A Fast Graph Program for Computing Minimum Spanning Trees

TL;DR

This paper introduces an efficient graph program in GP 2 for computing minimum spanning trees, achieving subquadratic performance on bounded degree graphs using rooted rules and Boruvka's algorithm.

Contribution

The paper presents a novel GP 2 program for MST computation that matches classical Boruvka's algorithm complexity using rooted rules and graph transformation techniques.

Findings

Program demonstrates subquadratic complexity on bounded degree graphs.

Empirical results confirm O(m log n) time complexity.

Uses depth-first search and rooted graph transformation for efficiency.

Abstract

When using graph transformation rules to implement graph algorithms, a challenge is to match the efficiency of programs in conventional languages. To help overcome that challenge, the graph programming language GP 2 features rooted rules which, under mild conditions, can match in constant time on bounded degree graphs. In this paper, we present an efficient GP 2 program for computing minimum spanning trees. We provide empirical performance results as evidence for the program's subquadratic complexity on bounded degree graphs. This is achieved using depth-first search as well as rooted graph transformation. The program is based on Boruvka's algorithm for minimum spanning trees. Our performance results show that the program's time complexity is consistent with that of classical implementations of Boruvka's algorithm, namely O(m log n), where m is the number of edges and n the number of nodes.