Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Quasiconvex analysis of backtracking algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An improved deterministic local search algorithm for 3-SAT
Theoretical Computer Science
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
3-coloring in time O (1.3289n)
Journal of Algorithms
A faster algorithm for the steiner tree problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Exact computation of maximum induced forest
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Algorithmics in exponential time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects 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
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
An exact algorithm for the minimum dominating clique problem
Theoretical Computer Science
A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs
Graph-Theoretic Concepts in Computer Science
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Better algorithms and bounds for directed maximum leaf problems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
A moderately exponential time algorithm for full degree spanning tree
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Solving capacitated dominating set by using covering by subsets and maximum matching
WG'10 Proceedings of the 36th 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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In the connected dominating set problem we are given an n-node undirected graph, and we are asked to find a minimum cardinality connected subset S of nodes such that each node not in S is adjacent to some node in S. This problem is also equivalent to finding a spanning tree with maximum number of leaves. Despite its relevance in applications, the best known exact algorithm for the problem is the trivial Ω(2n) algorithm which enumerates all the subsets of nodes. This is not the case for the general (unconnected) version of the problem, for which much faster algorithms are available. Such difference is not surprising, since connectivity is a global property, and non-local problems are typically much harder to solve exactly. In this paper we break the 2n barrier, by presenting a simple O(1.9407n) algorithm for the connected dominating set problem. The algorithm makes use of new domination rules, and its analysis is based on the Measure and Conquer technique.