Abstract
We study several bicriteria network design problems phrased as follows: given an undirected graph and two minimization objectives with a budget specified on one objective, find a subgraph satisfying certain connectivity requirements that minimizes the second objective subject to the budget on the first. First, we develop a formalism for bicriteria problems and their approximations. Secondly, we use a simple parametric search technique to provide bicriteria approximation algorithms for problems with two similar criteria, where both criteria are the same measure (such as the diameter or the total cost of a tree) but differ only in the cost function under which the measure is computed. Thirdly, we present an (O(log n), O(log n))-approximation algorithm for finding a diameter-constrained minimum cost spanning tree of an undirected graph on n nodes. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. These pseudopolynomial-time algorithms can be converted to fully polynomialtime approximation schemes using a scaling technique.
Supported by NSF Grants CCR 94-06611 and CCR 90-06396.
Research supported by the Department of Energy under Contract W-7405-ENG-36.
Research supported by a DIMACS postdoctoral fellowship.
Research supported by DARPA contract N0014-92-J-1799 and NSF CCR 92-12184.
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Marathe, M.V., Ravi, R., Sundaram, R., Ravi, S.S., Rosenkrantz, D.J., Hunt, H.B. (1995). Bicriteria network design problems. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_99
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