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Shortest paths between shortest paths and independent sets.

Пт, 08/27/2010 - 15:02 — SomNambul
Authors: Martin Milanic, Marcin Kaminski, Paul Medvedev
Subjects: Computational Complexity
link: http://arxiv.org/abs/1008.4563
Abstract

We study problems of reconfiguration of shortest paths in graphs. We prove
that the shortest reconfiguration sequence can be exponential in the size of
the graph and that it is NP-hard to compute the shortest reconfiguration
sequence even when we know that the sequence has polynomial length. Moreover,
we also study reconfiguration of independent sets in three different models and
analyze relationships between these models, observing that shortest path
reconfiguration is a special case of independent set reconfiguration in perfect
graphs, under any of the three models. Finally, we give polynomial results for
restricted classes of graphs (even-hole-free and $P_4$-free graphs).

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