Selected papers of the 14th British conference on Combinatorial conference
Approximation algorithms for NP-hard problems
Inequalities relating domination parameters in cubic graphs
Discrete Mathematics
Signed domination in regular graphs
Discrete Mathematics
Improved performance of the greedy algorithm for partial cover
Information Processing Letters
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Signed domination in regular graphs and set-systems
Journal of Combinatorial Theory Series B
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the Hardness of Approximating Minimum Monopoly Problems
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Complexity of approximating bounded variants of optimization problems
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Cost sharing and strategyproof mechanisms for set cover games
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
On the approximability and exact algorithms for vector domination and related problems in graphs
Discrete Applied Mathematics
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We consider approximability of two natural variants of classical dominating set problem, namely minimum majority monopoly and minimum signed domination. In the minimum majority monopoly problem, the objective is to find a smallest size subset X@?V in a given graph G=(V,E) such that |N[v]@?X|=12|N[v]|, for at least half of the vertices in V. On the other hand, given a graph G=(V,E), in the signed domination problem one needs to find a function f:V-{-1,1} such that f(N[v])=1, for all v@?V, and the cost f(V)=@?"v"@?"Vf(v) is minimized. We show that minimum majority monopoly and minimum signed domination cannot be approximated within a factor of (12-@e)lnn and (13-@e)lnn, respectively, for any @e0, unless NP@?Dtime(n^O^(^l^o^g^l^o^g^n^)). We also prove that, if @D is the maximum degree of a vertex in the graph, then both problems cannot be approximated within a factor of ln@D-Dlnln@D, for some constant D, unless P=NP. On the positive side, we give ln(@D+1)-factor approximation algorithm for minimum majority monopoly problem for general graphs. We show that minimum majority monopoly problem is APX-complete for graphs with degree at most 3 and at least 2 and minimum signed domination problem is APX-complete, for 3-regular graphs. For 3-regular graphs, these two problems are approximable within a factor of 43 (asymptotically) and 1.6, respectively.