Encoding cardinality constraints using multiway merge selection networks
Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been...
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| Autor*in: |
Karpiński, Michał [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Constraints - Springer US, 1996, 24(2019), 3-4 vom: 05. Apr., Seite 234-251 |
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| Übergeordnetes Werk: |
volume:24 ; year:2019 ; number:3-4 ; day:05 ; month:04 ; pages:234-251 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10601-019-09302-0 |
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| 520 | |a Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. | ||
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10.1007/s10601-019-09302-0 doi (DE-627)OLC2027270256 (DE-He213)s10601-019-09302-0-p DE-627 ger DE-627 rakwb eng 004 VZ Karpiński, Michał verfasserin (orcid)0000-0002-4190-3033 aut Encoding cardinality constraints using multiway merge selection networks 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. Cardinality constraint Selection network SAT-solver SAT encoding SAT translation Piotrów, Marek aut Enthalten in Constraints Springer US, 1996 24(2019), 3-4 vom: 05. Apr., Seite 234-251 (DE-627)230798985 (DE-600)1388291-0 (DE-576)060397772 1383-7133 nnns volume:24 year:2019 number:3-4 day:05 month:04 pages:234-251 https://doi.org/10.1007/s10601-019-09302-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 AR 24 2019 3-4 05 04 234-251 |
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10.1007/s10601-019-09302-0 doi (DE-627)OLC2027270256 (DE-He213)s10601-019-09302-0-p DE-627 ger DE-627 rakwb eng 004 VZ Karpiński, Michał verfasserin (orcid)0000-0002-4190-3033 aut Encoding cardinality constraints using multiway merge selection networks 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. Cardinality constraint Selection network SAT-solver SAT encoding SAT translation Piotrów, Marek aut Enthalten in Constraints Springer US, 1996 24(2019), 3-4 vom: 05. Apr., Seite 234-251 (DE-627)230798985 (DE-600)1388291-0 (DE-576)060397772 1383-7133 nnns volume:24 year:2019 number:3-4 day:05 month:04 pages:234-251 https://doi.org/10.1007/s10601-019-09302-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 AR 24 2019 3-4 05 04 234-251 |
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10.1007/s10601-019-09302-0 doi (DE-627)OLC2027270256 (DE-He213)s10601-019-09302-0-p DE-627 ger DE-627 rakwb eng 004 VZ Karpiński, Michał verfasserin (orcid)0000-0002-4190-3033 aut Encoding cardinality constraints using multiway merge selection networks 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. Cardinality constraint Selection network SAT-solver SAT encoding SAT translation Piotrów, Marek aut Enthalten in Constraints Springer US, 1996 24(2019), 3-4 vom: 05. Apr., Seite 234-251 (DE-627)230798985 (DE-600)1388291-0 (DE-576)060397772 1383-7133 nnns volume:24 year:2019 number:3-4 day:05 month:04 pages:234-251 https://doi.org/10.1007/s10601-019-09302-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 AR 24 2019 3-4 05 04 234-251 |
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10.1007/s10601-019-09302-0 doi (DE-627)OLC2027270256 (DE-He213)s10601-019-09302-0-p DE-627 ger DE-627 rakwb eng 004 VZ Karpiński, Michał verfasserin (orcid)0000-0002-4190-3033 aut Encoding cardinality constraints using multiway merge selection networks 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. Cardinality constraint Selection network SAT-solver SAT encoding SAT translation Piotrów, Marek aut Enthalten in Constraints Springer US, 1996 24(2019), 3-4 vom: 05. Apr., Seite 234-251 (DE-627)230798985 (DE-600)1388291-0 (DE-576)060397772 1383-7133 nnns volume:24 year:2019 number:3-4 day:05 month:04 pages:234-251 https://doi.org/10.1007/s10601-019-09302-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 AR 24 2019 3-4 05 04 234-251 |
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10.1007/s10601-019-09302-0 doi (DE-627)OLC2027270256 (DE-He213)s10601-019-09302-0-p DE-627 ger DE-627 rakwb eng 004 VZ Karpiński, Michał verfasserin (orcid)0000-0002-4190-3033 aut Encoding cardinality constraints using multiway merge selection networks 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. Cardinality constraint Selection network SAT-solver SAT encoding SAT translation Piotrów, Marek aut Enthalten in Constraints Springer US, 1996 24(2019), 3-4 vom: 05. Apr., Seite 234-251 (DE-627)230798985 (DE-600)1388291-0 (DE-576)060397772 1383-7133 nnns volume:24 year:2019 number:3-4 day:05 month:04 pages:234-251 https://doi.org/10.1007/s10601-019-09302-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 AR 24 2019 3-4 05 04 234-251 |
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Encoding cardinality constraints using multiway merge selection networks |
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Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. © The Author(s) 2019 |
| abstractGer |
Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. © The Author(s) 2019 |
| abstract_unstemmed |
Abstract Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195–221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1–26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings. © The Author(s) 2019 |
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| title_short |
Encoding cardinality constraints using multiway merge selection networks |
| url |
https://doi.org/10.1007/s10601-019-09302-0 |
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| author2 |
Piotrów, Marek |
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Piotrów, Marek |
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| doi_str |
10.1007/s10601-019-09302-0 |
| up_date |
2024-07-03T14:41:59.331Z |
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