Abstract
We usually use a digraph to represent a wireless network (WN). Correspondingly, a connected dominating set (CDS) of the digraph is usually used to denote a virtual backbone (VB) of the corresponding WN. In this article, focusing on the problem of a minimum strongly connected dominating and absorbing set (MSCDAS) with a bounded diameter (or guaranteed routing cost) for a digraph, which is strongly connected, we introduce two algorithms. One is called the guaranteed routing cost strongly connected dominating and absorbing set (GOC-SCDAS), which can generate a strongly connected dominating and absorbing set (SCDAS) with a performance ratio 14.4k+1/22 in respect of the optimal solution. Another is called the α guaranteed routing cost strongly connected bidirectional dominating and absorbing set (α-GOC-SCBDAS), which can generate a strongly connected bidirectional dominating and absorbing set (SCBDAS) with a performance ratio 8.8443k+1/22k+1/22 in respect of the optimal solution and a better routing cost, where k=rmax/rmin and rmin,rmax is the transmission range of nodes in the network. Through the simulation experiments, we obtain the conclusion that in terms of the diameter and average routing path length (ARPL) of CDS, the outputs of our algorithms are better than those of the algorithm in (Du et al. 2006).
Highlights
Owing to the development of wireless radio communication and very-large-scale technology, wireless network (WN) such as wireless sensor networks (WSNs) or ad hoc WNs have begun to be widely applied in a lot of fields
The advantages of a virtual backbone (VB) established in a network are as follows: when the routing-related tasks are performed to find routing paths, it is enough to search the space of the VB rather than the whole network, which implies that it takes a shorter time for searching routing paths and needs a smaller size of routing table, and it causes that the routing maintenance becomes simpler
(2) We propose another algorithm, called by α-GOCSCBDAS, which produces an strongly connected bidirectional dominating and absorbing set (SCBDAS) S with jSj ⩽ 8:844ð3k + ð1/2ÞÞ2ðk + ð1/2ÞÞ2opt + 13:635ð3k + ð1/ 2ÞÞ2 ðk + ð1/2ÞÞ2 such that for any x, y ∈ V, dSðx, yÞ ≤ 7dðx, yÞ, where opt denotes the cardinality of an minimum strongly connected dominating and absorbing set (MSCDAS) of G, k = ðrmax/rminÞ
Summary
Owing to the development of wireless radio communication and very-large-scale technology, WNs such as wireless sensor networks (WSNs) or ad hoc WNs have begun to be widely applied in a lot of fields. Most researchers in this area concentrate on how to find smaller CDSs. It is worth mentioning that [10] is the first paper to introduce the approximation algorithms computing an MCDS in a unit disk graph (UDG), which is utilized to model a WN with the same transmission radius (or range) for each node. Most of previous researches on the MCDS problem have focused on UDGs [11,12,13,14] These studies all aimed to obtain a smaller CDS to make the best of the existence of a minimum VB. Some research results on the MCDS problem considering the routing cost for a UDG have been obtained in [15,16,17,18,19].
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