Motivated by the problem of supporting energy–efficient broadcasting in ad hoc wireless networks, we study the Minimum Energy Consumption Broadcast Subgraph (MECBS) problem. We present the first logarithmic approximation algorithm for the problem which uses an interesting reduction to Node–Weighted Connected Dominating Set. We also show that an important special instance of the problem can be s...

In ad hoc wireless networks, a successful broadcasting requires that the nodes forwarding the broadcast packet form a connected dominating set to ensure the coverage. An efficient broadcast method should generate a small forward node set without excessive overhead. Neighbor-knowledgebased methods, including neighbor-designating methods and self-pruning methods, are localized algorithms that red...

A Connected Dominating Set (CDS) is used as a virtual backbone for Wireless Sensor Networks (WSNs). Most existing works focus on a Minimum CDS (MCDS), a k-connect mdominating CDS, a minimum routing cost CDS or a bounded-diameter CDS, ignoring the loadbalance factor of CDSs. In this paper, we propose a novel problem – the Load-Balanced CDS (LBCDS) problem, in which constructing an LBCDS and load...

We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm, is analysed on random n-vertex cubic graphs using differential equations. In this way, we prove that the expected size of the connected dominating set returned by the algorithm is asymptotically almost surely less tha...

Broadcasting is a key component of several networking mechanisms in mobile ad hoc networks. However, its traditional implementation suffers from resource consumption caused by message redundancy. Several efficient algorithms have been proposed to tackle this problem. Among them, the class of algorithms that construct on-demand a connected dominating set, known as dominant pruning, yields an imp...

We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf). We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class. To obtain this approximation we define a graph parameter x(G), and construct a tree with at least (n−x(G)+4)/3 leaves, and prove that no tree with m...

Energy efficiency is one of the major issues in wireless sensor networks (WSNs) and their applications. Distributed techniques with low message and time complexities are expected in WSNs. Connected dominating sets (CDSs) have been widely used for virtual backbone construction in WSNs to control topology, facilitate routing, and extend network lifetime. Most of the existing CDS approaches suffer...

We give efficient deterministic distributed algorithms which given a graph G from a proper minor-closed family C find an approximation of a minimum dominating set in G and a minimum connected dominating set in G. The algorithms are deterministic and run in a polylogarithmic number of rounds. The approximation accomplished differs from an optimal by a multiplicative factor of (1 + o(1)).

We study approximation hardness of the Minimum Dominating Set problem and its variants in undirected and directed graphs. Using a similar result obtained by Trevisan for Minimum Set Cover we prove the first explicit approximation lower bounds for various kinds of domination problems (connected, total, independent) in bounded degree graphs. Asymptotically, for degree bound approaching infinity, ...

A set S of vertices of a graph G is a connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by S is connected. The connected domination number γc(G) is the minimum size of a connected dominating set of G. In this paper we prove that γc(G) + γc(G) ≤ min{δ(G), δ(G)} + 4 for every n-vertex graph G such that G and G have diameter 2 and show that ...