of computer science at the University of Picardie Jules Verne. My research is
concerned with the practical resolution of NP-hard problems, including SAT, CSP, MaxSAT, MinSAT, MaxClique, GCP. I am particularly interested in the intrinsical relationships between these
problems. One of my research directions is to find and exploit these relationships to solve them.
Algorithms: The source codes of different procedures
are available below. Thanks for letting me
know all your remarks or suggestions.
MaxCLQ for MaxClique (Chu Min LI and Quan Zhe) (New)
Branch-and-bound algorithms for the Maximum Clique problem (MaxClique) usually partition a graph into independent sets to compute an upper bound for the size of a maximum clique of the graph, since every independent set can have at most one vertex in a clique. However, this upper bound cannot be very tight for two reasons : (1) partitioning a graph into independent sets is equivalent to coloring the graph, which is even harder than MaxClique in practice, so the partition cannot be optimal in every node of the search tree ; (2) even if the partition is optimal, the number of independent sets is strictly larger than the size of a maximum clique for imperfect graphs (by definition of imperfect graphs). Note that MaxClique and the graph coloring problem are polynomial for perfect graphs.
The upper bound based on independent sets can be significantly improved using MaxSAT reasoning. In every node of the search tree, we dynamically encode a MaxClique instance into a partial MaxSAT problem and use MaxSAT reasoning to underestimate the number of independent sets that cannot have a vertex in the maximum clique, obtaining MaxCLQ, a highly efficient branch-and-bound solver for MaxClique.
An executable MaxCLQ for Linux is available here. This version is described in the ICATI2010 paper and improved from the version presented in the AAAI2010 paper.
Chu Min LI, Zhe Quan. 2010. Combining Graph Structure Exploitation and Propositional Reasoning for the Maximum Clique Problem, in proceedings of the 22th IEEE International Conference on Tools with Artificial Intelligence (ICTAI2010), Arras, France, October 2010, Pages 344-351.
Li, C. M., and Quan, Z., 2010, An efﬁcient branch-and-bound algorithm based on maxsat for the maximum clique problem. In Proceedins of AAAI-10, Pages 128-133.
Sattime (Chu Min LI and Yu LI) (New)
Sattime is a Stochastic Local Search (SLS) solver for SAT, that exploits the satisfying history of clauses, instead of falsifying history of clauses as in most other SLS solvers, in selecting the next variable to flip. Sattime participated in the 2011 SAT competition and won a silver medal in the ran- dom category. Especially, Sattime beat easily all the Conflict Driven Clause Learning (CDCL) solvers in the crafted sat category (Sattime solved 109 instances while the best CDCL only solved 93 instances), although SLS has been considered less effective than CDCL for structured SAT problems for a long time. This is the first time that a SLS solver enters the final phase of the SAT competition in the crafted category and beats there all the CDCL algorithms on structured SAT problems.
Sattime confirmed its performance in the SAT challenge 2012, as the best SLS solver in the crafted (Hard Combinatorial SAT+UNSAT) category and the second best single engine solver in the random SAT category.
Chu Min Li and Yu Li, Satisfying versus Falsifying in Local Search for Satisfiability, in proceedings of SAT2012, Springer LNCS 7317, pp. 477–478, 2012.
Maxsatz (Chu Min Li, Felip Manya and Jordi Planes):
A branch and bound solver for Max-SAT that incorporates into a Max-SAT solver some of the technology developed for Satz (see below). At each node of the proof tree it transforms the formula into an equivalent formula that preserves the number of unsatisfied clauses by applying some efficient refinements of unit resolution that the authors have defined for Max-SAT (e.g., it replaces $x, y, \neg x \vee \neg y$ with $\Box, x \vee y$, it replaces $x, \neg x \vee y, \neg x \vee z, \neg y \vee \neg z$ with $\Box, \neg x \vee y \vee z, x \vee \neg y \vee \neg z$). MaxSatz implements a lower bound computation method that consists of incrementing the lower bound by one for every disjoint inconsistent subset that can be detected by unit propagation. Moreover, the lower bound computation method is enhanced with failed literal detection. The variable selection heuristics takes into account the number of positive and negative occurrences in binary and ternary clauses Maxsatz and its variants are the best performing solvers in the unweighted maxsat category in the 2006 maxsat solvers evaluation and the 2007 maxsat solvers evaluation.
