## The impact of branching heuristics in propositional satisfiability algorithms (1999)

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Venue: | In 9th Portuguese Conference on Artificial Intelligence (EPIA |

Citations: | 42 - 1 self |

### BibTeX

@INPROCEEDINGS{Marques-silva99theimpact,

author = {João Marques-silva},

title = {The impact of branching heuristics in propositional satisfiability algorithms},

booktitle = {In 9th Portuguese Conference on Artificial Intelligence (EPIA},

year = {1999},

pages = {62--74}

}

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### Abstract

Abstract. This paper studies the practical impact of the branching heuristics used in Propositional Satisfiability (SAT) algorithms, when applied to solving real-world instances of SAT. In addition, different SAT algorithms are experimentally evaluated. The main conclusion of this study is that even though branching heuristics are crucial for solving SAT, other aspects of the organization of SAT algorithms are also essential. Moreover, we provide empirical evidence that for practical instances of SAT, the search pruning techniques included in the most competitive SAT algorithms may be of more fundamental significance than branching heuristics.

### Citations

1075 |
A computing procedure for quantification theory
- Davis, Putnam
- 1960
(Show Context)
Citation Context ...of the clauses of CNF formula ϕ. In the following sections we shall address backtrack search algorithms for SAT. Most if not all backtrack search SAT algorithms apply extensively the unit clause rule =-=[6]-=-. If a clause is unit, then the sole free literal must be assigned value 63s64 J. Marques-Silva 1 for the formula to be satisfiable. The iterated application of the unit clause rule is often referred ... |

680 | A New Method for Solving Hard Satisfiability Problems
- Selman, Levesque, et al.
- 1992
(Show Context)
Citation Context ...rovements in the real world performance of SAT algorithms. On one hand, local search algorithms have been used for solving large random instances of SAT and some classes of practical instances of SAT =-=[21, 20, 15, 7]-=-. On the other hand, systematic backtrack search algorithms, based on new and effective search pruning techniques, have been used for solving large structured real-world instances of SAT, a significan... |

521 | Pushing the envelope: planning, propositional logic and stochastic search
- Kautz, Selman
(Show Context)
Citation Context ...rovements in the real world performance of SAT algorithms. On one hand, local search algorithms have been used for solving large random instances of SAT and some classes of practical instances of SAT =-=[21, 20, 15, 7]-=-. On the other hand, systematic backtrack search algorithms, based on new and effective search pruning techniques, have been used for solving large structured real-world instances of SAT, a significan... |

256 | Test pattern generation using Boolean satisfiability
- Larrabee
(Show Context)
Citation Context ...m the UCSC suite [14]. The number of instances for each class is also shown in the table. Of these classes of instances, bf and ssa represent practical applications of SAT models to Design Automation =-=[16]-=-. The others were proposed by different authors for the 1993 DIMACS Satisfiability Challenge [14]. For the instances considered, we ran rel sat, GRASP, SATO, POSIT and NTAB. While rel sat, GRASP and S... |

242 |
Forward reasoning and dependency-directed backtracking in a system for computer-aided circuit analysis
- Stallman, Sussman
- 1977
(Show Context)
Citation Context ...ularly useful for solving hard real-world instances of SAT. Relevant examples of these techniques are non-chronological backtracking search strategies and clause (nogood) identification and recording =-=[3, 10, 22]-=-. One key aspect of backtrack search SAT algorithms is how assignments are selected at each step of the algorithm, i.e. the branching heuristics. Over the years many branching heuristics have been pro... |

215 | Domain-independent extensions to GSAT: Solving large structured satisfiability problems
- Selman, Kautz
- 1993
(Show Context)
Citation Context ...rovements in the real world performance of SAT algorithms. On one hand, local search algorithms have been used for solving large random instances of SAT and some classes of practical instances of SAT =-=[21, 20, 15, 7]-=-. On the other hand, systematic backtrack search algorithms, based on new and effective search pruning techniques, have been used for solving large structured real-world instances of SAT, a significan... |

