The non-approximability of bicriteria network design problems

Authors:
Vojtech Bálint
Affiliations:
Department of Numerical and Optimization Methods, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovakia
Venue:
Journal of Discrete Algorithms
Year:
2003

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Abstract

Let G be an undirected graph with two edge costs (c-cost and d-cost). We want to minimize the diameter of a spanning subgraph S (under d-cost) subject to the constraint that the total cost of the edges in S (with respect to c) does not exceed a given budget. We prove that this problem is nonapproximable, even in some special cases. Similar results are proved if the stretch factor or the root stretch factor is considered instead of the diameter.