Solving the all-pair-shortest-length problem on chordal bipartite graphs

Abstract

The all-pairs-shortest-length(APSL) problem of a graph is to find the lengths of the shortest paths between all pairs of vertices. In this paper, we study the APSL problem on chordal bipartite graphs. By a simple reduction,we show that solving the APSL problem on chordal bipartite graphs can be transformed to solving the same problem on certain strongly chordal graphs. Consequently, there is an O(n²)time-optimal algorithm for this problem