201 | Experimental results on the cross-over point in satisfiability problems
- Crawford, Auton
- 1993
(Show Context)
Citation Context ...backtrack search SAT algorithms. There are of course other backtrack search SAT algorithms, which are competitive for specific classes of instances of SAT. Examples include satz [17], POSIT [9], NTAB =-=[5]-=-, 2cl [11] and CSAT [8], among others. It is interesting to note that the most competitive backtrack search SAT algorithms share a few common properties, which have empirically been shown to P. Baraho... |

193 | SATO: An efficient propositional prover
- Zhang
- 1997
(Show Context)
Citation Context ... large structured real-world instances of SAT, a significant fraction of which requires proving unsatisfiability. Among the many existing backtrack search algorithms, rel sat [2], GRASP [18] and SATO =-=[24]-=- have been shown, on a large number of real-world instances of SAT, to be among the most competitive backtrack search SAT algorithms. There are of course other backtrack search SAT algorithms, which a... |

174 | Performance measurement and analysis of certain search algorithms - Gaschnig - 1979 |

160 | Improvements to Propositional Satisfiability Search Algorithms
- Freeman
- 1995
(Show Context)
Citation Context ...mpetitive backtrack search SAT algorithms. There are of course other backtrack search SAT algorithms, which are competitive for specific classes of instances of SAT. Examples include satz [17], POSIT =-=[9]-=-, NTAB [5], 2cl [11] and CSAT [8], among others. It is interesting to note that the most competitive backtrack search SAT algorithms share a few common properties, which have empirically been shown to... |

156 |
Using CSP look-back techniques to solve real-world SAT instances
- Schrag
- 1997
(Show Context)
Citation Context ...ave been used for solving large structured real-world instances of SAT, a significant fraction of which requires proving unsatisfiability. Among the many existing backtrack search algorithms, rel sat =-=[2]-=-, GRASP [18] and SATO [24] have been shown, on a large number of real-world instances of SAT, to be among the most competitive backtrack search SAT algorithms. There are of course other backtrack sear... |

113 |
Solving propositional satisfiability problems
- Jeroslow, Wang
- 1990
(Show Context)
Citation Context ...ck search SAT algorithms is how assignments are selected at each step of the algorithm, i.e. the branching heuristics. Over the years many branching heuristics have been proposed by different authors =-=[5, 9, 13, 17]-=-. In this paper we propose to study several of the branching heuristics that have been shown to be more effective in practice. For this purpose we apply different backtrack search SAT algorithms and d... |

78 | Report on a sat competition
- Buro, Buning
- 1992
(Show Context)
Citation Context ...uld note that additional branching heuristics exist and have been studied in the past. See for example [9, 12, 13] for detailed accounts. 4.1 BOHM’s Heuristic Bohm’s heuristic is briefly described in =-=[4]-=-, where a backtrack search algorithm using this branching heuristic was shown to be the most competitive algorithm (at the time), for solving randomly generated instances of SAT. At each step of the b... |

78 | Branching rules for satisfiability
- Hooker, Vinay
- 1995
(Show Context)
Citation Context ...bed in the approximate chronological order in which they have been applied to solving SAT. We should note that additional branching heuristics exist and have been studied in the past. See for example =-=[9, 12, 13]-=- for detailed accounts. 4.1 BOHM’s Heuristic Bohm’s heuristic is briefly described in [4], where a backtrack search algorithm using this branching heuristic was shown to be the most competitive algori... |

74 | A rearrangement search strategy for determining propositional satisfiability
- Zabih
- 1988
(Show Context)
Citation Context ...iteral must be assigned value 63s64 J. Marques-Silva 1 for the formula to be satisfiable. The iterated application of the unit clause rule is often referred to as Boolean Constraint Propagation (BCP) =-=[23]-=-. For implementing some of the techniques common to some of the most competitive backtrack search algorithms for SAT [2, 18, 24], it is necessary to properly explain the truth assignments to the propo... |

