The hardest random SAT problems:
Abstract: "We describe a detailed experimental investigation of the phase transition for several different classes of satisfiability problems including random k-SAT, the constant probability model, and encodings of k-colourability and the independent set problem. We show that the conventional p...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Edinburgh
1994
|
| Schriftenreihe: | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper
680 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We describe a detailed experimental investigation of the phase transition for several different classes of satisfiability problems including random k-SAT, the constant probability model, and encodings of k-colourability and the independent set problem. We show that the conventional picture of easy-hard-easy behaviour is inadequate. In each of the problem classes, although median problem difficulty shows an easy-hard-easy pattern, there is also a region of very variable problem difficulty. Within this region, we have found problems [sic] orders of magnitude harder than those in the middle of the phase transition. These extraordinary problems can easily dominate the mean problem difficulty We report experimental evidence which strongly suggests that this behaviour is due to a 'constraint gap,' a region where the number of constraints on variables is minimal while simultaneously the depth of search required to solve problems is maximal. We also report results suggesting that better algorithms will be unable to eliminate this constraint gap and hence will continue to find very difficult problems in this region. Finally, we report an interesting correlation between these variable regions and a peak in the number of prime implicates. We predict that these extraordinarily hard problems will be of considerable use in analysing and comparing the performance of satisfiability algorithms. |
| Beschreibung: | 12 S. |
Internformat
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| 520 | 3 | |a Abstract: "We describe a detailed experimental investigation of the phase transition for several different classes of satisfiability problems including random k-SAT, the constant probability model, and encodings of k-colourability and the independent set problem. We show that the conventional picture of easy-hard-easy behaviour is inadequate. In each of the problem classes, although median problem difficulty shows an easy-hard-easy pattern, there is also a region of very variable problem difficulty. Within this region, we have found problems [sic] orders of magnitude harder than those in the middle of the phase transition. These extraordinary problems can easily dominate the mean problem difficulty | |
| 520 | 3 | |a We report experimental evidence which strongly suggests that this behaviour is due to a 'constraint gap,' a region where the number of constraints on variables is minimal while simultaneously the depth of search required to solve problems is maximal. We also report results suggesting that better algorithms will be unable to eliminate this constraint gap and hence will continue to find very difficult problems in this region. Finally, we report an interesting correlation between these variable regions and a peak in the number of prime implicates. We predict that these extraordinarily hard problems will be of considerable use in analysing and comparing the performance of satisfiability algorithms. | |
| 650 | 7 | |a Bionics and artificial intelligence |2 sigle | |
| 650 | 7 | |a Mathematics |2 sigle | |
| 650 | 4 | |a Künstliche Intelligenz | |
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| 650 | 4 | |a Artificial intelligence | |
| 700 | 1 | |a Walsh, Toby |e Verfasser |4 aut | |
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Datensatz im Suchindex
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| id | DE-604.BV010466726 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:53:00Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006974668 |
| oclc_num | 31445725 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 12 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| record_format | marc |
| series2 | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |
| spelling | Gent, Ian P. Verfasser aut The hardest random SAT problems Edinburgh 1994 12 S. txt rdacontent n rdamedia nc rdacarrier University <Edinburgh> / Department of Artificial Intelligence: DAI research paper 680 Abstract: "We describe a detailed experimental investigation of the phase transition for several different classes of satisfiability problems including random k-SAT, the constant probability model, and encodings of k-colourability and the independent set problem. We show that the conventional picture of easy-hard-easy behaviour is inadequate. In each of the problem classes, although median problem difficulty shows an easy-hard-easy pattern, there is also a region of very variable problem difficulty. Within this region, we have found problems [sic] orders of magnitude harder than those in the middle of the phase transition. These extraordinary problems can easily dominate the mean problem difficulty We report experimental evidence which strongly suggests that this behaviour is due to a 'constraint gap,' a region where the number of constraints on variables is minimal while simultaneously the depth of search required to solve problems is maximal. We also report results suggesting that better algorithms will be unable to eliminate this constraint gap and hence will continue to find very difficult problems in this region. Finally, we report an interesting correlation between these variable regions and a peak in the number of prime implicates. We predict that these extraordinarily hard problems will be of considerable use in analysing and comparing the performance of satisfiability algorithms. Bionics and artificial intelligence sigle Mathematics sigle Künstliche Intelligenz Mathematik Artificial intelligence Walsh, Toby Verfasser aut Department of Artificial Intelligence: DAI research paper University <Edinburgh> 680 (DE-604)BV010450646 680 |
| spellingShingle | Gent, Ian P. Walsh, Toby The hardest random SAT problems Bionics and artificial intelligence sigle Mathematics sigle Künstliche Intelligenz Mathematik Artificial intelligence |
| title | The hardest random SAT problems |
| title_auth | The hardest random SAT problems |
| title_exact_search | The hardest random SAT problems |
| title_full | The hardest random SAT problems |
| title_fullStr | The hardest random SAT problems |
| title_full_unstemmed | The hardest random SAT problems |
| title_short | The hardest random SAT problems |
| title_sort | the hardest random sat problems |
| topic | Bionics and artificial intelligence sigle Mathematics sigle Künstliche Intelligenz Mathematik Artificial intelligence |
| topic_facet | Bionics and artificial intelligence Mathematics Künstliche Intelligenz Mathematik Artificial intelligence |
| volume_link | (DE-604)BV010450646 |
| work_keys_str_mv | AT gentianp thehardestrandomsatproblems AT walshtoby thehardestrandomsatproblems |