A Theory and Algorithms for Combinatorial Reoptimization
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 cos...
Saved in:
Published in | LATIN 2012: Theoretical Informatics pp. 618 - 630 |
---|---|
Main Authors | , , |
Format | Book Chapter |
Language | English |
Published |
Berlin, Heidelberg
Springer Berlin Heidelberg
|
Series | Lecture Notes in Computer Science |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}${\cal A}$\end{document} is an (r, ρ)-reapproximation algorithm if it achieves a ρ-approximation 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. |
---|---|
Bibliography: | This research is supported by the Israel Science Foundation (grant number 1574/10), and by the Ministry of Trade and Industry MAGNET program through the NEGEV Consortium (www.negev-initiative.org). |
ISBN: | 3642293433 9783642293436 |
ISSN: | 0302-9743 1611-3349 |
DOI: | 10.1007/978-3-642-29344-3_52 |