TL;DR
This paper investigates the computational complexity of rerouting shortest paths in planar graphs, demonstrating polynomial-time solutions using dynamic programming, contrasting with the problem's general PSPACE-hardness.
Contribution
The paper introduces a dynamic programming approach to efficiently solve the shortest path rerouting problem specifically in planar graphs, where it is otherwise PSPACE-hard.
Findings
Polynomial-time algorithm for planar graphs
Dynamic programming method for reconfiguration
Contrast with PSPACE-hardness in general graphs
Abstract
A rerouting sequence is a sequence of shortest st-paths such that consecutive paths differ in one vertex. We study the the Shortest Path Rerouting Problem, which asks, given two shortest st-paths P and Q in a graph G, whether a rerouting sequence exists from P to Q. This problem is PSPACE-hard in general, but we show that it can be solved in polynomial time if G is planar. To this end, we introduce a dynamic programming method for reconfiguration problems.
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