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 < 2. En route to these algorithms, we introduce two general techniques for obtaining exact algorithms. One is through parameterized complexity algorithms, and the other is a ‘colored’ branch-and-bound technique.
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Raman, V., Saurabh, S., Sikdar, S. (2005). Improved Exact Exponential Algorithms for Vertex Bipartization and Other Problems. In: Coppo, M., Lodi, E., Pinna, G.M. (eds) Theoretical Computer Science. ICTCS 2005. Lecture Notes in Computer Science, vol 3701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11560586_30
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DOI: https://doi.org/10.1007/11560586_30
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