Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Improved upper bounds for 3-SAT
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Quasiconvex analysis of backtracking algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
An exact 2.9416n algorithm for the three domatic number problem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
An improved exact algorithm for the domatic number problem
Information Processing Letters
Improved fixed parameter tractable algorithms for two “edge” problems: MAXCUT and MAXDAG
Information Processing Letters
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
Counting minimum weighted dominating sets
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Branch and recharge: exact algorithms for generalized domination
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We show that the number of minimal dominating sets in a graph on n vertices is at most 1.7697n, thus improving on the trivial $\mathcal{O}(2^{n}/\sqrt{n})$ bound. Our result makes use of the measure and conquer technique from exact algorithms, and can be easily turned into an $\mathcal{O}(1.7697^{n})$ listing algorithm. Based on this result, we derive an $\mathcal{O}(2.8805^{n})$ algorithm for the domatic number problem, and an $\mathcal{O}(1.5780^{n})$ algorithm for the minimum-weight dominating set problem. Both algorithms improve over the previous algorithms.