Conference Paper

Generic ILP versus specialized 0-1 ILP: an update

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA;
DOI: 10.1109/ICCAD.2002.1167571 Conference: IEEE International Conference on Computer Aided Design (ICCAD), At San Jose, California
Source: IEEE Xplore

ABSTRACT Optimized solvers for the Boolean Satisfiability (SAT) problem have many applications in areas such as hardware and software verification, FPGA routing, planning, etc. Further uses are complicated by the need to express "counting constraints" in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by Integer Linear Programming (ILP), but generic ILP solvers may ignore the Boolean nature of 0-1 variables. Therefore specialized 0-1 ILP solvers extend SAT solvers to handle these so-called "pseudo-Boolean" constraints. This work provides an update on the on-going competition between generic ILP techniques and specialized 0-1 ILP techniques. To make a fair comparison, we generalize recent ideas for fast SAT-solving to more general 0-1 ILP problems that may include counting constraints and optimization. Another aspect of our comparison is evaluation on 0-1 ILP benchmarks that originate in Electronic Design Automation (EDA), but that cannot be directly solved by a SAT solver. Specifically, we solve instances of the Max-SAT and Max-ONEs optimization problems which seek to maximize the number of satisfied clauses and the "true" values over all satisfying assignments, respectively. Those problems have straightforward applications to SAT-based routing and are additionally important due to reductions from Max-Cut, Max-Clique, and Min Vertex Cover. Our experimental results show that specialized 0-1 techniques tend to outperform generic ILP techniques on Boolean optimization problems as well as on general EDA SAT problems.

  • [Show abstract] [Hide abstract]
    ABSTRACT: Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision Diagram (BDD) for the constraint, and then encode the BDD into a propositional formula. These BDD-based approaches have some important advantages, such as not being dependent on the size of the coefficients, or being able to share the same BDD for representing many constraints. We first focus on the size of the resulting BDDs, which was considered to be an open problem in our research community. We report on previous work where it was proved that there are Pseudo-Boolean constraints for which no polynomial BDD exists. We also give an alternative and simpler proof assuming that NP is different from Co-NP. More interestingly, here we also show how to overcome the possible exponential blowup of BDDs by phcoefficient decomposition. This allows us to give the first polynomial generalized arc-consistent ROBDD-based encoding for Pseudo-Boolean constraints. Finally, we focus on practical issues: we show how to efficiently construct such ROBDDs, how to encode them into SAT with only 2 clauses per node, and present experimental results that confirm that our approach is competitive with other encodings and state-of-the-art Pseudo-Boolean solvers.
    Journal of Artificial Intelligence Research 01/2014; 45(1). · 1.06 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Over the course of the last decade, there have been several improvements in the performance of Integer Linear Programming (ILP) and Boolean Satisfiability (SAT) solvers. These improvements have encouraged the application of SAT and ILP techniques in modeling complex engineering prob-lems. One such problem is the Clustering Problem in Mobile Ad-Hoc Networks (MANETs). The Clustering Problem in MANETs consists of selecting the most suitable nodes of a given MANET topology as clusterheads, and ensuring that regular nodes are connected to clusterheads such that the lifetime of the network is maximized. This paper proposes the development of an improved ILP formulation of the Clustering Problem. Addition-ally, various enhancements are implemented in the form of exten-sions to the improved formulation, including the establishment of intra-cluster communication, multihop connections and the enforcement of coverage constraints. The improved formulation and enhancements are implemented in a tool designed to visually create network topologies and cluster them using state-of-the art Generic ILP and SAT solvers. Through this tool, feasibility of using the proposed formulation and enhancements in a real-life practical environment is assessed. It is observed that the Generic ILP solvers, CPLEX, and SCIP, are able to handle large network topologies, while the 0–1 SAT-based ILP solver, BSOLO, is effective at handling the smaller scale networks. It is also observed that while these enhanced formulations enable the generation of complex network solutions, and are suitable for small scale networks, the time taken to generate the corresponding solution does not meet the strict requirements of a practical environment. Index Terms— Boolean satisfiability (SAT), integer linear pro-gramming, mobile ad-hoc networks (MANETs), optimization.
    IEEE Sensors Journal 06/2013; 13(6):2400-2412. · 1.48 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Maximum Satisfiability (MaxSAT) is an optimization version of SAT, and many real world applications can be naturally encoded as such. Solving MaxSAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in developing efficient algorithms and several families of algorithms have been proposed. This paper overviews recent approaches to handle MaxSAT and presents a survey of MaxSAT algorithms based on iteratively calling a SAT solver which are particularly effective to solve problems arising in industrial settings. First, classic algorithms based on iteratively calling a SAT solver and updating a bound are overviewed. Such algorithms are referred to as iterative MaxSAT algorithms. Then, more sophisticated algorithms that additionally take advantage of unsatisfiable cores are described, which are referred to as core-guided MaxSAT algorithms. Core-guided MaxSAT algorithms use the information provided by unsatisfiable cores to relax clauses on demand and to create simpler constraints. Finally, a comprehensive empirical study on non-random benchmarks is conducted, including not only the surveyed algorithms, but also other state-of-the-art MaxSAT solvers. The results indicate that (i) core-guided MaxSAT algorithms in general abort in less instances than classic solvers based on iteratively calling a SAT solver and that (ii) core-guided MaxSAT algorithms are fairly competitive compared to other approaches.
    Constraints 10/2013; · 0.74 Impact Factor

Full-text (2 Sources)

Available from
May 19, 2014