Irredundant complete cototal dominating set

Partial vs. Complete Domination: t-Dominating Set

Semidefinite relaxation for dominating set

‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exp...

Irredundant Set Faster Than O(2n)

In this paper we provide algorithms faster than O(2) for two variants of the IRREDUNDANT SET problem. More precisely, we give: – a branch-and-reduce algorithm solving LARGEST IRREDUNDANT SET in O(1.9657) time and polynomial space; the time complexity can be reduced using memoization to O(1.8475) at the cost of using exponential space, – and a simple iterative-DFS algorithm for SMALLEST INCLUSIO...

Online Dominating Set

This paper is devoted to the online dominating set problem and its variants on trees, bipartite, bounded-degree, planar, and general graphs, distinguishing between connected and not necessarily connected graphs. We believe this paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing the future, and being i...

Dominating set games

In this paper we study cooperative cost games arising from domination problems on graphs. We introduce three games to model the cost allocation problem and we derive a necessary and sufficient condition for the balancedness of all three games. Furthermore we study concavity of these games.