General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs
Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Jonsson, Peter [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Algorithmica - New York, NY : Springer, 1986, 85(2022), 1 vom: 11. Aug., Seite 188-215 |
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| Übergeordnetes Werk: |
volume:85 ; year:2022 ; number:1 ; day:11 ; month:08 ; pages:188-215 |
| Links: |
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| DOI / URN: |
10.1007/s00453-022-01017-8 |
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| Katalog-ID: |
SPR049081950 |
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| 100 | 1 | |a Jonsson, Peter |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs |
| 264 | 1 | |c 2022 | |
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| 520 | |a Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. | ||
| 650 | 4 | |a Constraint satisfaction |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Infinite domains |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Equality languages |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Fine-grained complexity |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Lower bounds |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Lagerkvist, Victor |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Algorithmica |d New York, NY : Springer, 1986 |g 85(2022), 1 vom: 11. Aug., Seite 188-215 |w (DE-627)253389704 |w (DE-600)1458414-1 |x 1432-0541 |7 nnns |
| 773 | 1 | 8 | |g volume:85 |g year:2022 |g number:1 |g day:11 |g month:08 |g pages:188-215 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00453-022-01017-8 |z kostenfrei |3 Volltext |
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10.1007/s00453-022-01017-8 doi (DE-627)SPR049081950 (SPR)s00453-022-01017-8-e DE-627 ger DE-627 rakwb eng Jonsson, Peter verfasserin aut General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. Constraint satisfaction (dpeaa)DE-He213 Infinite domains (dpeaa)DE-He213 Equality languages (dpeaa)DE-He213 Fine-grained complexity (dpeaa)DE-He213 Lower bounds (dpeaa)DE-He213 Lagerkvist, Victor aut Enthalten in Algorithmica New York, NY : Springer, 1986 85(2022), 1 vom: 11. Aug., Seite 188-215 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:85 year:2022 number:1 day:11 month:08 pages:188-215 https://dx.doi.org/10.1007/s00453-022-01017-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 85 2022 1 11 08 188-215 |
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10.1007/s00453-022-01017-8 doi (DE-627)SPR049081950 (SPR)s00453-022-01017-8-e DE-627 ger DE-627 rakwb eng Jonsson, Peter verfasserin aut General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. Constraint satisfaction (dpeaa)DE-He213 Infinite domains (dpeaa)DE-He213 Equality languages (dpeaa)DE-He213 Fine-grained complexity (dpeaa)DE-He213 Lower bounds (dpeaa)DE-He213 Lagerkvist, Victor aut Enthalten in Algorithmica New York, NY : Springer, 1986 85(2022), 1 vom: 11. Aug., Seite 188-215 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:85 year:2022 number:1 day:11 month:08 pages:188-215 https://dx.doi.org/10.1007/s00453-022-01017-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 85 2022 1 11 08 188-215 |
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10.1007/s00453-022-01017-8 doi (DE-627)SPR049081950 (SPR)s00453-022-01017-8-e DE-627 ger DE-627 rakwb eng Jonsson, Peter verfasserin aut General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. Constraint satisfaction (dpeaa)DE-He213 Infinite domains (dpeaa)DE-He213 Equality languages (dpeaa)DE-He213 Fine-grained complexity (dpeaa)DE-He213 Lower bounds (dpeaa)DE-He213 Lagerkvist, Victor aut Enthalten in Algorithmica New York, NY : Springer, 1986 85(2022), 1 vom: 11. Aug., Seite 188-215 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:85 year:2022 number:1 day:11 month:08 pages:188-215 https://dx.doi.org/10.1007/s00453-022-01017-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 85 2022 1 11 08 188-215 |
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10.1007/s00453-022-01017-8 doi (DE-627)SPR049081950 (SPR)s00453-022-01017-8-e DE-627 ger DE-627 rakwb eng Jonsson, Peter verfasserin aut General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. Constraint satisfaction (dpeaa)DE-He213 Infinite domains (dpeaa)DE-He213 Equality languages (dpeaa)DE-He213 Fine-grained complexity (dpeaa)DE-He213 Lower bounds (dpeaa)DE-He213 Lagerkvist, Victor aut Enthalten in Algorithmica New York, NY : Springer, 1986 85(2022), 1 vom: 11. Aug., Seite 188-215 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:85 year:2022 number:1 day:11 month:08 pages:188-215 https://dx.doi.org/10.1007/s00453-022-01017-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 85 2022 1 11 08 188-215 |
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10.1007/s00453-022-01017-8 doi (DE-627)SPR049081950 (SPR)s00453-022-01017-8-e DE-627 ger DE-627 rakwb eng Jonsson, Peter verfasserin aut General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. Constraint satisfaction (dpeaa)DE-He213 Infinite domains (dpeaa)DE-He213 Equality languages (dpeaa)DE-He213 Fine-grained complexity (dpeaa)DE-He213 Lower bounds (dpeaa)DE-He213 Lagerkvist, Victor aut Enthalten in Algorithmica New York, NY : Springer, 1986 85(2022), 1 vom: 11. Aug., Seite 188-215 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:85 year:2022 number:1 day:11 month:08 pages:188-215 https://dx.doi.org/10.1007/s00453-022-01017-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 85 2022 1 11 08 188-215 |
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Jonsson, Peter @@aut@@ Lagerkvist, Victor @@aut@@ |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR049081950</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230510060920.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230119s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00453-022-01017-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR049081950</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00453-022-01017-8-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jonsson, Peter</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Constraint satisfaction</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Infinite domains</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Equality languages</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fine-grained complexity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lower bounds</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lagerkvist, Victor</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Algorithmica</subfield><subfield code="d">New York, NY : Springer, 1986</subfield><subfield code="g">85(2022), 1 vom: 11. 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Jonsson, Peter |
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General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs Constraint satisfaction (dpeaa)DE-He213 Infinite domains (dpeaa)DE-He213 Equality languages (dpeaa)DE-He213 Fine-grained complexity (dpeaa)DE-He213 Lower bounds (dpeaa)DE-He213 |
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general lower bounds and improved algorithms for infinite–domain csps |
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General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs |
| abstract |
Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. © The Author(s) 2022 |
| abstractGer |
Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. © The Author(s) 2022 |
| abstract_unstemmed |
Abstract We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations over a relational structure (possibly containing more than just equality). We prove that under the randomised exponential-time hypothesis it is not possible to find %$c > 1%$ such that a CSP over an arbitrary finite equality language is solvable in %$O(c^n)%$ time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of %$2^{o(n \log n)}%$ time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each %$c > 1%$ there exists an NP-hard equality CSP solvable in %$O(c^n)%$ time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in %$O(c^n)%$ time for a fixed c, and manage to extend this algorithm to the much broader class of CSPs where constraints are formed by first-order formulas over a unary structure. © The Author(s) 2022 |
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| title_short |
General Lower Bounds and Improved Algorithms for Infinite–Domain CSPs |
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https://dx.doi.org/10.1007/s00453-022-01017-8 |
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| author2 |
Lagerkvist, Victor |
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| doi_str |
10.1007/s00453-022-01017-8 |
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2024-07-03T23:12:22.947Z |
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| score |
7.4024897 |