62 | Anbulagan: Look-ahead versus look-back for satisfiability problems
- Li
- 1997
(Show Context)
Citation Context ... the most competitive backtrack search SAT algorithms. There are of course other backtrack search SAT algorithms, which are competitive for specific classes of instances of SAT. Examples include satz =-=[17]-=-, POSIT [9], NTAB [5], 2cl [11] and CSAT [8], among others. It is interesting to note that the most competitive backtrack search SAT algorithms share a few common properties, which have empirically be... |

57 | A computing procedure for quanti theory - Davis, Putnam - 1960 |

51 | Satisfiability testing with more reasoning and less guessing
- Gelder, Tsuji
(Show Context)
Citation Context ... search SAT algorithms. There are of course other backtrack search SAT algorithms, which are competitive for specific classes of instances of SAT. Examples include satz [17], POSIT [9], NTAB [5], 2cl =-=[11]-=- and CSAT [8], among others. It is interesting to note that the most competitive backtrack search SAT algorithms share a few common properties, which have empirically been shown to P. Barahona and J.J... |

45 | A new method to solve hard satis problems - Selman, Levesque, et al. - 1992 |

39 | SATO: An ecient propositional prover - Zhang - 1997 |

31 |
Efficiency and stability of hypergraph SAT algorithms
- PRETOLANI
- 1996
(Show Context)
Citation Context ...n [4] the values suggested are α = 1 and β =2. 4.2 MOM’s Heuristic One of the most well-known and utilized branching heuristics is the Maximum Occurrences on clauses of Minimum size (MOM’s) heuristic =-=[8, 9, 19, 23]-=-. Let f ∗ (l) be the number of occurrences of a literal l in the smallest nonsatisfied clauses. It is widely accepted that a good variable to select is one that maximizes the function, [f ∗ (x)+f ∗ (¬... |

26 |
Grasp—a new search algorithm for satisfiability
- Marques-Silva, Sakallah
- 1996
(Show Context)
Citation Context ...ed for solving large structured real-world instances of SAT, a significant fraction of which requires proving unsatisfiability. Among the many existing backtrack search algorithms, rel sat [2], GRASP =-=[18]-=- and SATO [24] have been shown, on a large number of real-world instances of SAT, to be among the most competitive backtrack search SAT algorithms. There are of course other backtrack search SAT algor... |

22 | GRASP: A new search algorithm for satis - Marques-Silva, Sakallah - 1996 |

15 | Improvements to Propositional Satis Search Algorithms - Freeman - 1995 |

10 | Branching rules for satis - Hooker, Vinay - 1995 |

10 | Solving propositional satis problems - Jeroslow, Wang - 1990 |

9 | Test Pattern Generation Using Boolean Satis - Larrabee - 1992 |

7 |
Analysis of Dependencies to Improve the Behaviour of Logic Programs
- Bruynooghe
- 1980
(Show Context)
Citation Context ...alse otherwise. 4.3 Jeroslow-Wang Heuristics Two branching heuristics were proposed Jeroslow and Wang in [13], and are also analyzed in [1, 12]. For a given literal l, let us compute: J(l) = � 2 −|ω| =-=(3)-=- l∈ω∧ω∈ϕ The one-sided Jeroslow-Wang (JW-OS) branching heuristic selects the assignment that satisfies the literal with the largest value J(l). The two-sided Jeroslow-Wang (JW-TS) heuristic identifies... |

2 |
A davis-putnam enumeration procedure for linear pseudo-boolean optimization
- Barth
- 1995
(Show Context)
Citation Context ...ears in more smallest clauses as a positive literal, and value false otherwise. 4.3 Jeroslow-Wang Heuristics Two branching heuristics were proposed Jeroslow and Wang in [13], and are also analyzed in =-=[1, 12]-=-. For a given literal l, let us compute: J(l) = � 2 −|ω| (3) l∈ω∧ω∈ϕ The one-sided Jeroslow-Wang (JW-OS) branching heuristic selects the assignment that satisfies the literal with the largest value J(... |