顺序交换令牌：进一步介绍图类

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2025-07-17 DOI:10.1016/j.jcss.2025.103691

Hironori Kiya , Yuto Okada , Hirotaka Ono , Yota Otachi

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引用次数: 0

摘要

在本文中，我们研究了顺序令牌交换，它可以看作是广义15难题的一种变体。给定一个图和顶点上的两个令牌放置位置，问题要求找到最小长度的遍历（如果存在的话），使得沿遍历的令牌交换序列从另一个给定的令牌放置位置中获得一个。这个问题是由Yamanaka等人提出的[JGAA 2019]，他们表明这个问题一般来说是难以解决的，但对于树、完全图和循环来说是多项式时间可解的。在本文中，我们提出了一个多项式时间算法的块仙人掌图，其中包括所有已知的情况。我们也提供一般的工具来显示问题在受限图类，如弦图和弦二部图的硬度。我们还表明，这个问题在网格和国王图上是困难的，这是与15个谜题及其变体相对应的图，具有放松的移动。

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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Sequentially swapping tokens: Further on graph classes

In this paper, we study Sequential Token Swapping, which can be seen as a variant of the generalized 15 puzzle. Given a graph and two token placements on the vertices, the problem asks to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of the problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king's graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.