Reoptimization of Weighted Graph and Covering Problems

Bilò, Davide; Widmayer, Peter; Zych, Anna

doi:10.1007/978-3-540-93980-1_16

Cited by 28 publications

(35 citation statements)

References 11 publications

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“…In all cases, the goal is to propose reoptimization algorithm that outperform their deterministic counterparts in terms of complexity and/or approximation ratio. In [8], the max independent set problem, as well as min vertex cover and min set cover problems, are discussed in a similar setting up to the fact that perturbations there concerned the edge-set of the initial graph. The authors of [8] manage to provide optimal approximation results under the basic assumption that the initial solution is not necessarily optimal but ρ-approximate.…”

Section: Introductionmentioning

confidence: 99%

Reoptimization of maximum weight induced hereditary subgraph problems

Boria

Monnot

Paschos

2013

Theoretical Computer Science

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The reoptimization issue studied in this paper can be described as follows: given an instance I of some problem Π, an optimal solution OPT for Π in I and an instance I ′ resulting from a local perturbation of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Π in I ′ , either optimally or by guaranteeing an approximation ratio better than that guaranteed by an ex nihilo computation and with running time better that that needed for such a computation. We use this setting in order to study weighted versions of several representatives of a broad class of problems known in the literature as maximum induced hereditary subgraph problems. The main problems studied are max independent set, max k-colorable subgraph, max P k -free subgraph, max split subgraph and max planar subgraph. We also show, how the techniques presented allow us to handle also bin packing.

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Section: Introductionmentioning

confidence: 99%

Reoptimization of maximum weight induced hereditary subgraph problems

Boria

Monnot

Paschos

2013

Theoretical Computer Science

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“…Since then, reoptimization has been applied to various problems like the TSP [4][5][6][7], the Steiner tree problem [8][9][10][11], the shortest common superstring problem [12,13], the knapsack problem [14], and several covering problems [15].…”

Section: Overview Of Reoptimization Resultsmentioning

confidence: 99%

Knowing All Optimal Solutions Does Not Help for TSP Reoptimization

Böckenhauer

Hromkovič

Sprock

2011

Computation, Cooperation, and Life

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“…This concept of reoptimization was mentioned for the first time in [20] in the context of postoptimality analysis for a scheduling problem. Since then, the concept of reoptimization has been investigated for several different problems like the traveling salesman problem [1,3,8,12], knapsack problems [2], covering problems [7], and the shortest common superstring problem [6]. In these papers, it was shown that, for some problems, the reoptimization variant is exactly as hard as the original problem, whereas reoptimization can help a lot for improving the approximation ratio for other problems, for an overview of some results see also [11].…”

Section: Introductionmentioning

confidence: 99%

The Steiner Tree Reoptimization Problem with Sharpened Triangle Inequality

Böckenhauer

Freiermuth

Hromkovič

et al. 2010

Lecture Notes in Computer Science

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Abstract. In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-triangle inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened triangle inequality (and even in graphs where edge-costs are restricted to the values 1 and 1 + γ for an arbitrary small γ > 0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design lineartime (1/2 + β)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (β = 1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any β < 1/2 + ln(3)/4 ≈ 0.775.

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Reoptimization of Weighted Graph and Covering Problems

Cited by 28 publications

References 11 publications

Reoptimization of maximum weight induced hereditary subgraph problems

Reoptimization of maximum weight induced hereditary subgraph problems

Knowing All Optimal Solutions Does Not Help for TSP Reoptimization

The Steiner Tree Reoptimization Problem with Sharpened Triangle Inequality

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