A Fast Graph Program for Computing Minimum Spanning Trees

Brian Courtehoute
(University of York, United Kingdom)
Detlef Plump
(University of York, United Kingdom)

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.

In Berthold Hoffmann and Mark Minas: Proceedings of the Eleventh International Workshop on Graph Computation Models (GCM 2020), Online-Workshop, 24th June 2020, Electronic Proceedings in Theoretical Computer Science 330, pp. 163–180.
Published: 3rd December 2020.

ArXived at: https://dx.doi.org/10.4204/EPTCS.330.10 bibtex PDF
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