Speaker: Xianyue Li, professor, School of Mathematics and Statistics, Lanzhou University

Date: January 5, 2024

Time: 9:00-11:00

Location: Tencent Meeting: 420 385 644

Sponsor: School of Mathematics, Shandong University

Abstract:

Min-max spanning tree problem is a classical problem in combinatorial optimization. Its purpose is to find a spanning tree to minimize its maximum edge in a given edge weighted graph. Given a connected graph, an edge weight vector and a forest, the partial inverse min-max spanning tree problem (PIMMST) is to find a new weighted vector, so that the forest can be extended into a min-max spanning tree with respect to new weight vector and the gap between the two vectors is minimized. In this paper, we research PIMMST under the weighted bottleneck Hamming distance. Firstly, we study PIMMST with value of optimal tree restriction, a variant of PIMMST, and show that this problem can be solved in strongly polynomial time. Then, by characterizing the properties of the value of optimal tree, we present first“polynomial algorithm for PIMMST”under the weighted bottleneck Hamming distance. Finally, by giving anecessary and sufficient condition to determine the feasible solution of this problem, we present a better algorithm for this problem. Moreover, we show that these algorithms can be generalized to solve these problems with capacitated constraint.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/187113.htm