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An algorithm is developed which reduces the memory requirements of hash tables. This is achieved by storing only a part of each key along with a few extra bits needed to ensure that all keys are stored unambiguously. The fraction of each key stored decreases as the size of the hash table increases. Significant reductions in total memory usage can be achieved especially when the key size is not much larger than the size of a memory index and when only a small amount of data is stored with each key. The algorithm is based on bidirectional linear probing. Search and insertion times are shown by simulation to be similar to those for ordinary bidirectional linear probing.