ﻻ يوجد ملخص باللغة العربية
We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a $(5-varepsilon)$-approximation, for any $varepsilon>0$. Our algorithm only requires knowledge of the degree of a vertex and of its neighbors, so that large messages and unique identifiers are not needed.
The Minimum Dominating Set (MDS) problem is not only one of the most fundamental problems in distributed computing, it is also one of the most challenging ones. While it is well-known that minimum dominating sets cannot be approximated locally on gen
We show that there is no deterministic local algorithm (constant-time distributed graph algorithm) that finds a $(7-epsilon)$-approximation of a minimum dominating set on planar graphs, for any positive constant $epsilon$. In prior work, the best low
Given a graph $G=(V,E)$ and an integer $k ge 1$, a $k$-hop dominating set $D$ of $G$ is a subset of $V$, such that, for every vertex $v in V$, there exists a node $u in D$ whose hop-distance from $v$ is at most $k$. A $k$-hop dominating set of minimu
We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices.
Given a graph $G=(V,E)$, the dominating set problem asks for a minimum subset of vertices $Dsubseteq V$ such that every vertex $uin Vsetminus D$ is adjacent to at least one vertex $vin D$. That is, the set $D$ satisfies the condition that $|N[v]cap D