Patricio V. Poblete

On the analysis of linear probing hashing

Abstract. This paper presents moment analyses and characterizations of limit distributions for the construction cost of hash tables under the linear probing strategy. Two models are considered, that of full tables and that of sparse tables with a fixed filling ratio strictly smaller than one. For full tables, the construction cost has expectation O(n3/2) , the standard deviation is of the same order, and a limit law of the Airy type holds. (The Airy distribution is a semiclassical distribution that is defined in terms of the usual Airy functions or equivalently in terms of Bessel functions of indices

An implicit binomial queue with constant insertion time

-\frac{1}{3},\frac{2}{3}

The analysis of a fringe heuristic for binary search trees

.) For sparse tables, the construction cost has expectation O(n) , standard deviation O (

Permuting In Place

\sqrt{n}

Analysis of the expected search cost in skip lists

), and a limit law of the Gaussian type. Combinatorial relations with other problems leading to Airy phenomena (like graph connectivity, tree inversions, tree path length, or area under excursions) are also briefly discussed.

Last-come-first-served hashing

We introduce a new representation of a priority queue in an array such that the operation of insert can be performed in constant time and minimum extraction in logarithmic time. In developing this structure we first introduce a very simple scheme permitting insertions in constant amortized time. This is modified to achieve the worst-case behavior using roughly lg*n pairs of pointers, and finally this pointer requirement is removed.

Fault tolerance and storage reduction in binary search trees

Abstract A detailed analysis is presented for the behaviour of binary search trees built by using a heuristic that performs only local reorganizations at the bottom of the tree.

The diagonal Poisson transform and its application to the analysis of a hashing scheme

This paper addresses the fundamental problem of permuting the elements of an array of

The Binomial Transform and its Application to the Analysis of Skip Lists

n

The Analysis of Linear Probing Hashing with Buckets

elements according to some given permutation. Our goal is to perform the permutation quickly using only a polylogarithmic number of bits of extra storage. The main result is an algorithm whose worst case running time is