What are the least tractable instances of max independent set?
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms
ACM Transactions on Algorithms (TALG)
An exact algorithm for the minimum dominating clique problem
Theoretical Computer Science
Open problems around exact algorithms
Discrete Applied Mathematics
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
Efficiency in exponential time for domination-type problems
Discrete Applied Mathematics
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
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Exact algorithms for edge domination
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Algorithmics in exponential time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Fast Algorithms for max independent set
Algorithmica
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
A new algorithm for parameterized MAX-SAT
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Fast algorithms for min independent dominating set
Discrete Applied Mathematics
Computing the differential of a graph: Hardness, approximability and exact algorithms
Discrete Applied Mathematics
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The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems like Dominating Set and Independent Set. This approach is used in this paper to obtain a faster exact algorithm for Dominating Set. We obtain this algorithm by considering a series of branch and reduce algorithms. This series is the result of an iterative process in which a mathematical analysis of an algorithm in the series with measure and conquer results in a convex or quasiconvex programming problem. The solution, by means of a computer, to this problem not only gives a bound on the running time of the algorithm, but can also give an indication on where to look for a new reduction rule, often giving a new, possibly faster algorithm. As a result, we obtain an O(1.4969^n) time and polynomial space algorithm.