Freuder, E., and Elfe, C. 1996. Neighborhood Inverse Consistency Preprocessing. In Proc. of the 13th National Conference on Artificial Intelligence (AAAI-96), 202--208.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....iff it is node consistent, arc consistent, and path consistent. A problem is path inverse consistent (PIC) iff it is (1, 2) consistent. A problem is neighbourhood inverse consistent (NIC) iff any value for a variable can be extended to a consistent instantiation for its immediate neighbourhood [10]. A problem is restricted path consistent (RPC) iff it is arc consistent and if a value assigned to a variable is consistent with just a single value for an adjoining variable then for any other variable there exists a value compatible with these instantiations. A problem is singleton ....

....one problem in which B holds but A does not. We call a local consistency property A incomparable with B (A # B)iffA is not stronger than B nor vice versa. Finally, we call a local consistency property A equivalent to B iff A # B and B # A. The following identities summarize results from [5] and [10]: strong PC SAC PIC RPC AC, NIC PIC, NIC # SAC, and NIC # strong PC. Many algorithms enforce a certain level of consistency at every node in a search tree. For example, the forward checking algorithm (FC) maintains a restricted form of AC that ensures that the most recently ....

E. Freuder, C.D. Elfe, Neighborhood inverse consistency preprocessing, in: Proc. AAAI-96, Portland, OR, 1996, pp. 202--208.

....This can be expensive if k is great, the algorithm having to look for k 1 supports for each value on each constraint. Unconditionally looking for a path consistent support avoids this costly extra work. k inverse consistency The aim of Freuder and Elfe when they proposed inverse consistency (Freuder Elfe, 1996) was to achieve high order local consistencies with a good space complexity. A k consistency algorithm removes the instantiation of length k 1 that cannot 208 Domain Filtering Consistencies be extended to any k th variable. It requires O(n k 1 d k 1 ) space to keep track of the deleted ....

....to small values of k. Path inverse consistency The first level of k inverse consistency removing more values than AC is path inverse consistency (PIC, k = 3) By definition, i, a) is path inverse consistent if it can be extended to all the 3 tuples of variables containing i. However, as said in (Freuder Elfe, 1996), not all the 3 tuples need to be checked to enforce PIC. Only one of the tuples (i, j, k) and (i, k, j) has to be checked. Moreover, if i is linked to neither j nor k, i, a) can be deleted because of (i, j, k) only if all the values of j or k are path inverse inconsistent. In such a case, ....

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Freuder, E., & Elfe, C. (1996). Neighborhood inverse consistency preprocessing. In Proceedings of AAAI-96, Portland OR, pp. 202--208.

....This can be expensive if k is great, the algorithm having to look for k 1 supports for each value on each constraint. Unconditionally looking for a path consistent support avoids this costly extra work. k inverse consistency The aim of Freuder and Elfe when they proposed inverse consistency (Freuder Elfe, 1996) was to achieve high order local consistencies with a good space complexity. A k consistency algorithm removes the instantiation of length k 1 that cannot 208 Domain Filtering Consistencies be extended to any k th variable. It requires O(n k Gamma1 d k Gamma1 ) space to keep track of the ....

....to small values of k. Path inverse consistency The first level of k inverse consistency removing more values than AC is path inverse consistency (PIC, k = 3) By definition, i; a) is path inverse consistent if it can be extended to all the 3 tuples of variables containing i. However, as said in (Freuder Elfe, 1996), not all the 3 tuples need to be checked to enforce PIC. Only one of the tuples (i; j; k) and (i; k; j) has to be checked. Moreover, if i is linked to neither j nor k, i; a) can be deleted because of (i; j; k) only if all the values of j or k are path inverse inconsistent. In such a case, ....

[Article contains additional citation context not shown here]

Freuder, E., & Elfe, C. (1996). Neighborhood inverse consistency preprocessing. In Proceedings of AAAI-96, Portland OR, pp. 202--208.

....2. This kind of behavior multiplies. On backtrack we can pass back a shorter conflict, and this in turn can pass back shorter conflicts and generate better backtracks at the higher levels. Another feature of CFFC is its ability to detect and prune values that have become i inverse inconsistent [14] for arbitrary i. Thus, CFFC has the potential to achieve exponential savings over an algorithm that continually enforces k inverse consistency on the values of the future variables for any fixed k. However an algorithm that enforces k inverse consistency does the work required to discover all ....

E. Freuder and C. D. Elfe. Neighborhood inverse consistency preprocessing. In Proceedings of the AAAI National Conference, pages 202--208, 1996.

