ABSTRACT When open addressing IS used to resolve collisions in a hash table, a given set of keys may be arranged in many ways, typically this depends on the order in which the keys are inserted It is shown that arrangements minimizing either the average or worst-case number of probes required to retrieve any key in the table can be found using an algorithm for the assignment problem. The worst-case retrieval time can be reduced to O(log2(M)) with probablhty 1- e(M) when storing Mkeys In a table of size M, where ~(M) ~ 0 as M ~ ~ We also examine insertion algorithms to see how to apply these ideas for a dynamically changing set of keys