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Hidden Transformation
The hidden transformation reformulates a constraint satisfaction problem in such a way all constraints have at most two variables. The new problem is satisfiable if and only if the original problem was, and solutions can be converted easily from one problem to the other. There are a number of algorithms for constraint satisfaction that work only on constraints that have at most two variables. If a problem has constraints with a larger arity (number of variables), conversion into a problem made of binary constraints allows for execution of these solving algorithms. Constraints with one, two, or more variables are called unary, binary, or ''higher-order'' constraints. The number of variables in a constraint is called its ''arity''. The hidden transformation converts an arbitrary constraint satisfaction problem into a binary one. The transformation is similar to that generating the dual problem. The problem is added new variables, one for each constraint of the original problem. The d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Satisfaction Problem
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, Boolean satisfiability problem (SAT), the satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Satisfaction Dual Problem
The dual problem is a reformulation of a constraint satisfaction problem expressing each constraint of the original problem as a variable. Dual problems only contain binary constraints, and are therefore solvable by algorithms tailored for such problems. The join graphs and join trees of a constraint satisfaction problem are graphs representing its dual problem or a problem obtained from the dual problem removing some redundant constraints. The dual problem The dual problem of a constraint satisfaction problem contains a variable for each constraint of the original problem. Its domains and constraints are built so to enforce a sort of equivalence to the original problem. In particular, the domain of a variable of the dual problem contains one element for each tuple satisfying the corresponding original constraint. This way, a dual variable can take a value if and only if the corresponding original constraint is satisfied by the corresponding tuple. The constraints of the dual probl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipartite Graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets U and V may be thought of as a coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V red, each edge has endpoints of differing colors, as is required in the graph coloring problem.. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another red, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color. One often writes G=(U,V,E) to denote a bipartite graph whose partition has the parts U and V, with E denoting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fahiem Bacchus
Fahiem Bacchus (March 16, 1957 - September 22, 2022) was a Canadian professor of computer science at the University of Toronto and a fellow of the Association for the Advancement of Artificial Intelligence (2006). Early life and career Fahiem Bacchus was born in 1957. In 1979 he graduated with a Bachelor of Science degree in computer science from the University of Alberta. After working in industry for a couple of years he returned to academic pursuits and in 1983 received a Master of Science degree in mathematics from the University of Toronto. A year later he returned to the University of Alberta and graduated from there with a Ph.D. in computer science in 1988. Immediately after graduation he became a postdoc at the University of Rochester and in July of the same year he became an assistant professor at the University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario Waterloo is a ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
