A Novel Approximation for Multi-Hop Connected Clustering Problem in Wireless Networks

Wireless sensor networks (WSNs) have been widely used in a plenty of applications. To achieve higher efficiency for data collection, WSNs are often partitioned into several disjointed clusters, each with a representative cluster head in charge of the data gathering and routing process. Such a partition is balanced and effective, if the distance between each node and its cluster head can be bounded within a constant number of hops, and any two cluster heads are connected. Finding such a cluster partition with minimum number of clusters and connectors between cluster heads is defined as <italic>minimum connected <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-hop dominating set</italic> (<inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-MCDS) problem, which is proved to be NP-complete. In this paper, we propose a distributed approximation named <italic>CS-Cluster</italic> to address the <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-MCDS problem under <italic>unit disk graph</italic>. CS-Cluster constructs a sparser <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-hop maximal independent set (<inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-MIS), connects the <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-MIS, and finally checks and removes redundant nodes. We prove the approximation ratio of CS-Cluster is <inline-formula> <tex-math notation="LaTeX">$(2d+1)\lambda $ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> is a parameter related with <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> but is no more than 18.4. Compared with the previous best result <inline-formula> <tex-math notation="LaTeX">$O(d^{2})$ </tex-math></inline-formula>, our approximation ratio is a great improvement. Our evaluation results demonstrate the outstanding performance of our algorithm compared with previous works.

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