Related papers: An $O(n^5)$-Time Algorithm for Optimal Broadcast D…
The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each…
In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and…
For a graph $ G = (V, E) $ with a vertex set $ V $ and an edge set $ E $, a function $ f : V \rightarrow \{0, 1, 2, . . . , diam(G)\} $ is called a \emph{broadcast} on $ G $. For each vertex $ u \in V $, if there exists a vertex $ v $ in $…
In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the…
For an undirected graph $G$, a dominating broadcast on $G$ is a function $f : V(G) \rightarrow \mathbb{N}$ such that for any vertex $u \in V(G)$, there exists a vertex $v \in V(G)$ with $f(v) \geqslant 1$ and $d(u,v) \leqslant f(v)$. The…
Consider a wireless network of n nodes represented by a graph G=(V, E) where an edge (i,j) models the fact that transmissions of i and j interfere with each other, i.e. simultaneous transmissions of i and j become unsuccessful. Hence it is…
We present a polynomial-space algorithm that computes the number independent sets of any input graph in time $O(1.1387^n)$ for graphs with maximum degree 3 and in time $O(1.2355^n)$ for general graphs, where n is the number of vertices.…
We study the problem of broadcasting packets in wireless networks. At each time slot, a network controller activates non-interfering links and forwards packets to all nodes at a common rate; the maximum rate is referred to as the broadcast…
A dominating broadcast on a graph G with vertex set V is a function f that maps V to {0,1,...,diam(G)} such that f(v) does not exceed e(v) (the eccentricity of v) for all vertices v, and each vertex u is at distance at most f(v) from a…
This paper studies the problem of broadcasting in synchronous point-to-point networks, where one initiator owns a piece of information that has to be transmitted to all other vertices as fast as possible. The model of fractional dynamic…
Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard…
In this paper we provide algorithms faster than O*(2^n) for several NP-complete domination-type problems. More precisely, we provide: an algorithm for CAPACITATED DOMINATING SET that solves it in O(1.89^n), a branch-and-reduce algorithm…
A broadcast on a nontrivial connected graph G=(V,E) is a function f from V(G) to {0,1,...,diam(G)} such that f(v) does not exceed the eccentricity of v. The cost of f is the sum of the function values. A broadcast f is dominating if each…
We consider the problem of throughput-optimal broadcast- ing in time-varying wireless networks, whose underlying topology is restricted to Directed Acyclic Graphs (DAG). Previous broadcast algorithms route packets along spanning trees. In…
A directed dominating set in a directed graph $D$ is a set $S$ of vertices of $V$ such that every vertex $u \in V(D) \setminus S$ has an adjacent vertex $v$ in $S$ with $v$ directed to $u$. The directed domination number of $D$, denoted by…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover Problem in which the frequency of every…
While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a…
Information dissemination is a fundamental problem in parallel and distributed computing. In its simplest variant, the broadcasting problem, a message has to be spread among all nodes of a graph. A prominent communication protocol for this…
In this paper we merge recent developments on exact algorithms for finding an ordering of vertices of a given graph that minimizes bandwidth (the BANDWIDTH problem) and for finding an embedding of a given graph into a line that minimizes…
We revisit the minimum dominating set problem on graphs with arboricity bounded by $\alpha$. Bansal and Umboh [BU17] gave an $O(\alpha)$-approximation LP rounding algorithm, which also translates into a near-linear time algorithm using…