  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.
