Approximating the minimum maximal independence number
Information Processing Letters
Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Vertex cover: further observations and further improvements
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Quasiconvex analysis of backtracking algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Local approximation schemes for ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Pathwidth of cubic graphs and exact algorithms
Information Processing Letters
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Algorithms based on the treewidth of sparse graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in 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
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In this paper, we consider the Minimum Independent Dominating Set problem and develop exact exponential algorithms that break the trivial O(2|V |) bound. A simple $O^{*}({\sqrt{3}}^{|V|})$ time algorithm is developed to solve this problem on general graphs. For sparse graphs, e.g. graphs with degree bounded by 3 and 4, we show that a few new branching techniques can be applied to these graphs and the resulting algorithms have time complexities O*(20.465|V |) and O*(20.620|V |), respectively. All our algorithms only need polynomial space.