The Parametrized Complexity of Some Fundamental Problems in Coding Theory
SIAM Journal on Computing
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Fixed Parameter Algorithms for PLANAR DOMINATING SET and Related Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
An Exact Algorithm for the Maximum Leaf Spanning Tree Problem
Parameterized and Exact Computation
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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In the Connected Red-Blue Dominating Set problem we are given a graph G whose vertex set is partitioned into two parts R and B (red and blue vertices), and we are asked to find a connected subgraph induced by a subset S of B such that each red vertex of G is adjacent to some vertex in S. The problem can be solved in $\mathcal{O}^*(2^{n - |B|})$ time by reduction to the Weighted Steiner Tree problem. Combining exhaustive enumeration when |B| is small with the Weighted Steiner Tree approach when |B| is large, solves the problem in $\mathcal{O}^*(1.4143^n)$. In this paper we present a first non-trivial exact algorithm whose running time is in $\mathcal{O}^*(1.3645^n)$. We use our algorithm to solve the Connected Dominating Set problem in $\mathcal{O}^*(1.8619^n)$. This improves the current best known algorithm, which used sophisticated run-time analysis via the measure and conquer technique to solve the problem in $\mathcal{O}^*(1.8966^n)$.