The source codes of maxsatz are available here.
version of maxsatz (wmaxsatz2009) is available here.
Chu Min LI,
Felip Manya, Nouredine Mohamedou, Jordi Planes, "Exploiting
Cycle Structures in Max-SAT". In proceedings of 12th international conference
on the Theory and Applications of Satisfiability Testing (SAT2009), Springer, LNCS 5584, pages 467-480, June-July
2009, Swansea, United Kindom.
Chu Min LI, Felip Manya, Jordi Planes, "New Inference Rules for Max-SAT", in Journal of Artificial Intelligence Research, October 2007, Volume 30, pages 321-359
Chu Min LI, Felip Manya, Jordi Planes, "Detecting disjoint inconsistent subformulas for computing lower bounds for Max-SAT". In Proceedings of the 21st National Conference on Artificial Intel ligence (AAAI-06), Boston, USA, pp. 86–91. AAAI Press.
TNM (Wanxia Wei, Chu Min Li):
A local search procedure based on G2wsat (see below) and using two different adaptive noise mechanisms: Hoos mechanism and a new adaptive noise mechanism based on the history of the most recent consecutive falsiﬁcations of a clause. TNM automatically switches between these two mechanisms during search according to the variable weight distribution. No parameter is needed to adjust when using TNM. TNM won a GOLD Medal in the SAT2009 competition in satisfiable random formula category. The version used in the competition (using input and output format of the competition) as well as a short presentation of the procedure can be obtained here.
Chu Min Li, Wanxia Wei, and Yu Li, Exploiting Historical Relationships of Clauses and Variables in Local Search for Satisfiability, in proceedings of SAT2012, Springer LNCS 7317, pp. 479–480, 2012.
Adaptg2wsat2009++ (Chu Min Li, Wanxia Wei):
A local search procedure based on G2wsat (see below) by integrating the adaptive noise mechanism of Hoos. No parameter is needed to adjust when using adaptg2wsat2009++. Adaptg2wsat2009++ won a Bronze Medal in the SAT2009 competition in satisfiable random formula category. The version used in the competition (using input and output format of the competition) as well as a short presentation of the procedure can be obtained here.
Adaptg2wsat0 (Chu Min Li, Wanxia Wei and Harry Zhang):
A local search procedure based on G2wsat (see below) by integrating the adaptive noise mechanism of Hoos. No parameter is needed to adjust when using adaptg2wsat0. Adaptg2wsat0 won a Silver Medal in SAT2007 competition in satisfiable random formula category. The version used in the competition (using input and output format of the competition) as well as a short presentation of the procedure can be obtained here. The normal version can be found here.
Adaptg2wsat+ (Chu Min Li, Wanxia Wei and Harry Zhang):
A local search procedure based on G2wsat by integrating the adaptive noise and random walk mechanisms of Hoos. No parameter is needed to adjust when using adaptg2wsat+. Adaptg2wsat+ won a Bronze Medal in SAT2007 competition in satisfiable random formula category. The version used in the competition (using input and output formats of the competition) as well as a short presentation of the procedure can be obtained here.
References for Adaptg2wsat0 and Adaptg2wsat+:
Chu Min Li, Wanxia Wei, Harry Zhang, "Combining Adaptive Noise and Look-Ahead in Local Search for SAT". In proceedings of 10th international conference on the Theory and Applications of Satisfiability Testing (SAT2007), Lisbon, Portugal, May 2007.
G2wsat (Chu Min LI & Wenqi HUANG):
A local search procedure which won a Silver Medal in SAT2005 competition in satisfiable random formula category. The version used in the competition as well as a short presentation of the procedure can be obtained here. The current version (2005) is optimized after the competition and is generally more than 50% faster. To get the source code of current g2wsat (version 2005), click here.
Chu Min LI & Wenqi HUANG, "Diversification
and Determinism in Local search
for Satisfiability", in proceedings of 8th international conference, SAT2005, LNCS 3569 Springer, St Andrews, UK, June 2005, Pages 158-172
Satz215 is Satz214
+ Detection of implied literals suggested by Daniel Le Berre. Satz215 solves
more structured instances than Satz214. Particularly, Satz215 solves 3bitadd_31
and 3bitadd_32 in a few seconds. Satz215.1 is Satz215 modified in which the
preprocessing only adds up to 10*INIT_NB_CLAUSE ternary resolvents into a
formule with initially INIT_NB_CLAUSE clauses.
