The Third Haifa Workshop on Interdisciplinary Applications of Graph Theory, Combinatorics, and Algorithms

Irith Ben-Arroyo Hartman, Seffi Naor, Michal Penn, Uriel G. Rothblum
2008 Discrete Applied Mathematics  
and the list has grown since the workshop). During the workshop, Professor Hammer delivered the Third annual Rothschild Lecture on "Logical Analysis of Data with Applications to Medical Informatics". The papers in this volume focus on discrete mathematics and combinatorial algorithms and their applications to realworld problems in engineering and communication networks, as well as studies in the interface of Discrete Mathematics and other areas of Mathematics. The tools that are used are from a
more » ... variety of fields. The papers are divided into four clusters. The first cluster addresses three applications to production planning and multi-agent systems (games). The second cluster addresses applications to communication networks and graphs. The third cluster consists of three studies in the interface of Combinatorics and Algebra, and finally, the fourth cluster contains two studies in the interface of Combinatorics and Logic. All papers were peer reviewed and edited. A brief summary of each of the 11 chapters (papers) that make up this volume is given below. In the first chapter, "A Polynomial Time Algorithm for Solving a Quality Control Station Configuration Problem", Penn and Raviv study the problem of incorporating quality control stations (QCS) into unreliable multi-stage production systems. The problem they consider is well-studied and concerns simultaneous decisions whether to install QCS, and where to install them. The authors use dynamic programming to solve an auxiliary problem that is used as a subroutine to give a polynomial time algorithm to solve the profit maximization QCS configuration problem. Chapters 2 and 3 address games. In Chapter 2, "Games Played by Boole and Galois", Fraenkel introduces a new class of games that he calls "2-pile subtraction games" which generalize Wythoff's game. These games are defined and motivated by the use of Boolean functions and the work illustrates some of Professor Hammer's contributions to the theory and applications in this field. The paper explores winning positions of players and discusses strategy complexity questions. Some open problems are presented. In Chapter 3, "The Partition Bargaining Problem", Rothblum and Tangir study problems of dividing property consisting of finally many items among several agents through a mechanism that applies John Nash's bargaining games. The analysis generalizes earlier work that was restricted to the presence of two agents. The main result shows that the Nash solution can be computed in polynomial time. The key tool is the demonstration that a lottery that is associated with any point in the Pareto-optimal surface, has a representation with only (relatively) few items being assigned non-deterministically. Chapters 4-6 are related to network applications. In Chapter 4, "The Complete Optimal Stars-Clustering-Tree Problem", Korach and Stern provide an efficient algorithm for finding a minimum cost communication tree network for a collection of groups of customers such that each group induces a complete star. Other related problems and applications from database systems are considered. In Chapter 5, "The k-edge Intersection Graphs of Paths in a Tree", Golumbic, Lipshteyn and Stern investigate a generalization of the intersection graph of paths in a tree. In this generalization two paths in a tree are considered intersecting only if they share k-edges. The authors prove that the 0166-218X/$ -see front matter
doi:10.1016/j.dam.2007.09.015 fatcat:it62epefvnbrzkc3e4ew6vtmgu