5 research outputs found
A unified approach to linear probing hashing with buckets
We give a unified analysis of linear probing hashing with a general bucket
size. We use both a combinatorial approach, giving exact formulas for
generating functions, and a probabilistic approach, giving simple derivations
of asymptotic results. Both approaches complement nicely, and give a good
insight in the relation between linear probing and random walks. A key
methodological contribution, at the core of Analytic Combinatorics, is the use
of the symbolic method (based on q-calculus) to directly derive the generating
functions to analyze.Comment: 49 page
Distributional Analysis of the Parking Problem and Robin Hood Linear Probing Hashing with Buckets
This paper presents the first distributional analysis of both, a parking problem and a linear probing hashing scheme with buckets of size b. The exact distribution of the cost of successful searches for a b alpha-full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform distributional results are also obtained for tables of size m and n elements. A key element in the analysis is the use of a new family of numbers, called Tuba Numbers, that satisfies a recurrence resembling that of the Bernoulli numbers. These numbers may prove helpful in studying recurrences involving truncated generating functions, as well as in other problems related with buckets
Advances in knowledge discovery and data mining Part II
19th Pacific-Asia Conference, PAKDD 2015, Ho Chi Minh City, Vietnam, May 19-22, 2015, Proceedings, Part II</p