The 'two paths problem' is stated as follows. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two vertex-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂ respectively. In this paper we give a linear (O(|V|+ |E|)) algorithm to solve the above problem on a permutation graph.
In this paper we consider the following problem. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two edge-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂, respectively. We give a linear (O(|V|+|E|)) algorithm to solve this problem on a permutation graph.
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|²) 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.
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