2,607 research outputs found
Effective Lower Bounding Techniques for Pseudo-Boolean Optimization
Linear Pseudo-Boolean Optimization (PBO) is a widely used modeling framework in Electronic Design Automation (EDA). Due to significant advances in Boolean Satisfiability (SAT), new algorithms for PBO have emerged, which are effective on highly constrained instances. However, these algorithms fail to handle effectively the information provided by the cost function of PBO. This paper addresses the integration of lower bound estimation methods with SAT-related techniques in PBO solvers. Moreover, the paper shows that the utilization of lower bound estimates can dramatically improve the overall performance of PBO solvers for most existing benchmarks from EDA. 1
A Novel SAT-Based Approach to the Task Graph Cost-Optimal Scheduling Problem
The Task Graph Cost-Optimal Scheduling Problem consists in scheduling a certain number of interdependent tasks onto a set of heterogeneous processors (characterized by idle and running rates per time unit), minimizing the cost of the entire process. This paper provides a novel formulation for this scheduling puzzle, in which an optimal solution is computed through a sequence of Binate Covering Problems, hinged within a Bounded Model Checking paradigm. In this approach, each covering instance, providing a min-cost trace for a given schedule depth, can be solved with several strategies, resorting to Minimum-Cost Satisfiability solvers or Pseudo-Boolean Optimization tools. Unfortunately, all direct resolution methods show very low efficiency and scalability. As a consequence, we introduce a specialized method to solve the same sequence of problems, based on a traditional all-solution SAT solver. This approach follows the "circuit cofactoring" strategy, as it exploits a powerful technique to capture a large set of solutions for any new SAT counter-example. The overall method is completed with a branch-and-bound heuristic which evaluates lower and upper bounds of the schedule length, to reduce the state space that has to be visited. Our results show that the proposed strategy significantly improves the blind binate covering schema, and it outperforms general purpose state-of-the-art tool
Low-rank semidefinite programming for the MAX2SAT problem
This paper proposes a new algorithm for solving MAX2SAT problems based on
combining search methods with semidefinite programming approaches. Semidefinite
programming techniques are well-known as a theoretical tool for approximating
maximum satisfiability problems, but their application has traditionally been
very limited by their speed and randomized nature. Our approach overcomes this
difficult by using a recent approach to low-rank semidefinite programming,
specialized to work in an incremental fashion suitable for use in an exact
search algorithm. The method can be used both within complete or incomplete
solver, and we demonstrate on a variety of problems from recent competitions.
Our experiments show that the approach is faster (sometimes by orders of
magnitude) than existing state-of-the-art complete and incomplete solvers,
representing a substantial advance in search methods specialized for MAX2SAT
problems.Comment: Accepted at AAAI'19. The code can be found at
https://github.com/locuslab/mixsa
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