Catálogo de publicaciones - libros

The following problems are worth studying:

We believe that to attack these new and old open problems new techniques are still required and the Steiner tree is still an attractive topic for researchers in combinatorial optimization and computer science.

In this chapter, we have addressed several issues regarding the use of network-based mathematical programming techniques for solving various problems arising in the broad area of data mining. We have pointed out that applying these approaches often proved to be effective in many applications, including biomedicine, finance, telecommunications, etc. In particular, if a real-world massive dataset can be appropriately represented as a network structure, its analysis using standard graph-theoretical techniques often yields important practical results.

However, one should clearly understand that the success or failure of applying a certain methodology essentially depends on the structure of the considered dataset, and there is no “universal recipe” that would allow one to obtain useful information from any type of data. This indicates that despite the availability of a great variety of data mining techniques and software packages, choosing an appropriate method of the analysis of a certain dataset is a non-trivial task.

Moreover, as technological progress continues, new types of datasets may emerge in different practical fields, which would lead to further research in the field of data mining algorithms. Therefore, developing and modifying mathematical programming approaches in data mining is an exciting and challenging research area for years to come.

In this chapter we have described the state of the art in solving the Generalized Assignment Problem, as well as many extensions thereof. The approach we have taken is to generalize the GAP to a much larger class of Convex Assignment Problems, show that many of the extensions of the GAP proposed in the literature are members of this class, and describe many of the proposed solution approaches to the GAP in terms of the larger class of problems. Throughout the chapter we have paid particular attention to the Generalized Assignment Problem, the Multi-Resource Generalized Assignment Problem, and the Multi-Period Single-Sourcing Problem.

The following problems are worth studying:

We believe that to attack these new and old open problems new techniques are still required and the Steiner tree is still an attractive topic for researchers in combinatorial optimization and computer science.

In this chapter, we have addressed several issues regarding the use of network-based mathematical programming techniques for solving various problems arising in the broad area of data mining. We have pointed out that applying these approaches often proved to be effective in many applications, including biomedicine, finance, telecommunications, etc. In particular, if a real-world massive dataset can be appropriately represented as a network structure, its analysis using standard graph-theoretical techniques often yields important practical results.

However, one should clearly understand that the success or failure of applying a certain methodology essentially depends on the structure of the considered dataset, and there is no “universal recipe” that would allow one to obtain useful information from any type of data. This indicates that despite the availability of a great variety of data mining techniques and software packages, choosing an appropriate method of the analysis of a certain dataset is a non-trivial task.

Moreover, as technological progress continues, new types of datasets may emerge in different practical fields, which would lead to further research in the field of data mining algorithms. Therefore, developing and modifying mathematical programming approaches in data mining is an exciting and challenging research area for years to come.

In this chapter we have described the state of the art in solving the Generalized Assignment Problem, as well as many extensions thereof. The approach we have taken is to generalize the GAP to a much larger class of Convex Assignment Problems, show that many of the extensions of the GAP proposed in the literature are members of this class, and describe many of the proposed solution approaches to the GAP in terms of the larger class of problems. Throughout the chapter we have paid particular attention to the Generalized Assignment Problem, the Multi-Resource Generalized Assignment Problem, and the Multi-Period Single-Sourcing Problem.

The case studies discussed in this book have several implications on the society and policymakers and can be translated into policy recommendations as follows:

In this chapter we have described the state of the art in solving the Generalized Assignment Problem, as well as many extensions thereof. The approach we have taken is to generalize the GAP to a much larger class of Convex Assignment Problems, show that many of the extensions of the GAP proposed in the literature are members of this class, and describe many of the proposed solution approaches to the GAP in terms of the larger class of problems. Throughout the chapter we have paid particular attention to the Generalized Assignment Problem, the Multi-Resource Generalized Assignment Problem, and the Multi-Period Single-Sourcing Problem.