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The Shortest Path Problem with Edge Information Reuse is NP-Complete
We show that the following variation of the single-source shortest path
problem is NP-complete. Let a weighted, directed, acyclic graph
with source and sink vertices and be given. Let in addition a mapping
on be given that associates information with the edges (e.g., a
pointer), such that means that edges and carry the same
information; for such edges it is required that . The length of a
simple path is the sum of the weights of the edges on but edges
with are counted only once. The problem is to determine a shortest
such path. We call this problem the \emph{edge information reuse shortest
path problem}. It is NP-complete by reduction from 3SAT