Efficient algorithms for minimal disjoint path problems on chordal graphs

Disjoint paths have applications in establishing bottleneck-free communication between processors in a network. The problem of finding minimum delay disjoint paths in a network directly reduces to the problem of finding the minimal disjoint paths in the graph which models the network. Previous results for this problem on chordal graphs were an O(| V | | E |) algorithm for 2 edge disjoint paths and an O(| V | | E |) algorithm for 2 vertex disjoint paths. In this paper, we give an O(| V | | E |) algorithm for 2 vertex disjoint paths and an O(| V | + | E |) algorithm for 2 edge disjoint paths, which is a significant improvement over the previous result.