[1] J.-P. Barthélemy, B. Leclerc, “The median procedure for partitions”, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 19, 1995, 3-34. [2] I. Charon, O. Hudry, “The noising method: a new combinatorial optimization method”, Operations Research Letters 14, 1993, 133-137. [3] P. Hansen, B. Jaumard, “Cluster analysis and mathematical programming”, Mathematical Programming 7...

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles...

Biographical notes: Dr. Said Ben Messaoud received his Diploma of “Maîtrise” in Applied Mathematics from the Faculty of Sciences of Monastir in 1998, his MS degree from the INPGGrenoble, in 2000 and his PhD degree in Optimization in 2004 from the Technology University of Troyes. He is a Assistant Professor at the Higher Institute for Informatics and Mathematics of Monastir-Tunisia. His research...

Squier introduced the notion finite derivation type which is a combinatorial condition satisfied by certain rewriting systems. The main result in this paper states that the Chinese monoid has finite derivation type property. Mathematics Subject Classification: 16S15; 20F05; 20F10; 20M50; 68Q42

Multi-objective (vector) combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability) are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05...

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. Key-Words: Linear Programming; Network Optimization; Integer Programming; Traveling Salesman Problem; Combinatorial Optimization; Scheduling; Sequencing. (Forthco...

Combinatorial Programs and Efficient Property Testers ∗ Artur Czumaj Department of Computer Science New Jersey Institute of Technology University Heights Newark, NJ 07102-1982, USA E-mail: [email protected] Christian Sohler Heinz Nixdorf Institute and Department of Mathematics & Computer Science University of Paderborn D-33095 Paderborn, Germany E-mail: [email protected]

The class will focus on two themes: linear algebra and probability, and their many applications in algorithm design. We will cover a number of classical examples, including: fast matrix multiplication, FFT, error correcting codes, cryptography, efficient data structures, combinatorial optimization, routing, and more. We assume basic familiarity (undergraduate level) with linear algebra, probabi...

Abstract: This paper analyzes the dynamic programming construction of bundles within the framework of the Winner Determination Problem in Combinatorial Auctions, based on constraint processing. We discuss different approaches to its representation and highlight the corresponding complexity, employing suitable combinatorics from Discrete Mathematics. Our view may enlighten us about the exponenti...

Combinatorial optimization problems arise in situations where discrete choices must be made and solving them amounts to finding an optimal solution among a finite or countably infinite number of alternatives. Optimality relates to some cost criterion, which provides a quantitative measure of the quality of each solution. This area of discrete mathematics is of great practical use and has attrac...