A Novel Heuristics for the Strong Generalized Minimum Label Spanning Tree Problem

Abstract

The strong generalized minimum label spanning tree problem (SGMLSTP) is to search the minimum label spanning tree (MLST) from an Edge-labeled graph (ELG), in which each edge is associated with one or more labels. SGMLSTP is commonly existed in reality and proven NP-hard. In recent years, researchers have proposed some algorithms; however, high computational costs are still severe obstacle, especially for large size graphs. In this paper, we propose a novel heuristics to solve SGMLSTP. We decompose the problem into two sub-problems, one is to search a connected subgraph with minimum labels from the original graph, the other is to search a spanning tree from the subgraph. As the latter sub-problem is solved, we focus on the former sub-problem and propose a community-based zigzag piloting algorithm: Firstly a label graph is derived from the original edge-labeled graph; then the label graph is partitioned and some label community (or community combinations) is chosen to form an initial solution; finally, the zigzag piloting process is applied to refine the initial solution. Label partition finds the initial solution quickly, the zigzag piloting process improves solution refinement. Experimental results on typical benchmark datasets show better effectiveness and performance of our algorithm than that of the state-of-the-art algorithms.