Abstract
We study the shortest path problem in weighted polygonal subdivisions of the plane, with the additional constraint of an upper bound, k, on the number of links (segments) in the path. We prove structural properties of optimal paths and utilize these results to obtain approximation algorithms that yield a path having O(k) links and weighted length at most (1+ε) times the weighted length of an optimal k-link path, for any fixed ε> 0. Some of our results make use of a new solution for the 1-link case, based on computing optimal solutions for a special sum-of-fractionals (SOF) problem. We have implemented a system, based on the CORE library, for computing optimal 1-link paths; we experimentally compare our new solution with a previous method for 1-link optimal paths based on a prune-and-search scheme.
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Daescu, O., Mitchell, J.S.B., Ntafos, S., Palmer, J.D., Yap, C.K. (2005). k-Link Shortest Paths in Weighted Subdivisions. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_29
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DOI: https://doi.org/10.1007/11534273_29
Publisher Name: Springer, Berlin, Heidelberg
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