Matching through Embedding in Dense Graphs

TL;DR

This paper introduces a novel heuristic that uses network embedding to efficiently approximate solutions to matching problems in dense graphs, especially when vertices are points in Euclidean space.

Contribution

It is the first to apply network embedding techniques to solve various matching problems in dense graphs, improving computational efficiency.

Findings

The embedding-based heuristic outperforms traditional algorithms in speed.

Experimental results show high-quality matchings with reduced computation time.

The approach is effective for graphs with vertices in Euclidean space.

Abstract

Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running times of the fastest available optimal matching algorithms are too costly. However, when the vertices of the graphs are point-sets in $R^d$ and edge weights correspond to the euclidean distances, the available optimal matching algorithms are substantially faster. In this paper, we propose a novel network embedding based heuristic algorithm to solve various matching problems in dense graphs. In particular, using existing network embedding techniques, we first find a low dimensional representation of the graph vertices in $R^d$ and then run faster available matching algorithms on the embedded vertices. To the best of our knowledge, this is the first work that applies network embedding to solve various matching problems. Experimental results validate the efficacy of our proposed algorithm.