Vijaya Ramachandran

Publications (4)0 Total impact

• Source

  Available from: psu.edu

  Article: Computing Minimal Spanning Subgraphs in Linear Time.

  Xiaofeng Han, Pierre Kelsen, Vijaya Ramachandran, Robert Endre Tarjan
  SIAM J. Comput. 01/1995; 24:1332-1358.
• Source

  Available from: psu.edu

  Article: On Finding Minimal Two-Connected Subgraphs

  Pierre Kelsen, Vijaya Ramachandran
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  ABSTRACT: We present efficient parallel algorithms for the problems of finding a minimal2-edge-connected spanning subgraph of a 2-edge-connected graph and finding a minimal biconnected spanning subgraph of a biconnected graph. The parallel algorithms run in polylog time using a linear number of PRAM processors. We also give linear time sequential algorithms for minimally augmenting a spanning tree into a 2-edge-connected or biconnected graph. 1 Introduction In this paper we consider the following two related problems: given a 2-edge-connected (biconnected) graph G, compute a minimal 2-edge-connected (biconnected) spanning subgraph of G, i.e., a 2-edge-connected (biconnected) subgraph in which the deletion of any edge destroys 2-edgeconnectivity (biconnectivity). We present efficient parallel algorithms for these problems. It is known that the corresponding problems of finding minimum spanning subgraphs with these properties are NP-hard ([6]). Thus, it is natural to study the simpler probl...
  01/1993;
• Article: The Complexity of Finding Minimal Spanning Subgraphs

  Pierre Kelsen, Vijaya Ramachandran
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  ABSTRACT: Let P be a property of graphs (directed or undirected). We consider the following problem: given a graph G that has property P , find a minimal spanning subgraph of G with property P . We describe an algorithm for this problem and prove that it is correct under some rather weak assumptions about P . We then analyze the number of iterations of this algorithm. By suitably restricting the graph properties, we devise a general technique to construct graphs for which the algorithm requires a large number of iterations. We apply the above technique to three concrete graph properties: 2-edge-connectivity, biconnectivity, and strong connectivity. We obtain a tight lower bound ofOmegaGamma/45 n) on the number of iterations of the algorithm for finding minimal spanning subgraphs with these properties; this resolves open questions posed earlier with regard to these properties. This also implies that the worst case sequential running time of the algorithm for these three properties is OmegaGa...
  01/1993;
• Conference Proceeding: Computing Minimal Spanning Subgraphs in Linear Time.

  Xiaofeng Han, Pierre Kelsen, Vijaya Ramachandran, Robert Endre Tarjan
  Proceedings of the Third Annual ACM/SIGACT-SIAM Symposium on Discrete Algorithms, 27-29 January 1992, Orlando, Florida.; 01/1992