Abstract

We present lower bounds on the competitive ratio of randomized algorithms for a wide class of on-line graph optimization problems and we apply such results to on-line virtual circuit and optical routing problems. Lund and Yannakakis [LY93a] give inapproximability results for the problem of finding the largest vertex induced subgraph satisfying any non-trivial, hereditary, property . E.g., independent set, planar, acyclic, bipartite, etc. We consider the on-line version of this family of problems, where some graph G is fixed and some subgraph H is presented on-line, vertex by vertex. The on-line algorithm must choose a subset of the vertices of H , choosing or rejecting a vertex when it is presented, whose vertex induced subgraph satisfies property . Furthermore, we study the on-line version of graph coloring whose off-line version has also been shown to be inapproximable [LY93b], on-line max edge-disjoint paths and on-line path coloring problems. Irrespective of the time complexity, w...

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