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- W1522668611 abstract "We establish optimal bounds on the number of nested propagation steps in k-consistency tests. It is known that local consistency algorithms such as arc-, path- and k-consistency are not efficiently parallelizable. Their inherent sequential nature is caused by long chains of nested propagation steps, which cannot be executed in parallel. This motivates the question “What is the minimum number of nested propagation steps that have to be performed by k-consistency algorithms on (binary) constraint networks with n variables and domain size d?” It was known before that 2-consistency requires Ω(nd) and 3-consistency requires Ω(n 2) sequential propagation steps. We answer the question exhaustively for every k ≥ 2: there are binary constraint networks where any k-consistency procedure has to perform Ω(n k − 1 d k − 1) nested propagation steps before local inconsistencies were detected. This bound is tight, because the overall number of propagation steps performed by k-consistency is at most n k − 1 d k − 1." @default.
- W1522668611 created "2016-06-24" @default.
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- W1522668611 date "2014-01-01" @default.
- W1522668611 modified "2023-10-17" @default.
- W1522668611 title "The Propagation Depth of Local Consistency" @default.
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- W1522668611 doi "https://doi.org/10.1007/978-3-319-10428-7_14" @default.
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