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Grid technology is a promising distributed paradigm that can be used for applications that involves high performance computing. It involves sharing of heterogeneous resources. Scheduling is imperative for the optimal utilization of the heterogeneous resources that spans across multiple organizations. Approximation algorithms which offer a quick solution for optimization of scheduling processes in the Grid environment are needed. Various techniques based on fuzzy, evolutionary and swarm intelligence have been proposed for grid scheduling in literature. This book provides an over view of various Grid scheduling algorithms available in literature and details about new algorithm, Cluster Heterogeneous Earliest First Min-Min ABC (CHMM-ABC) technique for grid scheduling. Grid computing finds its utilization in numerous research ventures for storing of high dimensional data and complex computation. Telemedicine and bioinformatics are two fields that broaden the horizons of utilizing thegrid. Case studies which apply the proposed CHMM -ABC algorithm and an extended version of this algorithm in these two environments to prove the efficiency is also available.