Abstract
In the Touring Polygons Problem (TPP) there is a start point s, a sequence of simple polygons \(\mathcal{P}=(P_1,\dots,P_k)\) and a target point t in the plane. The goal is to obtain a path of minimum possible length that starts from s, visits in order each of the polygons in \(\mathcal{P}\) and ends at t. This problem has a polynomial time algorithm when the polygons in \(\mathcal{P}\) are convex and is NP-hard in general case. But, it has been open whether the problem is NP-hard when the polygons are pairwise disjoint. In this paper, we prove that TPP is also NP-hard when the polygons are pairwise disjoint in any L p norm even if each polygon consists of at most two line segments. This result solves an open problem from STOC ’03 and complements recent approximation results.
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Ahadi, A., Mozafari, A., Zarei, A. (2013). Touring Disjoint Polygons Problem Is NP-Hard. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_31
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DOI: https://doi.org/10.1007/978-3-319-03780-6_31
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03779-0
Online ISBN: 978-3-319-03780-6
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