CIDEC     ÜIK Estonian Winter Schools in Computer Science     Eesti arvutiteaduse talvekoolid EWSCS 2005EATTK 2005 ## Implementing Algorithms

### Abstract

Algorithms are problem solving recipes intended for humans; they are usually expressed in a mixture of natural language, mathematical notation, and programming notation. In contrast, programs are intended for machine execution; they are expressed in a programming language.

How do we go from a correct algorithm to a correct program?

The background for my lectures is the experience with LEDA, CGAL, and EXACUS, three algorithm library projects I was involved with.

In the first main part, I discuss certifying algorithms. Certifying algorithms return not only the value they are supposed to compute but also a witness (certificate) which allows the user of the algorithm to convince itself of the correctness of the value returned. I give examples of certifying algorithms and discuss the limits of certification.

In the second main part, I discuss the implementation of geometric algorithms. Their implementation is particularly difficult, because geometric algorithms are usually designed for inputs in general position and for the Real-RAM model of computation. I give examples, how miserably naive implementations can fail, show how to realize a Real-RAM as needed for computational geometry, discuss approaches to overcome the general position problem, and finally come to exact algorithms for curves and surfaces.

#### Course materials

• Web page for this course at MPI

• K. Mehlhorn. Certifying algorithms. Slides. [pdf]
• K. Mehlhorn. Certifying algorithms: an attempt of a theory. Slides. [pdf]
• K. Mehlhorn. Certification of data structures. Slides. [pdf]
• K. Mehlhorn et al. Classroom examples of robustness problems in geometric computations. [ppt]
• K. Mehlhorn et al. A Descartes algorithm for polynomials with approximate coefficients. Slides. [pdf]
• K. Mehlhorn et al. Conic polygons. Slides. [pdf]

• K. Mehlhorn, S. Näher, C. Uhrig. Some of the theory behind LEDA. [pdf]
• K. Mehlhorn, A. Eigenwillig, K. Kanegossi, D. Kratsch, R. McConnel, U. Meyer, J. Spinrad. Certifying algorithms.
• U. Finkler, K. Mehlhorn. Checking priority queues.
• L. Kettner, K. Mehlhorn, S. Pion, S. Schirra, C. Yap. Classroom examples of robustness problems in geometric computations.
• E. Berberich, A. Eigenwillig, M. Hemmer, S. Hert, K. Mehlhorn, E. Schömer. A computational basis for conic arcs and Boolean operations on conic polygons.
• A. Eigenwillig, L. Kettner, W. Krandick, K. Mehlhorn, S. Schmitt, N. Wolpert. An exact Descartes algorithm with approximate coefficients.