Approximation Algorithms for the Minimum Bends Traveling Salesman Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Information Processing Letters
An O(n5/2logn) algorithm for the Rectilinear Minimum Link-Distance Problem in three dimensions
Computational Geometry: Theory and Applications
Parallel Optimal Weighted Links
Transactions on Computational Science III
k-link shortest paths in weighted subdivisions
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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The authors consider the problem of finding a shortest polygonal path from s to t within a simple polygon P, subject to the restriction that the path have at most k links (edges). They give an algorithm to compute a k-link path with length at most (1 + epsilon ) times the length of a shortest k-link path, for any error tolerance epsilon 0. The algorithm runs in time O(n/sup 3/k/sup 3/ log (Hk/ epsilon /sup 1/k/)), where N is the largest integer coordinate among the n vertices of P. They also study the more general problem of approximating shortest k-link paths in polygons with holes. In this case, they give an algorithm that returns a path with at most 2k links and length at most that of a shortest k-link path; the running time is O(kE/sup 2/), where E is the number of edges in the visibility graph. Finally, they study the bicriteria path problem in which the two criteria are link length and 'total turn' (the integral of mod Delta theta mod along a path). They obtain in an exact polynomial-time algorithm for polygons with holes.