Token shifting on graphs

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
W. Myint, Ryuhei Uehara, G. Viglietta
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引用次数: 0

Abstract

ABSTRACT We investigate a new variation of a token reconfiguration problem on graphs using the cyclic shift operation. A coloured or labelled token is placed on each vertex of a given graph, and a ‘move’ consists in choosing a cycle in the graph and shifting tokens by one position along its edges. Given a target arrangement of tokens on the graph, our goal is to find a shortest sequence of moves that will re-arrange the tokens as in the target arrangement. The novelty of our model is that tokens are allowed to shift along any cycle in the graph, as opposed to a given subset of its cycles. We first discuss the problem on special graph classes: we give efficient algorithms for optimally solving the 2-Coloured Token Shifting Problem on complete graphs and block graphs, as well as the Labelled Token Shifting Problem on complete graphs and variants of barbell graphs. We then show that, in the 2-Coloured Token Shifting Problem, the shortest sequence of moves is NP-hard to approximate within a factor of , even for grid graphs. The latter result settles an open problem posed by Sai et al.
图上的记号移动
我们研究了图上使用循环移位操作的令牌重构问题的一个新变体。在给定图形的每个顶点上放置一个彩色或标记的标记,“移动”包括在图形中选择一个循环,并沿着其边缘移动一个位置。给定图上标记的目标排列,我们的目标是找到一个最短的移动序列,使标记按照目标排列重新排列。我们模型的新颖之处在于,令牌可以沿着图中的任何周期移动,而不是沿着其周期的给定子集移动。我们首先讨论了特殊图类的问题:我们给出了最优解决完全图和块图上的2色令牌移动问题的有效算法,以及完全图和杠铃图变体上的标记令牌移动问题。然后我们证明,在2色令牌移动问题中,即使对于网格图,最短的移动序列也是np -难以在因子内近似的。后一个结果解决了Sai等人提出的一个开放性问题。
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来源期刊
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
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