Joseph Cheriyan

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Abstract An e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an undirected or directed simple graph G V E There are four versions of the problem and the approximation guarantees are as followsAn e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an(More)
1 Introduction. We initiate the algorithmic study of an important but NP-hard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem,, for each source node v. (2) A small set of cable types, where each cable type(More)
A k-separator (k-shredder) of a graph is a set of k nodes whose removal results in two or more (three or more) cunnect ed components. Let the given (undirected) graph be k-node connected, and let n denote the number of nodes. Solving au open question, we show that the problem of counting the number of k-separators is #P-complete. However, we present an(More)
We present an approximation algorithm for the problem of finding a minimum-cost k-vertex connected spanning subgraph, assuming that the number of vertices is at least 6k. The approximation guarantee is six times the kth harmonic number (which is O(log k)), and this is also an upper bound on the integrality ratio for a standard linear programming relaxation.
A typical problem in network design is to nd a minimum-cost sub-network H of a given network G such that H satisses some prespeciied connectivity requirements. Our focus is on approximation algorithms for designing networks that satisfy vertex connectivity requirements. Our main tool is a linear programming relaxation of the following setpair formulation(More)