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Divide and concur: a general approach to constraint satisfaction
1Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, New York 14853-2501, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
We developed a geometric framework to solve complex computational problems with multiple constraints. This new method shows competitive performance against existing algorithms in Boolean satisfaction and optimization challenges.
Area of Science:
- Computational science
- Optimization
- Geometric algorithms
Background:
- Many complex computational problems require satisfying multiple constraints, which can be challenging.
- Constraints often arise from diverse sources like measurements, physical interactions, or biological processes.
Purpose of the Study:
- To introduce a novel, simple geometric framework for expressing and solving constraint satisfaction problems.
- To demonstrate the framework's applicability and efficiency on benchmark problems.
Main Methods:
- Developed a unified geometric framework applicable to various constraint satisfaction problems.
- Applied the framework to two distinct problems: 3SAT (Boolean satisfaction) and sphere packing (optimization).
Main Results:
- The method achieved performance comparable to leading algorithms like WALKSAT for 3SAT.
- The framework successfully yielded improved solutions for established sphere packing optimization problems.
Conclusions:
- The proposed geometric framework offers a simple yet powerful approach to complex computational problems.
- It presents a competitive alternative to traditional stochastic methods like simulated annealing for constraint satisfaction and optimization.
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