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Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 76 (5 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
AC3_d an Efficient ArcConsistency Algorithm with a Low SpaceComplexity
, 2002
"... Arcconsistency algorithms prune the searchspace of Constraint Satisfaction Problems (CSPs). They use supportchecks to find out about the properties of CSPs. Their archeuristics select the constraint and their domainheuristics select the values for the next supportcheck. We shall combine AC3 a ..."
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Cited by 15 (6 self)
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Arcconsistency algorithms prune the searchspace of Constraint Satisfaction Problems (CSPs). They use supportchecks to find out about the properties of CSPs. Their archeuristics select the constraint and their domainheuristics select the values for the next supportcheck. We shall combine AC3 and DEE and equip the resulting hybrid with a doublesupport domainheuristic. The resulting hybrid AC3_d is easy to implement and requires the same data structures as AC3 thereby improving on AC7's spacecomplexity. We shall present experimental results which indicate that AC3_d can compete with AC7.
Lightweight ArcConsistency Algorithms
, 2003
"... Arcconsistency algorithms are the workhorse of many backtrack algorithms. Most research on arcconsistency algorithms is focusing on the design of algorithms that are optimal when it comes to worst case scenarios. This report will provide experimental evidence that, despite common belief to the con ..."
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Cited by 6 (2 self)
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Arcconsistency algorithms are the workhorse of many backtrack algorithms. Most research on arcconsistency algorithms is focusing on the design of algorithms that are optimal when it comes to worst case scenarios. This report will provide experimental evidence that, despite common belief to the contrary, the ability to deal efficiently with such worst case scenarios may not be a prerequisite for solving quickly. It will compare on the one hand AC2001 , which has an optimal worst case timecomplexity and is considered efficient, and on the other AC3 d , which is not optimal when it comes to its worst case timecomplexity, but which has a better spacecomplexity than AC2001. Both algorithms will be compared for MAC search and for stand alone arcconsistency (the task of making a single CSP arcconsistent). For stand alone arcconsistency AC3 d is the better algorithm when it comes to time but there is no clear winner when it comes to minimising the number of checks. For search the results are more interesting. MAC2001 is by far the better algorithm when it comes to minimising the number of checks. However, MAC3 d is considerably faster on average. For difficult random problems, that took between minutes and 1.5 hour to solve, MAC3 d was about 1.5 times faster on average than MAC2001. As soon as MAC2001 starts to become successful in avoiding the duplication of many checks it begins to invest much more additional solution time. These observations suggest that being worst case optimal may come at a price of being less efficient on average in search and that algorithms like MAC3 d are promising. Contents 1
Lightweight MAC Algorithms
, 2003
"... Arcconsistency algorithms are the workhorse of backtrackers that Maintain ArcConsistency (MAC). This report will provide experimental evidence that, despite common belief to the contrary, it is not always necessary for a good arcconsistency algorithm to have an optimal worst case timecomplexity. ..."
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Cited by 3 (1 self)
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Arcconsistency algorithms are the workhorse of backtrackers that Maintain ArcConsistency (MAC). This report will provide experimental evidence that, despite common belief to the contrary, it is not always necessary for a good arcconsistency algorithm to have an optimal worst case timecomplexity. To sacrifice this optimality allows MAC solvers that (1) do not need additional data structures during search, (2) have an excellent average timecomplexity, and (3) have a spacecomplexity which improves significantly on that of MAC solvers that have optimal arcconsistency components. Results will be presented from an experimental comparison between MAC2001, MAC3 d and related algorithms. MAC2001 has an arcconsistency component with an optimal worst case timecomplexity, whereas MAC3 d does not. MAC2001 requires additional data structures during search, whereas MAC3 d does not. MAC3 d has a spacecomplexity of O(e + nd), where n is the number of variables, d the maximum domain size, and e the number of constraints. We shall demonstrate that MAC2001's spacecomplexity is O(ed min(n; d)). MAC2001 required about 35% more solution time on average than MAC3 d for easy and hard random problems. MAC3 d recorded the least solution time for 21 of the 25 realworld problems. Our results indicate that if checks are cheap then lightweight algorithms like MAC3 d are promising.
A Theoretical Analysis of DomainHeuristics for ArcConsistency Algorithms
, 2000
"... Arcconsistency algorithms are widely used to prune the searchspace of constraint satisfaction problems (CSPs). Arcconsistency algorithms require supportchecks to find out about the properties of CSPs. They use two kinds of heuristics to select their next supportcheck. The first kind operates at ..."
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Arcconsistency algorithms are widely used to prune the searchspace of constraint satisfaction problems (CSPs). Arcconsistency algorithms require supportchecks to find out about the properties of CSPs. They use two kinds of heuristics to select their next supportcheck. The first kind operates at arclevel and selects the constraint that will be used for the next check. The second kind operates at domainlevel and decides which values will be used for the next check. It is our intention to investigate the effect of domainheuristics by studying the average timecomplexity of two arcconsistency algorithms which only differ in the domainheuristics they use. We will assume that there are only two variables. We will discuss the consequences of this simplification. The first algorithm, called L, uses a lexicographical heuristic. The second algorithm, called D, uses a heuristic based on the notion of a doublesupport check. We present a detailed case study and present three good reasons why arcconsistency algorithms should give preference to doublesupport checks at domainlevel. For sufficiently large domainsizes a and b our average timecomplexity analysis provides
A Theoretical Analysis of DomainHeuristics for ArcConsistency Algorithms
, 2000
"... Arcconsistency algorithms are widely used to prune the searchspace of constraint satisfaction problems (CSPs). Arcconsistency algorithms require supportchecks to find out about the properties of CSPs. They use two kinds of heuristics to select their next supportcheck. The first kind operates at ..."
Abstract
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Arcconsistency algorithms are widely used to prune the searchspace of constraint satisfaction problems (CSPs). Arcconsistency algorithms require supportchecks to find out about the properties of CSPs. They use two kinds of heuristics to select their next supportcheck. The first kind operates at arclevel and selects the constraint that will be used for the next check. The second kind operates at domainlevel and decides which values will be used for the next check.