Experimental results on the application of satisfiability algorithms to scheduling problems
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
A linear-time transformation of linear inequalities into conjunctive normal form
Information Processing Letters
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
Algorithms for solving Boolean satisfiability in combinational circuits
DATE '99 Proceedings of the conference on Design, automation and test in Europe
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
SATIRE: a new incremental satisfiability engine
Proceedings of the 38th annual Design Automation Conference
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Pruning Techniques for the SAT-Based Bounded Model Checking Problem
CHARME '01 Proceedings of the 11th IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Robust Search Algorithms for Test Pattern Generation
FTCS '97 Proceedings of the 27th International Symposium on Fault-Tolerant Computing (FTCS '97)
An Exact Approach to the Strip-Packing Problem
INFORMS Journal on Computing
A competitive and cooperative approach to propositional satisfiability
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
A New Placement Heuristic for the Orthogonal Stock-Cutting Problem
Operations Research
Reusing Learned Information in SAT-based ATPG
VLSID '07 Proceedings of the 20th International Conference on VLSI Design held jointly with 6th International Conference: Embedded Systems
Reactive GRASP for the strip-packing problem
Computers and Operations Research
Scalable exploration of functional dependency by interpolation and incremental SAT solving
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
A greedy randomized adaptive search procedure for the point-feature cartographic label placement
Computers & Geosciences
A least wasted first heuristic algorithm for the rectangular packing problem
Computers and Operations Research
Compiling finite linear CSP into SAT
Constraints
The effect of restarts on the efficiency of clause learning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Some experiments with a simple tabu search algorithm for the manufacturer's pallet loading problem
Computers and Operations Research
The log-support encoding of CSP into SAT
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Fundamenta Informaticae - RCRA 2008 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Azucar: a SAT-based CSP solver using compact order encoding
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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We propose a satisfiability testing (SAT) based exact approach for solving the two-dimensional strip packing problem (2SPP). In this problem, we are given a set of rectangles and one large rectangle called a strip. The goal of the problem is to pack all rectangles without overlapping, into the strip by minimizing the overall height of the packing. Although the 2SPP has been studied in Operations Research, some instances are still hard to solve. Our method solves the 2SPP by translating it into a SAT problem through a SAT encoding called order encoding. The translated SAT problems tend to be large; thus, we apply several techniques to reduce the search space by symmetry breaking and positional relations of rectangles. To solve a 2SPP, that is, to compute the minimum height of a 2SPP, we need to repeatedly solve similar SAT problems. We thus reuse learned clauses and assumptions from the previously solved SAT problems. To evaluate our approach, we obtained results for 38 instances from the literature and made comparisons with a constraint satisfaction solver and an ad-hoc 2SPP solver.