Enhanced algorithms for deploying the minimum sensors to construct a wireless sensor network having full coverage of critical square grids

With the rapid technological development of sensors, many applications have been designed to use wireless sensor networks to monitor a certain area and provide quality-of-service guarantees. Therefore, the coverage problem had an important issue for constructing wireless sensor networks. Recently, a coverage problem of constructing a minimum size wireless sensor network to fully cover critical squares in a sensor field, termed CRITICAL-SQUARE-GRID COVERAGE, has received much attention. CRITICAL-SQUARE-GRID COVERAGE is shown to be NP-Complete, and an approximation algorithm, termed Steiner-tree-based critical grid covering algorithm (STBCGCA), is proposed accordingly. In STBCGCA, a sensor is selected to cover critical squares only if at least one of the critical squares is fully covered by the sensor. However, a critical square grid can be cooperatively covered by two or more sensors; that is, one sensor covers one part of the critical square, and the other sensors cover the other part of the critical square. This motivates us to propose two efficient algorithms based on STBCGCA, termed critical-grid-partitioned (CGP-STBCGCA) and reference-point-covered (RPC-STBCGCA), that select sensors that can cooperatively cover critical squares in an attempt to minimize the size of the wireless sensor network. The theoretical analysis shows that sensors deployed by CGP-STBCGCA and RPC-STBCGCA can form a connected wireless sensor network that fully covers all critical grids. In addition, a performance guarantee for CGP-STBCGCA is provided. Simulation results show that the ratio of the average number of deployed sensors in STBCGCA to that in CGP-STBCGCA and RPC-STBCGCA in about 90 % of the cases was between 1.08 and 2.52 for CRITICAL-SQUARE-GRID COVERAGE.