Upper bounds on the broadcast function using minimum dominating sets

Bounds on the maximum number of minimum dominating sets

Counting Minimum Weighted Dominating Sets

We show how to count all minimumweighted dominating sets of a graph on n vertices in timeO(1.5535).

Tight Bounds on Minimum Broadcast Networks

A broadcast graph is an n-vertex communication network that supports a broadcast from any one vertex to all other vertices in optimal time dlg ne, given that each message transmission takes one time unit and a vertex participates in at most one transmission per time step. This paper establishes tight bounds for B(n), the minimum number of edges of a broadcast graph, and D(n), the minimum maxdeg...

Routing in Ad-Hoc Networks Using Minimum Connected Dominating Sets

1 Motivation An ad-hoc network is a multihop wireless network in which mobile hosts communicate over a shared, scarce wireless channel. An ad-hoc network is characterized by the absence of a wired backbone or any sort of centralized network management system to maintain routes as hosts move or turn oo or on. Since routes change quickly not only because end nodes move but also because intermedia...

New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs

Given a node-weighted graph, the minimum-weighted dominating set (MWDS) problem is to find a minimum-weighted vertex subset such that, for any vertex, it is contained in this subset or it has a neighbor contained in this set. And the minimum-weighted connected dominating set (MWCDS) problem is to find a MWDS such that the graph induced by this subset is connected. In this paper, we study these ...