Abstract

The general objective of the Algorithms Project is the design, analysis, and optimization of major Algorithms and data structures of computer science. The main activity revolves around the construction of analytic models permitting a precise performance evaluation and fine optimization of Algorithms. A unified theory for a large class of combinatorial and Algorithmic processes has been built over the past few years. It is based in part on combinatorial analysis and discrete mathematics structures and in part on asymptotic analysis through complex function theory. In this way, very precise complexity characterizations can be obtained concerning the average-case or probabilistic behaviour of fundamental Algorithms. This systematic approach connects itself nicely with computer algebra. It has become in particular possible to develop a large computer algebra program that can assist the analysis of structurally complex Algorithms. On this occasion, interest has also developed for computer algebra and symbolic manipulation systems. The approach taken there is prototypical of the possibility of developing computer algebra libraries dedicated to the analysis of complex systems. At the same time, all members of the project are engaged in research dealing with specific fields of application in computer science listed below.

-: Trees and data structures for fast retrieval of information in the context of multidimensional data or secondary storage systems.
-: Telecommunication networks.
-: Strings and pattern matching Algorithms with implications for DNA sequence processing.
-: Computational number theory in relation to cryptography.
-: Computer algebra, especially new functionalities related to combinatorial libraries, revues and asymptotics.

The project is a component of the ALCOM-IT Basic Research Action of the European Union.

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