92. Mathematical Colloquium

Peter van Emde Boas

Universiteit van Amsterdam


Tuesday November 18, 2014, 11:00
refektář, 1st floor
Malostranské nám. 25
118 00 Praha 1


The stratified tree, also called van Emde Boas tree, is a data structure implementing the full repertoire of instructions manipulating a single subset of a finite ordered universe of size $u$ with the processing time per instruction $O(\log\log(u))$. Hence it improves upon the traditional comparison based tree structures for dense subsets. Examples exist where this improvement helps to speed-up algorithmic solutions of real problems; such applications can be found for example in graph algorithms, computational geometry and forwarding of packets on the internet.

This data structure was invented during a three months postdoc residence at Cornell University in the fall of 1974. In my talk I want to describe the historical backgrounds against which the stratified trees were discovered and implemented.

In the literature today, the data structure is usually described by a direct recursive approach. However, this requires address calculations on the arguments which use multiplicative arithmetical instructions. These instructions were not allowed in the Random Access Machine model (RAM) which was the standard model in 1974. Therefore my early implementations of the stratified trees were based on a different approach which is best described as a binary-search-on-levels strategy. In this approach the address calculations were not required, and the structure could be implemented using pointers. The downside of this approach is that it leads to rather complex algorithms, which are still hard to present correctly even today. Another bad consequence was the super linear space consumption of the data structure, which was only eliminated three years later.

About the speaker

Peter van Emde Boas studoval matematiku na Amsterdamske univerzite v letech 1962 až 1969, tam take obhajil Ph.D. praci v roce 1974 na tema z teoreticke informatiky. Na jeho priklon k teoreticke informatice mely zasadni vliv pobyty na univerzite Cornell v Ithace, NY, kde se seznamil s praci Jurise Hartmanise a kde take objevil datovou strukturu dnes znamou pod jeho jmenem. Od roku 1964 do 1977 pusobil v Matematickem centru v Amsterdamu (nyni CWI). Od roku 1969 pusobil na Amsterdamske univerzite, kde je profesorem od roku 1977 (od roku 2009 emeritnim profesorem). Krome datovych struktur se zabyval semantikou programovacich i prirozenych jazyku, teorii databazi, umelou inteligenci, logikou a teorii her. Vyznamna je napriklad jeho role pri nalezeni LLL algoritmu (viz I. Smets, A. Lenstra, H. Lenstra, L. Lovasz, P. van Emde Boas: The History of the LLL-Algorithm. In: The LLL Algorithm, Springer 2010, pp.1-17). Skolil 22 studentu, mezi nimi jsou Arjen Lenstra nebo Harry Buhrman. Prof. Emde Boas je dlouholetym organizatorem evropske informatiky, byl clenem mnoha programovych vyboru informatickych konferenci. O jeho vztahu k ceske komunite svedci i to, že byl predsedou programoveho vyboru ICALP 1999 v Praze a konferenci SOFSEM 2004 a 2013, ucastnil se a byl v programovem vyboru rady konferenci MFCS.