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Two-stage Robust Network Design with Exponential Scenarios

Two-stage Robust Network Design with Exponential Scenarios We study two-stage robust variants of combinatorial optimization problems on undirected graphs, like Steiner tree, Steiner forest, and uncapacitated facility location. Robust optimization problems, previously studied by Dhamdhere et al. (Proc. of 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05), pp. 367–378, 2005), Golovin et al. (Proc. of the 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), 2006), and Feige et al. (Proc. of the 12th International Integer Programming and Combinatorial Optimization Conference, pp. 439–453, 2007), are two-stage planning problems in which the requirements are revealed after some decisions are taken in Stage 1. One has to then complete the solution, at a higher cost, to meet the given requirements. In the robust k-Steiner tree problem, for example, one buys some edges in Stage 1. Then k terminals are revealed in Stage 2 and one has to buy more edges, at a higher cost, to complete the Stage 1 solution to build a Steiner tree on these terminals. The objective is to minimize the total cost under the worst-case scenario. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

Two-stage Robust Network Design with Exponential Scenarios

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References (12)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
DOI
10.1007/s00453-011-9596-0
Publisher site
See Article on Publisher Site

Abstract

We study two-stage robust variants of combinatorial optimization problems on undirected graphs, like Steiner tree, Steiner forest, and uncapacitated facility location. Robust optimization problems, previously studied by Dhamdhere et al. (Proc. of 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05), pp. 367–378, 2005), Golovin et al. (Proc. of the 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), 2006), and Feige et al. (Proc. of the 12th International Integer Programming and Combinatorial Optimization Conference, pp. 439–453, 2007), are two-stage planning problems in which the requirements are revealed after some decisions are taken in Stage 1. One has to then complete the solution, at a higher cost, to meet the given requirements. In the robust k-Steiner tree problem, for example, one buys some edges in Stage 1. Then k terminals are revealed in Stage 2 and one has to buy more edges, at a higher cost, to complete the Stage 1 solution to build a Steiner tree on these terminals. The objective is to minimize the total cost under the worst-case scenario.

Journal

AlgorithmicaSpringer Journals

Published: Nov 19, 2011

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