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In this chapter, we provide an overview of query processing with the emphasis on optimizing queries in centralized and distributed database environments. It is a welldocumented fact that for a given query there are many evaluation alternatives. The reason for the existence of a large number of alternatives (solution space) is the vast number of factors that affect query evaluation. These factors include the number of relations in the query, the number of operations to be performed, the number of predicates applied, the size of each relation in the query, the order of operations to be performed, the existence of indexes, and the number of alternatives for performing each individual operation-just to name a few. In a distributed system, there are other factors, such as the fragmentation details for the relations, the location of these fragments/tables in the system, and the speed of communication links connecting the sites in the system. The overhead associated with sending messages and the overhead associated with the local processing speed increase exponentially as the number of available alternatives increases. It is therefore generally acceptable to merely try to find a "good" alternative execution plan for a given query, rather than trying to find the "best" alternative.A query running against a distributed database environment (DDBE) will have to go through two types of optimization. The first type of optimization is done at the global level, where communication cost is a prominent factor. The second type of optimization is done at the local level. This is what each local DBE performs on the fragments that are stored at the local site, where the local CPU and, more importantly, the disk input/output (I/O) time are the main drivers. Almost all global optimization alternatives ignore the local processing time. When these alternatives were being developed, it was believed that the communication cost was a more dominant factor than the local processing cost. Now, it is believed that both the local query cost and the global communication cost are important to query optimization. 111 112 QUERY OPTIMIZATIONSuppose we have two copies of a relation at two different servers, where the first server is a lot faster than the second server, but at the same time, the connection to the first server is a lot slower than the connection to the second server (perhaps we are closer to the second server). An optimization strategy that only considered communication cost would choose the second server to run the local query. This will not necessarily be the best strategy, due to the speed of the chosen (second) server. The overall time to run a query in a distributed system consists of the time it takes to communicate local queries to local DBEs; the time it takes to run local query fragments; the time it takes to assemble the data and generate the final results; and the time it takes to display the results to the user. Therefore, to study distributed query optimization, we need to understand how a query is optimized both locally an...