A Theory and Algorithms for Combinatorial Reoptimization

Autor: Gal Tamir, Tami Tamir, Baruch Schieber, Hadas Shachnai
Rok vydání: 2017
Předmět:
Zdroj: Algorithmica. 80:576-607
ISSN: 1432-0541
0178-4617
Popis: 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 framework for combinatorial repotimization, encompassing classical objective functions as well as the goal of minimizing the transition cost from one solution to the other. Formally, we say that $$\mathcal{A}$$ is an $$(r, \rho )$$ -reapproximation algorithm if it achieves a $$\rho $$ -approximation for the optimization problem, while paying a transition cost that is at most r times the minimum required for solving the problem optimally. Using our model we derive reoptimization and reapproximation algorithms for several classes of combinatorial reoptimization problems. This includes a fully polynomial time $$(1+\varepsilon _1, 1+\varepsilon _2)$$ -reapproximation scheme for the wide class of DP-benevolent problems introduced by Woeginger (Proceedings of Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, 1999), a (1, 3)-reapproximation algorithm for the metric k-Center problem, 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 the objective of minimizing transition costs, while guaranteeing a good approximation for the underlying optimization problem.
Databáze: OpenAIRE
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