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We present techniques for optimizing queries in memory-resident database systems. Optimization techniques in memory-resident database systems differ significantly from those in conventional disk-resident database systems. In this paper we address the following aspects of query optimization in such systems and present specific solutions for them: (1) a new approach to developing a CPU-intensive cost model; (2) new optimization strategies for main-memory query processing; (3) new insight into join algorithms and access structures that take advantage of memory residency of data; and (4) the effect of the operating system's scheduling algorithm on the memory-residency assumption. We present an interesting result that a major cost of processing queries in memory-resident database systems is incurred by evaluation of predicates. We discuss optimization techniques using the Office-by-Example (OBE) that has been under development at IBM Research. We also present the results of performance measurements, which prove to be excellent in the current state of the art. Despite recent work on memory-resident database systems, query optimization aspects in these systems have not been well studied. We believe this paper opens the issues of query optimization in memory-resident database systems and presents practical solutions to them.