Wireless Sensor Network is an emerging branch of latest technology that is growing and improving day by day. Network lifetime management of sensor network is highly prioritized in its advancement issues. Routing techniques decide the transmission path in network that is main cause of energy consumption. In this paper three routing protocols LEACH, LEACH-C and PEGASIS are studied and compared on the basis of different factors that have to be considered while choosing methodology for particular project of wireless sensor network.

Routing algorithm decides which route will be followed by packets for communication between sender and receiver. Wireless Sensor Network consists of nodes with limited power source and low bandwidth. Optimal route for communication saves more amount of energy of the network. PEGASIS protocol is based on hierarchical network architecture proposed for Wireless Sensor Network. In this paper, PEGASIS is discussed and evaluated with simulator NS2 for performance issue.

Summary: The paper formulates a dual program for a given linear fractional functionals program (L. F. F. P.) and proves the duality theorem and its converse for the same. Special feature of the paper is that both the primal and the dual programs are L. F. F. Ps. and can easily be solved by the existing standard techniques.Zusammenfassung: Fiir ein lineares Optimierungsproblem, dessen Zielfnnktion als Quotient zweier linearer Funktionen gegeben ist (LP-Problem mit gebrochener Zielfunktion), wird ein duales Problem formuliert und das Dualit~itstheorem bewiesen. Es wird gezeigt, dab sowohl das primale als auch das duale Problem lineare Probleme mit gebrochener Zielfunktion sind und leicht mit den bekannten Standardtechniken gel~Sst werden k6nnen.

Purpose The purpose of this paper is to review the existing routing algorithms for wireless ad hoc networks to evaluate the methods according to the current requirements. Wireless ad hoc network can provide communication in emergency situations. Active nodes in ad hoc network work as sender, receiver and router at the same time. Nodes are equipped with limited bandwidth and energy. Optimal routing method can help in “smart use” of available resources. Evolvement of routing method based on need is a continuous process. Numerous applications of ad hoc network motivates researcher for further development to fulfill the need of society. Design/methodology/approach In this paper, routing algorithms for ad hoc network based on ant colony optimization, multipath routing and with multiple input multiple output (MIMO) antenna support have been discussed. Findings Comparative analysis has been drawn among existing algorithms of different categories. Transmitting message packets parallel through multiple paths in the network can save overall resource usage in the network. Originality/value The authors have discussed the future area of development for optimal routing in ad hoc networks. Considering signal noise ratio and congestion status while selecting path can provide better energy use in the network. Rather than leaving less prioritized route paths, multiple paths can be used for sending data packets parallel.

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