To get the source code of Satz215.2, click here.
Satz214.2 (Li and Anbulagan) :
Satz214 is a very fast and a very simple Davis-Putnam procedure to solve satisfiablility problems in DIMACS format. Satz214 adds binary and ternary resolvents into a formule when preprocessing it. Satz214.1 is the last version in which only up to 10*INIT_NB_CLAUSE ternary resolvents can be added into a formule with initially INIT_NB_CLAUSE clauses To get the source code of Satz214.2, click here. To compile it under Unix or Linux system, the commande line looks like: gcc satz214.1.c -O3 -o satz
Chu Min LI, "A constrained-based approach to narrow search trees for satisfiability", Information processing letters 71(1999) page 75-80.
Chu Min LI & Anbulagan, "Look-ahead versus look-back for satisfiability problems", in preceedings of third international conference on Principles and Practice of Constraint Programming--CP97, Springer-Verlag, LNCS 1330, Page 342-356, Autriche, 1997.
Chu Min LI & Anbulagan, "Heuristics based on unit propagation for satisfiability problems", in proceedings of 15th International Joint Conference on Artificial Interlligence (IJCAI'97), Morgan Kaufmann Publishers, ISBN 1-55860-480-4, Page 366-371, Japon, 1997.
EqSatz (Chu Min LI) :
EqSatz is equivalency reasoning enhanced satz to solve satisfiability problems involving equivalency clauses (Xor or modulo 2 arithmetics) such as 1<->2<->3 (equivalent to four CNF clauses: -1 or -2 or 3, -1 or 2 or -3, 1 or -2 or -3, 1 or 2 or 3). EqSatz is the first method to solve all the ten DIMACS 32 bit parity par32-* instances (second IJCAI-97 challenge on propositional reasoning and search) in reasonable time. To get its source code click here. To compile it under Unix or Linux system, the commande line looks like: gcc eqsatz20.c -O3 -o eqsatz
Chu Min LI, "Integrating Equivalency reasoning into Davis-Putnam procedure", in the proceedings of AAAI-2000. Austin Texas, USA, July 2000, Page 291-296.
Chu Min LI, ``Equivalent literal propagation in Davis-Putnam procedure'', in Discrete Applied Mathematics, Vol 130/2 pp 251-276, 2003.
Compactor (Chu Min LI) :
The compactor is used to simplify an input formula in DIMACS format. It is Satz without branching. To get its source code, click here. Four operations are performed given an input formula:
(i) the input formula is performed by adding resolvent of length < 4; e.g. if 1 2 3 and -1 2 4 are clauses, add a clause 2 3 4 into the formula.
(ii) elimination of pure literals;
(iii) detection of failure literals ;
(iv) rename remaining variables to be continuous;
The simplified formula is written into the file named "out" in the directory where the compactor is run. The old and new variables are written into the file named "var_table" in the directory where the compactor runs. This is a two-column file. The first column is the old variables in the original input formula which are replaced in the simplified formula by the variables in the second column.
Please don't hesitate to contact the author for any question and any suggestion.
ParaSatz (Bernard Jurkowiak, Chu Min LI, Gil Utard) :
ParaSatz is the distributed/parallel version of Satz which can run on any machines in a local network. For example, it can run on any Linux or Unix machines in a local network. Based on sequential Satz, ParaSatz is developed by Bernard Jurkowiak, Chu Min Li and Gil Utard. Particular thanks to Dominique Lazure for material help.
ParaSatz uses the simple master/slave model for communication and dynamically balances workload among slaves, i.e. a slave cannot be idle whenever the resolution is not finished, since the most loaded working slave is capable of giving a part of its work to the slave which has finished its own work.
Moreover, ParaSatz supports fault-tolerant computing, i.e. the work of any died slave will be continued by other slaves. ParaSatz also supports partial computing, i.e. the entire resolution can be stopped at any moment and continued later, which is important for the so-called "global computing" using idle machines in the world.
To get the source code of ParaSatz, click here.
Bernard Jurkowiak, Chu Min LI, and Gil Utard, A parallelization scheme based on work stealing for a class of SAT solvers, in Journal of Automated Reasoning (2005) 34:73-101.