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Published in:
2012 | OriginalPaper | Chapter
The Complexity of Rerouting Shortest Paths
Author : Paul Bonsma
Published in: Mathematical Foundations of Computer Science 2012
Publisher: Springer Berlin Heidelberg
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The Shortest Path Reconfiguration problem has as input a graph
G
(with unit edge lengths) with vertices
s
and
t
, and two shortest
st
-paths
P
and
Q
. The question is whether there exists a sequence of shortest
st
-paths that starts with
P
and ends with
Q
, such that subsequent paths differ in only one vertex. This is called a rerouting sequence.
This problem is shown to be PSPACE-complete. For claw-free graphs and chordal graphs, it is shown that the problem can be solved in polynomial time, and that shortest rerouting sequences have linear length. For these classes, it is also shown that deciding whether a rerouting sequence exists between
all
pairs of shortest
st
-paths can be done in polynomial time.