Abstract
We consider node-weighted network design in planar and minor-closed families of graphs. In particular we focus on the edge-connectivity survivable network design problem (EC-SNDP). The input consists of a node-weighted undirected graph G = (V,E) and integral connectivity requirements r(uv) for each pair of nodes uv. The goal is to find a minimum node-weighted subgraph H of G such that, for each pair uv, H contains r(uv) edge-disjoint paths between u and v. Our main result is an O(k)-approximation algorithm for EC-SNDP where k = max uv r(uv) is the maximum requirement. This improves the O(k logn)-approximation known for node-weighted EC-SNDP in general graphs [15]. Our algorithm and analysis applies to the more general problem of covering a proper function with maximum requirement k. Our result is inspired by, and generalizes, the work of Demaine, Hajiaghayi and Klein [5] who gave constant factor approximation algorithms for node-weighted Steiner tree and Steiner forest problems (and more generally covering 0-1 proper functions) in planar and minor-closed families of graphs.
The authors are partially supported by NSF grant CCF-1016684.
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Chekuri, C., Ene, A., Vakilian, A. (2012). Node-Weighted Network Design in Planar and Minor-Closed Families of Graphs. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_18
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DOI: https://doi.org/10.1007/978-3-642-31594-7_18
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