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Spanning simple path inside a simple polygon

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Abstract

Given a set S of n colored points of m colors inside a simple polygon P, each point within the polygon has a specific color that is not necessarily unique, i.e., they may exhibit the same color. The study aims to find a simple path that traverses at least one point of each color using a set of S points contained within a simple polygon P. Two results are presented in this study. First, we demonstrate that finding such simple paths inside a simple polygon is an \(NP-complete\) problem. Moreover, we provide a polynomial-time algorithm that computes the simple path when P is an orthogonal spiral simple polygon, and our objective is to locate a simple Hamiltonian path L using all points of S inside P. Our algorithm has a time complexity of \(O(r+rn^4)\), where r is the number of reflex vertices in P and n is the number of points in S.

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Author notes

  1. Mohammadreza Razzazi the author contributed equally to this work.

Authors and Affiliations

  1. Department of Computer Engineering, Amirkabir University of Technology, Hafez, Tehran, 100190, Iran

    Abdolah Sepahvand & Mohammadreza Razzazi

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  1. Abdolah Sepahvand
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  2. Mohammadreza Razzazi
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Correspondence to Mohammadreza Razzazi.

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Sepahvand, A., Razzazi, M. Spanning simple path inside a simple polygon. J Supercomput 79, 2740–2766 (2023). https://doi.org/10.1007/s11227-022-04765-0

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