A Polynomial Time Algorithm for Longest Paths in Biconvex Graphs
- Cite this paper as:
- Ghosh E., Narayanaswamy N.S., Pandu Rangan C. (2011) A Polynomial Time Algorithm for Longest Paths in Biconvex Graphs. In: Katoh N., Kumar A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg
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.
KeywordsLongest path problem biconvex graphs polynomial algorithm complexity dynamic programming
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