ﻻ يوجد ملخص باللغة العربية
Many discrete optimization problems amount to select a feasible subgraph of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is to minimize the sum of the distances in the chosen subgraph for the worst positions of the vertices in their uncertainty sets. We first prove that these problems are NP-hard even when the feasible subgraphs consist either of all spanning trees or of all s-t paths. In view of this, we propose en exact solution algorithm combining integer programming formulations with a cutting plane algorithm, identifying the cases where the separation problem can be solved efficiently. We also propose two types of polynomial-time approximation algorithms. The first one relies on solving a nominal counterpart of the problem considering pairwise worst-case distances. We study in details the resulting approximation ratio, which depends on the structure of the metric space and of the feasible subgraphs. The second algorithm considers the special case of s-t paths and leads to a fully-polynomial time approximation scheme. Our algorithms are numerically illustrated on a subway network design problem and a facility location problem.
In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some objective function
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The problems are r
In this paper we study a natural special case of the Traveling Salesman Problem (TSP) with point-locational-uncertainty which we will call the {em adversarial TSP} problem (ATSP). Given a metric space $(X, d)$ and a set of subsets $R = {R_1, R_2, ...
The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is guarantee
In this paper, we present a framework used to construct and analyze algorithms for online optimization problems with deadlines or with delay over a metric space. Using this framework, we present algorithms for several different problems. We present a