Optimal distribution of signatures in signature hashing

G.H. Gonnet and P.A. Larson (1982) proposed a hashing scheme for external files which guarantees single access retrieval. They provided an asymptotic analysis of the scheme assuming uniform distribution of the signatures. This paper addresses an open problem posed by them in a second work (J. ACM, vol.35, no.1, p.161-84, 1988) about the performance of signatures having a skew distribution. An optimization problem is formulated to obtain the optimal signature distribution which maximizes the resulting load factor. Numerical results indicate that the optimal signature distribution results in significant reduction in the cost of insertions, which is of practical significance