Abstract
We study a problem related to finding shortest paths in weighted graphs. We ask whether or not there is a path between two nodes that is of a given cost. The edge weights of the graph can be both positive and negative integers, or even integer vectors. We show that most variants of this problem are NP-complete. We also develop a pseudopolynomial algorithm for the case where the edge weights are integers. The running time of this algorithm is O(M 2 N 3 + |w|min(|w|, M)N 2) where N is the number of nodes in the graph, M is the largest absolute value of any edge weight, and w is the target cost. The algorithm is based on preprocessing the graph with a relaxation algorithm to eliminate the effects of weight sign alternations along a path.
Supported by Academy of Finland grant number 42977.
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© 1999 springer-Verlag Berlin Heidelberg
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Nykänen, M., Ukkonen, E. (1999). Finding Paths with the Right Cost. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_32
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DOI: https://doi.org/10.1007/3-540-49116-3_32
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