A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. We introduce and study the class of connected-domishold graphs, which are graphs that admit non-negative real weights associated to their vertices such that a set of vertices is a connected dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. We sho...

It was a long-standing open problem whether the minimum weight dominating set in unit disk graphs has a polynomial-time constant-approximation. In 2006, Ambühl et al solved this problem by presenting a 72-approximation for the minimum weight dominating set and also a 89-approximation for the minimum weight connected dominating set in unit disk graphs. In this paper, we improve their results by ...

Efficient routing between nodes is the most important challenge in a Mobile Ad Hoc Network (MANET). A Connected Dominating Set (CDS) acts as a virtual backbone for routing in a MANET. Hence, the construction of CDS based on the need and its application play a vital role in the applications of the MANET. The PipeLined Strategic CDS (PLS-CDS) is constructed based on strategy, dynamic diameter and...

Most existing algorithms used for constructing virtual backbones are based on the ideal deterministic network model (DNM) in which any pair of nodes is either fully connected or completely disconnected. Different from DNM, the probabilistic network model (PNM), which presumes that there is a probability to connect and communicate between any pair of nodes, is more suitable to the practice in ma...

A critical issue in battery-powered sensor networks is to construct energy efficient virtual backbones for network routing. Recent study in battery technology reveals that batteries tend to discharge more power than needed and reimburse the over-discharged power if they are recovered. In this paper we first provide a mathematical battery model suitable for implementation in sensor networks. We ...

An important question in multi-radio multi-channel and multi-hop networks is how to perform efficient network-wide broadcast. Currently almost all broadcasting protocols assume a single-radio single-channel network model. Simply using them in multi-channel environment without careful enhancement will result in unnecessary redundancy. In this paper, we focus on reducing the amount of redundant t...

Given a simple undirected graph, the minimum connected dominating set problem is to find a minimum cardinality subset of vertices D inducing a connected subgraph such that each vertex outside D has at least one neighbor in D. Approximations of minimum connected dominating sets are often used to represent a virtual routing backbone in wireless networks. This paper first proposes a constant-ratio...

Let G = (V,E) be a graph. A subset S ⊆ V is a dominating set of G if every vertex not in S is adjacent to a vertex in S. A set D̃ ⊆ V of a graph G = (V,E) is called an outer-connected dominating set for G if (1) D̃ is a dominating set for G, and (2) G[V \ D̃], the induced subgraph of G by V \ D̃, is connected. The minimum size among all outer-connected dominating sets of G is called the outerconnec...

Weakly connected dominating set (WCDS) has been proposed to cluster mobile ad hoc networks and be used as a virtual backbone. There have been some distributed approximation algorithms proposed in the literature for minimum WCDS. But none of them have constant approximation factors. Thus these algorithms can not guarantee to generate a WCDS of small size. Their message complexities may also be a...

Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts in the system are either in the set or neighbors of hosts in the set. In this paper, we first review a distributed formation of a connected dominating set called marking process and dominating-set-based routing. Then we ...