An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...

An independent broadcast on a connected graph G is function f:V(G)→N0 such that, for every vertex x of G, the value f(x) at most eccentricity in and f(x)>0 implies that f(y)=0 y within distance from x. The independence number αb(G) largest weight ∑x∈V(G)f(x) an f G. We describe efficient algorithm determines given tree. Furthermore, we show NP-hardness planar graphs maximum degree four, hardnes...

An independent broadcast on a graph G is function f : V −→ {0,. .. , diam(G)} such that (i) (v) ≤ e(v) for every vertex v ∈ (G), where diam(G) denotes the diameter of and eccentricity v, (ii) d(u, v) > max{f (u), (v)} two distinct vertices u with (u)f 0. The independence number β b (G) then maximum value v∈V (v), taken over all broadcasts G. We prove circulant form C(n; 1, a), 3 ⌊ n 2 ⌋, admits...

Let G be a simple undirected graph. A broadcast on G is a function f : V (G) → N such that f(v) ≤ eG(v) holds for every vertex v of G, where eG(v) denotes the eccentricity of v in G, that is, the maximum distance from v to any other vertex of G. The cost of f is the value cost(f) = ∑ v∈V (G) f(v). A broadcast f on G is independent if for every two distinct vertices u and v in G, dG(u, v) > max{...

Let~$G$ be a simple undirected graph. A broadcast on~$G$ is a function $f : V(G)\rightarrow\NNNNN$ such that $f(v)\le e_G(v)$ holds for every vertex~$v$ of~$G$, where $e_G(v)$ denotes the eccentricity of~$v$ in~$G$, is, maximum distance from~$v$ to any other vertex of~$G$. The cost of~$f$ is value $\cost(f)=\sum_{v\in V(G)}f(v)$. A broadcast~$f$ independent if two distinct vertices $u$ an...

Independence or simultaneous broadcast is a fundamental tool to achieve security in fault tolerant distributed computing. It allows n players to commit to independently chosen values. In this paper we present a constant round protocol to perform this task. Previous solutions were all O(log n) rounds. In the process we develop a new and stronger formal deenition from this problem. As an example ...

Independence or simultaneous broadcast is a fundamental tool to achieve security in fault tolerant distributed computing. It allows n players to commit to independently chosen values. In this paper we present a constant round protocol to perform this task. Previous solutions were all O(logn) rounds. In the process we develop a new and stronger formal de nition from this problem. As an example o...