We give efficient deterministic distributed algorithms which given a graph G from a proper minor-closed family C find an approximation of a minimum dominating set in G and a minimum connected dominating set in G. The algorithms are deterministic and run in a polylogarithmic number of rounds. The approximation accomplished differs from an optimal by a multiplicative factor of (1 + o(1)).

In this paper, we study the Dominating Set problem in random graphs. In a random graph, each pair of vertices are joined by an edge with a probability of p, where p is a positive constant less than 1. We show that, given a random graph in n vertices, a minimum dominating set in the graph can be computed in expected 2 2 2 n) time. For the parameterized dominating set problem, we show that it can...

The Roman imperial monarchy is generally studied from the vantage point of ancient Roman history: the “Roman emperor” is viewed and analyzed as an element of the Roman world. This conventional approach fails to place this institution in a broader comparative context, that of monarchical rulers across world history. Systematic comparison opens up new perspectives and is indispensable in identify...

In this paper, we consider the dominance properties of the set of the pignistic k-additive belief functions. Then, given k, we conjecture the shape of the polytope of all the k-additive belief functions dominating a given belief function, starting from an analogy with the case of dominating probability measures. Under such conjecture, we compute the analytical form of the barycenter of the poly...

In this paper, we consider r-dominating cliques in homogeneously orderable graphs (a common generalization of dually chordal and distance-hereditary graphs) and their relation to strict r-packing sets. We prove that a homogeneously orderable graph G possesses an r-dominating clique if and only if for any pair of vertices x , y of G d (x , y ) ° r ( x ) / r ( y ) / 1 holds where r : V r N is a g...

Let D be a finite and simple digraph with the vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If∑ x∈N[v] f(x) ≥ 1 for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V (D)) is called the weight w(f) of f . The minimum of weights w(f), taken over all signed dominating function...

Inflammation is the body's response to injury or infection. As early as 2000 years ago, the Roman encyclopaedist Aulus Cornelius Celsus recognised four cardinal signs of this response-redness, heat, swelling and pain; a fifth sign is loss of function.[...].

The Roman god Janus (Figure) was the guardian of gates and doors and was believed to represent beginnings and endings; he is hence represented by a double-faced head. He particularly presided over all that is double-edged in life and represented the transition between the primitive and civilization, between the countryside and the city, peace and war, and the growing-up of young people. The con...

a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...