- Xuding Zhu, "Graph Theory model for scheduling problems"
Scheduling is the process of deciding how to commit resources between a variety of possible tasks. A typical phenomenon is that there are conflicts between pairs of tasks that forbids them to share a resource. In this case, graphs provide an ideal model for the problem. Vertices represent tasks, and two vertices are connected by an edge if there are conflicts between the corresponding tasks.
- Jaroslav Nesetril & Patrice Ossona de Mendez: "Sparsity (Graphs, Structures, and Algorithms)"
This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a fuzzy notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants.
This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms.
This book is related to the material presented by the first author at ECM 1998 and ICM 2010.
Dernière mise à jour : 16 mai 2013