Exact algorithms for finding minimum transversals in rank-3 hypergraphs
Journal of Algorithms
Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms
ACM Transactions on Algorithms (TALG)
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Exact Exponential Algorithms
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Solving Capacitated Dominating Set by using covering by subsets and maximum matching
Discrete Applied Mathematics
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Measure and Conquer is a recently developed technique to analyze worst-case complexity of backtracking algorithms. The traditional measure and conquer analysis concentrates on one branching at once by using only small number of variables. In this paper, we extend the measure and conquer analysis and introduce a new analyzing technique named "potential method" to deal with consecutive branchings together. In potential method, the optimization problem becomes sparse; therefore, we can use large number of variables. We applied this technique to the minimum dominating set problem and obtained the current fastest algorithm that runs in O(1.4864n) time and polynomial space. We also combined this algorithm with a precalculation by dynamic programming and obtained O(1.4689n) time and space algorithm. These results show the power of the potential method and possibilities of future applications to other problems.