Reoptimization of the Shortest Common Superstring Problem

Bilò, Davide; Böckenhauer, Hans-Joachim; Komm, Dennis; Královič, Rastislav; Mömke, Tobias; Seibert, Sebastian; Zych, Anna

doi:10.1007/978-3-642-02441-2_8

Cited by 11 publications

(9 citation statements)

References 19 publications

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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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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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“…In particular, for some problems it is possible to develop algorithms guaranteeing better approximation ratio for the reoptimization version than for the original problem. Among the problems studied in this setting are TSP, [4,6], Steiner Tree on weighted graphs [11], Knapsack [1], and Pattern Matching problems [5]. A survey of other research in this direction is given in [3].…”

Section: Related Workmentioning

confidence: 99%

A Theory and Algorithms for Combinatorial Reoptimization

et al. 2017

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Many real-life applications involve systems that change dynamically over time. Thus, throughout the continuous operation of such a system, it is required to compute solutions for new problem instances, derived from previous instances. Since the transition from one solution to another incurs some cost, a natural goal is to have the solution for the new instance close to the original one (under a certain distance measure). In this paper we develop a general model for combinatorial reoptimization, encompassing classical objective functions as well as the goal of minimizing the transition cost from one solution to the other. Formally, we say that A is an (r, ρ)-reapproximation algorithm if it achieves a ρapproximation for the optimization problem, while paying a transition cost that is at most r times the minimum required for solving the problem optimally. When ρ = 1 we get an (r, 1)-reoptimization algorithm. Using our model we derive reoptimization and reapproximation algorithms for several important classes of optimization problems. This includes fully polynomial time reapproximation schemes for DP-benevolent problems, a class introduced by Woeginger (Proc. Tenth ACM-SIAM Symposium on Discrete Algorithms, 1999 ), reapproximation algorithms for metric Facility Location problems, and (1, 1)-reoptimization algorithm for polynomially solvable subset-selection problems. Thus, we distinguish here for the first time between classes of reoptimization problems, by their hardness status with respect to minimizing transition costs while guaranteeing a good approximation for the underlying optimization problem. ⋆

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“…The concept of reoptimization was already successfully applied to several variants of the TSP [1,3,7,8,18], the Steiner tree problem [4,11,15], the 0-1 knapsack problem [2], various covering problems [6], and the shortest common superstring problem [5]. A survey of reoptimization problems can also be found in [12].…”

Section: Introductionmentioning

confidence: 98%

Reoptimization of the metric deadline TSP

Böckenhauer

Komm

2010

Journal of Discrete Algorithms

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The reoptimization version of an optimization problem deals with the following scenario: Given an input instance together with an optimal solution for it, the objective is to find a high-quality solution for a locally modified instance. In this paper, we investigate several reoptimization variants of the traveling salesman problem with deadlines in metric graphs ( -DlTSP). The objective in the -DlTSP is to find a minimum-cost Hamiltonian cycle in a complete undirected graph with a metric edge cost function which visits some of its vertices before some prespecified deadlines. As types of local modifications, we consider insertions and deletions of a vertex as well as of a deadline. We prove the hardness of all of these reoptimization variants and give lower and upper bounds on the achievable approximation ratio which are tight in most cases.

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Reoptimization of the Shortest Common Superstring Problem

Cited by 11 publications

References 19 publications

Knowing All Optimal Solutions Does Not Help for TSP Reoptimization

Knowing All Optimal Solutions Does Not Help for TSP Reoptimization

A Theory and Algorithms for Combinatorial Reoptimization

Reoptimization of the metric deadline TSP

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