Vertex cover: further observations and further improvements
Journal of Algorithms
Clique Is Hard to Approximate within n1-o(1)
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact 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
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Many exact algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as deletions, that reduce the problem instance and have to be "taken back" frequently during the search process. The use of efficient data structures is necessary for fast graph modification modules as well as fast take-back procedures. In this paper, we investigate practical implementation-based aspects of exact algorithms by providing a hybrid graph representation that addresses the take-back challenge and combines the advantage of O(1) adjacency-queries in adjacency-matrices with the advantage of efficient neighborhood traversal in adjacency-lists.