Message-optimal connected dominating sets in mobile ad hoc networks

Abstract

A connected dominating set (CDS) for a graph G(V, E) is a subset V of V , such that each node in V − V is adjacent to some node in V , and V induces a connected subgraph. A CDS has been proposed as a virtual backbone for routing in wireless ad hoc networks. However, it is NP-hard to find a minimum connected dominating set (MCDS). Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a very poor approximation ratio, and from high time complexity and message complexity. Recently, new distributed heuristics for constructing a CDS were developed, with constant approximation ratio of 8. These new heuristics are based on a construction of a spanning tree, which makes it very costly in terms of communication overhead to maintain the CDS in the case of mobility and topology changes.In this paper, we propose the first distributed approximation algorithm to construct a MCDS for the unit-disk-graph with a constant approximation ratio, and linear time and linear message complexity. This algorithm is fully localized, and does not depend on the spanning tree. Thus, the maintenance of the CDS after changes of topology guarantees the maintenance of the same approximation ratio. In this algorithm each node requires knowledge of its singlehop neighbors, and only a constant number of two-hop and three-hop neighbors. The message length is O(log n) bits.

Routing Transient Traffic in Mobile Ad Hoc Networks

“…Therefore, the congestion impact of one route discovery packet worsens in a bigger network since it is broadcast on the backbone. Note that, even though the theoretical maximum dominator degree can be 47 [25], in practice it stays around 7 with little deviations as long as the backbone is not chain-like.…”

“…One is to reduce the backbone complexity by building a small connected graph in the network. Building a backbone that has good approximation ratio to the ideal Minimum Connected Dominating Set (MCDS) has been the research focus of ad hoc clustering in recent years [22][23][24][25][26][27][28]. Another method is to reduce the protocol overhead forwarded on the backbone.…”

“…The backbone is constructed using a variant of the message-optimal connected dominating set algorithm [25] that we modified to work incrementally and to be resilient to communication failures. The algorithm selects certain nodes to act as cluster heads, called dominators; all other nodes are called dominatees.…”

Virtual Backbone Construction in MANETs Using Adjustable Transmission Ranges

“…Quasi-global solutions, such as Alzoubi et al's tree-based approach [4], require network-wide coordination, which causes slow convergence in large scale networks. Many cluster-based approaches [3,23,38] are quasi-local. The status (clusterhead/non-clusterhead) of each node depends on the status of its neighbors, which in turn depends on the status of neighbors' neighbors and so on.…”

“…The local scheme, applied to the derived graph, has constant message and time cost and is very effective in reducing the final CDS size for average cases. Several schemes exist that connect clusterheads to form a CDS [3,4,11,23], but these schemes have either relatively high redundancy [3,23] or high overhead [4,11]. Therefore, a low-cost scheme to form a small CDS is still desirable.…”