We introduce a process that inserts elements into a hash table with a bounded number of probes, motivated by an application in cryptography. The cost of this algorithm is the number of insertion trials, whether successful or failed, until the table gets completely filled. This gives an interpolation between linear probing hashing and the coupon collector problem. We show that the process is related to a non-linear differential equation, which allows us to obtain the generating function of full tables. The proofs involve a full algebra of operators, which are themselves of independent interest. Then, we obtain the asymptotic behaviour of the expected number of insertion trials to get a full table.
Alharbi et al. (Tue,) studied this question.
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