A characterization of linearizable instances of the quadratic minimum spanning tree problem

被引：11

作者：

Custic, Ante ^{[1
]}

Punnen, Abraham P. ^{[1
]}

机构：

[1] Simon Fraser Univ Surrey, Dept Math, 250-13450 102nd AV, Surrey, BC V3T 0A3, Canada

来源：

JOURNAL OF COMBINATORIAL OPTIMIZATION | 2018年 / 35卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Minimum spanning tree; Quadratic; 0-1; problems; Quadratic minimum spanning tree; Polynomially solvable cases; Linearization; QAP LINEARIZATION; LOWER BOUNDS; ALGORITHM; PRODUCT; SEARCH; FPTAS; TERM;

D O I：

10.1007/s10878-017-0184-3

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We investigate special cases of the quadratic minimum spanning tree problem (QMSTP) on a graph that can be solved as a linear minimum spanning tree problem. We give a characterization of such problems when G is a complete graph, which is the standard case in the QMSTP literature. We extend our characterization to a larger class of graphs that include complete bipartite graphs and cactuses, among others. Our characterization can be verified in time. In the case of complete graphs and when the cost matrix is given in factored form, we show that our characterization can be verified in O(|E|) time. Related open problems are also indicated.

引用

页码：436 / 453

页数：18

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