Improved exact exponential algorithms for vertex bipartization and other problems

Authors:
Venkatesh Raman;Saket Saurabh;Somnath Sikdar
Affiliations:
The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India
Venue:
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Year:
2005

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Abstract

We develop efficient exact algorithms for several NP-hard problems including Vertex Bipartization, Feedback Vertex Set, 4-Hitting Set, and Max Cut in graphs with maximum degree at most 4. Our main results include: – an O*(1.9526n) algorithm for Vertex Bipartization problem in undirected graphs; – an O*(1.8384n) algorithm for Vertex Bipartization problem in undirected graphs of maximum degree 3; – an O*(1.945n) algorithm for Feedback Vertex Set and Vertex Bipartization problem in undirected graphs of maximum degree 4; – an O*(1.9799n) algorithm for 4-Hitting Set problem; – an O*(1.5541m) algorithm for Feedback Arc Set problem in tournaments. To the best of our knowledge, these are the best known exact algorithms for these problems. In fact, these are the first exact algorithms for these problems with the base of the exponent