The Longest Path Problem in Odd-Sized O-Shaped Grid Graphs

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

International Journal of Foundations of Computer Science Pub Date : 2023-03-29 DOI:10.1142/s0129054123500065

Fatemeh Keshavarz-Kohjerdi, A. Bagheri

引用次数: 0

Abstract

One of the well-known NP-hard optimization problems in graph theory is finding the longest path in a graph. This problem remains NP-hard for general grid graphs, and its complexity is open for grid graphs that have a limited number of holes. In this paper, we study this problem for odd-sized [Formula: see text]-shaped grid graphs, i.e. a rectangular grid graph with a rectangular hole. We show that this problem can be solved in linear time.

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奇数尺寸O形网格图的最长路径问题

图论中一个著名的NP难优化问题是寻找图中的最长路径。这个问题对于一般的网格图仍然是NP困难的，并且对于具有有限数量孔的网格图，它的复杂性是开放的。在本文中，我们研究了奇数尺寸[公式：见正文]形状网格图的这个问题，即具有矩形孔的矩形网格图。我们证明了这个问题可以在线性时间内解决。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Foundations of Computer Science 工程技术-计算机：理论方法

CiteScore

1.60

自引率

12.50%

发文量

审稿时长

3 months

期刊介绍： The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing