A polynomial time algorithm for longest paths in biconvex graphs

Authors:
Esha Ghosh;N. S. Narayanaswamy;C. Pandu Rangan
Affiliations:
Dept. of Computer Science and Engineering, IIT Madras, Chennai, India;Dept. of Computer Science and Engineering, IIT Madras, Chennai, India;Dept. of Computer Science and Engineering, IIT Madras, Chennai, India
Venue:
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Year:
2011

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Abstract

The longest path problem is the problem of finding a simple path of maximum length in a graph. Polynomial solutions for this problem are known only for special classes of graphs, while it is NP-hard on general graphs. In this paper we are proposing a O(n6) time algorithm to find the longest path on biconvex graphs, where n is the number of vertices of the input graph. We have used Dynamic Programming approach.