The number of maximal independent sets in triangle-free graphs
SIAM Journal on Discrete Mathematics
Approximating the minimum maximal independence number
Information Processing Letters
Theoretical Computer Science
Polynomially bounded minimization problems that are hard to approximate
Nordic Journal of Computing
Hardness of Approximating Independent Domination in Circle Graphs
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Efficient approximation of min set cover by moderately exponential algorithms
Theoretical Computer Science
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Approximation of min coloring by moderately exponential algorithms
Information Processing Letters
Exponential-time approximation of weighted set cover
Information Processing Letters
An Exponential Time 2-Approximation Algorithm for Bandwidth
Parameterized and Exact Computation
Exact and approximate bandwidth
Theoretical Computer Science
Exact algorithms for dominating set
Discrete Applied Mathematics
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
Fast Algorithms for max independent set
Algorithmica
Fixed-parameter approximation: conceptual framework and approximability results
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized approximation problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Fast algorithms for min independent dominating set
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
Dominating problems in swapped networks
Information Sciences: an International Journal
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We first devise a branching algorithm that computes a minimum independent dominating set with running time O^*(1.3351^n)=O^*(2^0^.^4^1^7^n) and polynomial space. This improves upon the best state of the art algorithms for this problem. We then study approximation of the problem by moderately exponential time algorithms and show that it can be approximated within ratio 1+@e, for any @e0, in a time smaller than the one of exact computation and exponentially decreasing with @e. We also propose approximation algorithms with better running times for ratios greater than 3 in general graphs and give improved moderately exponential time approximation results in triangle-free and bipartite graphs. These latter results are based upon a new bound on the number of maximal independent sets of a given size in these graphs, which is a result interesting per se.