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Backjumping
In backtracking algorithms, backjumping is a technique that reduces search space, therefore increasing efficiency. While backtracking always goes up one level in the search tree when all values for a variable have been tested, backjumping may go up more levels. In this article, a fixed order of evaluation of variables x_1,\ldots,x_n is used, but the same considerations apply to a dynamic order of evaluation. Image:Backtracking-no-backjumping.svg, A search tree visited by regular backtracking Image:Backtracking-with-backjumping.svg, A backjump: the grey node is not visited Definition Whenever backtracking has tried all values for a variable without finding any solution, it reconsiders the last of the previously assigned variables, changing its value or further backtracking if no other values are to be tried. If x_1=a_1,\ldots,x_k=a_k is the current partial assignment and all values for x_ have been tried without finding a solution, backtracking concludes that no solution extendin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patrick Prosser
Patrick Prosser (born 8 September 1952) is a Computer Scientist who spent the bulk of his career at the University of Glasgow , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , .... His research has centred on constraint programming, although it has extended into the application of those techniques into other areas. For his major contributions to the theory and practice of constraint programming, Patrick was awarded the Association for Constraint Programming's Research Excellence Award on 15 September 2011: he is only the sixth recipient of this award. He gave a prerecorded acceptance speech, which is available on YouTube. His most notable contribution is his invention of conflict-directed backjumping, an advanced technique for reducing search in constraint problems by avoiding un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backtracking
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Learning
In constraint satisfaction backtracking algorithms, constraint learning is a technique for improving efficiency. It works by recording new constraints whenever an inconsistency is found. This new constraint may reduce the search space, as future partial evaluations may be found inconsistent without further search. Clause learning is the name of this technique when applied to propositional satisfiability. Definition Backtracking algorithms work by choosing an unassigned variable and recursively Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ... solve the problems obtained by assigning a value to this variable. Whenever the current partial solution is found inconsistent, the algorithm goes back to the previously assigned variable, as expected by recursion. A constraint learning algor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backtracking
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Satisfaction Problems
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 focusing ... [...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] |
