Approximation of functions of several variables by multidimensional $S$-fractions with independent variables

The paper deals with the problem of approximation of functions of several variables by branched continued fractions. We study the correspondence between formal multiple power series and the so-called "multidimensional $S$-fraction with independent variables". As a result, the necessary and sufficient conditions for the expansion of the formal multiple power series into the corresponding multidimensional $S$-fraction with independent variables have been established. Several numerical experiments show the efficiency, power and feasibility of using the branched continued fractions in order to numerically approximate certain functions of several variables from their formal multiple power series.

A new approach to solving target coverage problem in wireless sensor networks using an effective hybrid genetic algorithm and tabu search

Literature in recent years has introduced several studies conducted to solve the target coverage problem in wireless sensor networks (WSNs). Sensors are conventionally assumed as devices with only a single power level. However, real applications may involve sensors with multiple power levels (i.e., multiple sensing ranges each of which possesses a unique power consumption). Consequently, one of the key problems in WSNs is how to provide a full coverage on all targets distributed in a network containing sensors with multiple power levels and simultaneously prolong the network lifetime as much as possible. This problem is known as Maximum Network Lifetime With Adjustable Ranges (MNLAR) and its NP-completeness has been already proved. To solve this problem, we proposed an efficient hybrid algorithm containing Genetic Algorithm (GA) and Tabu Search (TS) aiming at constructing cover sets that consist of sensors with appropriate sensing ranges to provide a desirable coverage for all the targets in the network. In our hybrid model, GA as a robust global searching algorithm is used for exploration purposes, while TS with its already-proved local searching ability is utilized for exploitation purposes. As a result, the proposed algorithm is capable of creating a balance between intensification and diversification. To solve the MNLR problem in an efficient way, the proposed model was also enriched with an effective encoding method, genetic operators, and neighboring structure. In the present paper, different experiments were performed for the purpose of evaluating how the proposed algorithm performs the tasks defined. The results clearly confirmed the superiority of the proposed algorithm over the greedy-based algorithm and learning automata-based algorithm in terms of extending the network lifetime. Moreover, it was found that the use of multiple power levels altogether caused the extension of the network lifetime.