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PW-1
science fiction / inspirational PW-1 is the incredible story of Ralph Diamond who lives with his wife Tina, on a 40-acre ranch in the mountains of central California. While enjoying a ride on his ATV, he spots a large translucent elliptical shaped object resting on his property. When fear turns to excitement and curiosity, he investigates and to his amazement finds himself inside a UFO with five alien beings who have been stranded on Earth for six days. Their ship has lost all main power, and their auxiliary power is rapidly depleting. Coming to Earth simply to observe our society, they are now practically in a state of panic as to what fate awaits them if they are discovered on such a primi...
Tractability
An overview of the techniques developed to circumvent computational intractability, a key challenge in many areas of computer science.
Fundamental Computational Problems and Algorithms for SuperHyperGraphs
Hypergraphs extend traditional graphs by allowing edges (known as hyperedges) to connect more than two vertices, rather than just pairs. This paper explores fundamental problems and algorithms in the context of SuperHypergraphs, an advanced extension of hypergraphs enabling modeling of hierarchical and complex relationships. Topics covered include constructing SuperHyperGraphs, recognizing SuperHyperTrees, and computing SuperHyperTree-width. We address a range of optimization problems, such as the SuperHy-pergraph Partition Problem, Reachability, Minimum Spanning SuperHypertree, and Single-Source Shortest Path. Furthermore, adaptations of classical problems like the Traveling Salesman Problem, Chinese Postman Problem, and Longest Simple Path Problem are presented in the SuperHypergraph framework.
Finite Model Theory and Its Applications
Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical log...
The Complexity of Valued Constraint Satisfaction Problems
The topic of this book is the following optimisation problem: given a set of discrete variables and a set of functions, each depending on a subset of the variables, minimise the sum of the functions over all variables. This fundamental research problem has been studied within several different contexts of discrete mathematics, computer science and artificial intelligence under different names: Min-Sum problems, MAP inference in Markov random fields (MRFs) and conditional random fields (CRFs), Gibbs energy minimisation, valued constraint satisfaction problems (VCSPs), and, for two-state variables, pseudo-Boolean optimisation. In this book the author presents general techniques for analysing t...
Elements of Finite Model Theory
Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.
