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The Minimum Stretch Spanning Tree Problem for Typical Graphs

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Abstract

With applications in communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The problem has been proved NP-hard and fixed-parameter polynomial algorithms have been obtained for some special families of graphs. In this paper, we concentrate on the optimality characterizations for typical classes of graphs. We determine the exact formulae for the complete k-partite graphs, split graphs, generalized convex graphs, and several planar grids, including rectangular grids, triangular grids, and triangulated-rectangular grids.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Tongji University, Shanghai, 200092, China

    Lan Lin

  2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Yi-xun Lin

Authors
  1. Lan Lin
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  2. Yi-xun Lin
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Correspondence to Yi-xun Lin.

Additional information

This paper is supported by National Key R&D Program of China (No. 2019YFB2101604).

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Lin, L., Lin, Yx. The Minimum Stretch Spanning Tree Problem for Typical Graphs. Acta Math. Appl. Sin. Engl. Ser. 37, 510–522 (2021). https://doi.org/10.1007/s10255-021-1028-6

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  • DOI: https://doi.org/10.1007/s10255-021-1028-6

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