering and voting

Mixed integer programming with convex/concave constraints: Fixed-parameter tractability and applications to multicovering and voting

Representative families: A unified tradeoff-based approach

Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints

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