## Analysis of hashing algorithms and a new mathematical transform (1995)

Citations: | 1 - 0 self |

### BibTeX

@TECHREPORT{Viola95analysisof,

author = {Alfredo Viola},

title = {Analysis of hashing algorithms and a new mathematical transform},

institution = {},

year = {1995}

}

### OpenURL

### Abstract

The main contribution of this report is the introduction of a new mathematical tool that we call the Diagonal Poisson Transform, and its application to the analysis of some linear probing hashing schemes. We also present what appears to be the rst exact analysis of a linear probing hashing scheme with buckets of size b. First, we present the Diagonal Poisson Transform. We show its main properties and apply it to solve recurrences, nd inverse relations and obtain several generalizations of Abel's summation formula. We follow with the analyisis of LCFS hashing with linear probing. It is known that the Robin Hood linear probing algorithm minimizes the variance of the cost of successful searches for all linear probing algorithms. We prove that the variance of the LCFS scheme is within lower order terms of this optimum. Finally we present the rst exact analysis of linear probing hashing with buckets of size b. From the generating function for the Robin Hood heuristic, we obtain exact expressions for the cost of successful searches when the table is full. Then, with the help

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