Approximation algorithms for minimum power k backbone node r-connected subgraph problem in wireless sensor networks

Abstract

The minimum power assignment problem in a Wireless Sensor Network (WSN) is to assign transmission range to the nodes of the network with specified connectivity constraints minimizing the total power. This problem is termed as Strong Minimum Energy Topology (SMET) problem. Fault tolerance addresses the issue of a node or link failure in a WSN. So, with an objective of achieving high connectivity, we consider SMET problem with an additional property, i.e., the resultant network must satisfy the property of two or high connectivity. Minimum Power [Formula: see text]-Connected Subgraph (MP[Formula: see text]CS) problem is to contrive an [Formula: see text]-connected network with minimum power. Minimum Power [Formula: see text]-Connected Subgraph (MP2CS) problem is proved to be NP -hard. Minimum Power [Formula: see text] Backbone node [Formula: see text]-Connected Subgraph (MP[Formula: see text]B[Formula: see text]CS) problem is a special case of MP[Formula: see text]CS problem, which seeks a power assignment satisfying [Formula: see text]-connectivity with [Formula: see text] backbone nodes. We study MP[Formula: see text]B[Formula: see text]CS problem for [Formula: see text] backbone nodes, [Formula: see text]-connectivity and derive the approximation ratios. We also propose an algorithm of approximation ratio [Formula: see text], for Minimum Power [Formula: see text] Backbone node 3-Connected Subgraph (MP[Formula: see text]B3CS) problem for [Formula: see text] that runs in [Formula: see text] time and generalize for the case [Formula: see text] for any [Formula: see text] and [Formula: see text].