Shortest paths between shortest paths and independent sets

We study problems of reconguration of shortest paths in graphs. We prove that the shortest reconguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconguration sequence even when we know that the sequence has polynomial length. Moreover, we also study reconguration of independent sets in three dierent models and analyze relationships between these models, observing that shortest path reconguration is a special case of independent set reconguration in perfect graphs, under any of the three models. Finally, we give polynomial results for restricted classes of graphs (even-hole-free and P4-free graphs).

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Marcin Kaminski, Paul Medvedev, Martin Milanic
• Keywords: CORR 2010, Education, Independent Set, Shortest Path, Shortest Reconguration Sequence