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

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].

A Modified TopDisc Algorithm in WSN

TopDisc algorithm, one classic algorithm based on minimum dominating set, puts forward an effective method—approximate topology to set up network. TopDisc algorithm, which only needs local information, is a fully distributed and expandable network-control algorithm. The shortcomings of such algorithm are as follows: the algorithm expense is considerable without taking nodes residual energy into account. After a close analysis of TopDisc algorithm, the author proposes a modified algorithm. The modified algorithm makes good use of the nodes residual energy and reasonably chooses backbone node form heavily energy-loaded ones, which makes the energy evenly consumed, network topology stable and network lifetime endurable. Simulation data indicate that the modified algorithm is very flexible, making the energy evenly consumed, net work topology stable and network lifetime endurable.