Efficient parallel algorithms for breadth first spanning forests of general graphs

Ghosh and Bhattacharjee propose [2] (Intern. J. Computer Math., 1984, Vol. 15, pp. 255-268) an algorithm of determining breadth first spanning trees for graphs, which requires that the input graphs contain some vertices, from which every other vertex in the input graph can be reached. These vertices are called starting vertices. The complexity of the GB algorithm is O(log² n) using O{n ³) processors. In this paper an algorithm, named BREADTH, also computing breadth first spanning trees, is proposed. The complexity is O(log² n) using O{n ³/logn) processors. Then an efficient parallel algorithm, named- BREADTHFOREST, is proposed, which generalizes algorithm BREADTH. The output of applying BREADTHFOREST to a general graph, which may not contain any starting vertices, is a breadth first spanning forest of the input graph. The complexity of BREADTHFOREST is the same as BREADTH.