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Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, engineering, mathematical, technological and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology, digital art and software engineering. The term computing is also synonymous with counting and calculating. In earlier times, it was used in reference to the action performed by mechanical computing machines, and before that, to human computers. History History of computing The history of computing is longer than the history of computing hardware and includes the history of methods intended for pen and paper (or for chalk and slate) with or without the aid of tables. Computing is intimately tied to the repr

Constraint consistency techniques for continuous domains

Jamila Sam

Constraint Satisfaction Problems (CSPs) are ubiquitous in computer science. Many problems, ranging from resource allocation and scheduling to fault diagnosis and design, involve constraint satisfaction as an essential component. A CSP is given by a set of variables and constraints on small subsets of these variables. It is solved by finding assignments of values to the variables such that all constraints are satisfied. In its most general form, a CSP is combinatorial and complex. In this thesis, we consider constraint satisfaction problems with variables in continuous, numerical domains. Contrary to most existing techniques, which focus on computing a single optimal solution, we address the problem of computing a compact representation of the space of all solutions that satisfy the constraints. This has the advantage that no optimization criterion has to be formulated beforehand, and that the space of possibilities can be explored systematically. In certain applications, such as diagnosis and design, these advantages are crucial. In consistency techniques, the solution space is represented by labels assigned to individual variables or combinations of variables. When the labeling is globally consistent, each label contains only those values or combinations of values which appear in at least one solution. This kind of labeling is a compact, sound and complete representation of the solution space, and can be combined with other reasoning methods. In practice, computing a globally consistent labeling is too complex. This is usually tackled in two ways. One way is to enforce consistencies locally, using propagation algorithms. This prunes the search space and hence reduces the subsequent search effort. The other way is to identify simplifying properties which guarantee that global consistency can be enforced tractably using local propagation algorithms. When constraints are represented by mathematical expressions, implementing local consistency algorithms is difficult because it requires tools for solving arbitrary systems of equations. In this thesis, we propose to approximate feasible solution regions by 2k-trees, thus providing a means of combining constraints logically rather than numerically. This representation, commonly used in computer vision and image processing, avoids using complex mathematical tools. We propose simple and stable algorithms for computing labels of arbitrary degrees of consistency using this representation. For binary constraints, it is known that simplifying convexity properties reduces the complexity of solving a CSP. These properties guarantee that local degrees of consistency are sufficient to ensure global consistency. We show how, in continuous domains, these results can be generalized to ternary and in fact arbitrary n-ary constraints. This leads to polynomial-time algorithms for computing globally consistent labels for a large class of constraint satisfaction problems with continuous variables. We describe and justify our representation of constraints and our consistency algorithms. We also give a complete analysis of the theoretical results we present. Finally, the developed techniques are illustrated using practical examples.

EPFL1995

MATHICSE Technical Report : An algorithm for computing minimal Geršgorin sets

Agnieszka Katarzyna Miedlar

The first algorithms for computing the minimal Geršgorn set were developed by Varga et all. in [17] for the use on small and medium size (dense) matrices. Here, we first discuss the existing methods and present a new approach based on the modified Newton’s method to find zeros of the parameter dependent left-most eigenvalue of a Z-matrix. Additionally, sampling technique used in the original work is replaced by a special curve tracing procedure. The advantages of the new approach are presented on several test examples that arise in practical applications.

MATHICSE2015

Constraint consistency techniques for continuous domains

Jamila Sam

EPFL1995