....A problem is strong pathconsistent i it is strong (2; 1) consistent. A problem is path inverse consistent (PIC) i it is (1; 2) consistent. A problem is neighbourhood inverse consistent (NIC) i any value for a variable can be extended to a consistent instantiation for its immediate neighbourhood [FE96]. A problem is restricted path consistent (RPC) i it is arc consistent and if a variable assigned to a value is consistent with just a single value for an adjoining variable then for any other variable there exists a value compatible with these instantiations. A problem is singleton ....

E. Freuder and C.D. Elfe. Neighborhood inverse consistency preprocessing. In Proceedings of the 12th National Conference on AI, pages 202-208. American Association for Articial Intelligence, 1996.

.... Starting from these observations, more attention has been recently turned to inverse local consistency levels, such as path inverse consistency, k inverse consistency, neighborhood inverse consistency, restricted path consistency, max restricted path consistency or singleton arc consistency (Freuder Elfe 1996; Debruyne Bessiere 1997a) which do not suffer from all the drawbacks of the previous local consistency levels. Informally speaking, for all these levels but the last three, inverse local consistency enforcing removes from the domain of a variable v the values that cannot be consistently ....

.... considers the sub instance P 0 involving the set v(c) of variables linked by c and the constraint c itself; it requires that each variable in v(c) be viable in P 0 ; then, def ac ( V; C) f( v(c) fcg) v(c) c 2 Cg; ffl For each variable v 2 V , neighborhood inverse consistency (nic) (Freuder Elfe 1996) considers the subinstance P 0 involving the set lv(v) of variables directly linked to v and the set clv(v) of constraints linking these variables 2 ; it requires that v be viable in P 0 ; then, def nic ( V; C) f( lv(v) clv(v) fvg) v 2 V g; ffl Global consistency (gc) Freuder 1991; ....

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Freuder, E., and Elfe, C. 1996. Neighborhood Inverse Consistency Preprocessing. In Proc. of the 13th National Conference on Artificial Intelligence (AAAI-96), 202--208.

....is strong path consistent iff it is (j; 1) consistent for j 2. A problem is path inverse consistent (PIC) iff it is (1; 2) consistent. A problem is neighbourhood inverse consistent (NIC) iff any value for a variable can be extended to a consistent instantiation for its immediate neighbourhood [9]. A problem is restricted path consistent (RPC) iff it is arc consistent and if a variable assigned to a value is consistent with just a single value for an adjoining variable then for any other variable there exists a value compatible with these instantiations. A problem is singleton ....

E. Freuder and C.D. Elfe. Neighborhood inverse consistency preprocessing. In Proceedings of AAAI-96, pages 202--208.

....the domain V 0 such that the assignments V v and V 0 v 0 are consistent. MAC removes any values v that fail to satisfy this condition. Using this idea we can define MIkC maintaining inverse k consistency. Inverse k consistency first appeared in [Fre85] and was explored more fully in [FE96]. Definition 3.8 For any k N , where N is the number of variables in the CSP, the MIkC algorithm is a tree search algorithm that backtracks when a DWO is detected. After every new instantiation MIkC performs FC constraint propagation, furthermore it removes all values v from the domain all ....

E. Freuder and C. D. Elfe. Neighborhood inverse consistency preprocessing. In Proceedings of the AAAI National Conference, pages 202--208, 1996.

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E.C. Freuder and C.D. Elfe. Neighborhood inverse consistency preprocessing. In Proceedings AAAI'96, pages 202--208, Portland OR, 1996. 58

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Freuder, E., and Elfe, C. 1996. Neighborhood Inverse Consistency Preprocessing. In Proc. of the 13th National Conference on Artificial Intelligence (AAAI-96), 202--208.

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E. Freuder and C.D. Elfe. Neighborhood inverse consistency preprocessing. In Proceedings of AAAI-96, pages 202--208.

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E. Freuder and C.D. Elfe. Neighborhood inverse consistency preprocessing. In for Artificial Intelligence, 1996.

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E. Freuder, C.D. Elfe, Neighborhood inverse consistency preprocessing, in: Proc. AAAI-96, Portland, OR, 1996, pp. 202--208.

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E. Freuder and C.D. Elfe. Neighborhood inverse consistency preprocessing. In for Artificial Intelligence, 1996.

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E. Freuder and C.D. Elfe. Neighborhood inverse consistency preprocessing. In Proceedings of the National Conference on Arti cial Intelligence (AAAI-96), pages 202-208, 1996. 164

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E.C. Freuder & C.D. Elfe, Neighborhood Inverse Consistency Preprocessing, Proc. AAAI/IAAI, Vol. 1, 202--208, 1996.

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