Solving Linux Upgradeability Problems Using Boolean Optimization

Managing the software complexity of package-based systems can be regarded as one of the main challenges in software architectures. Upgrades are required on a short time basis and systems are expected to be reliable and consistent after that. For each package in the system, a set of dependencies and a set of conflicts have to be taken into account. Although this problem is computationally hard to solve, efficient tools are required. In the best scenario, the solutions provided should also be optimal in order to better fulfill users requirements and expectations. This paper describes two different tools, both based on Boolean satisfiability (SAT), for solving Linux upgradeability problems. The problem instances used in the evaluation of these tools were mainly obtained from real environments, and are subject to two different lexicographic optimization criteria. The developed tools can provide optimal solutions for many of the instances, but a few challenges remain. Moreover, it is our understanding that this problem has many similarities with other configuration problems, and therefore the same techniques can be used in other domains.Comment: In Proceedings LoCoCo 2010, arXiv:1007.083

Technology Mapping for Circuit Optimization Using Content-Addressable Memory

The growing complexity of Field Programmable Gate Arrays (FPGA's) is leading to architectures with high input cardinality look-up tables (LUT's). This thesis describes a methodology for area-minimizing technology mapping for combinational logic, specifically designed for such FPGA architectures. This methodology, called LURU, leverages the parallel search capabilities of Content-Addressable Memories (CAM's) to outperform traditional mapping algorithms in both execution time and quality of results. The LURU algorithm is fundamentally different from other techniques for technology mapping in that LURU uses textual string representations of circuit topology in order to efficiently store and search for circuit patterns in a CAM. A circuit is mapped to the target LUT technology using both exact and inexact string matching techniques. Common subcircuit expressions (CSE's) are also identified and used for architectural optimization---a small set of CSE's is shown to effectively cover an average of 96% of the test circuits. LURU was tested with the ISCAS'85 suite of combinational benchmark circuits and compared with the mapping algorithms FlowMap and CutMap. The area reduction shown by LURU is, on average, 20% better compared to FlowMap and CutMap. The asymptotic runtime complexity of LURU is shown to be better than that of both FlowMap and CutMap

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

Automatic Algorithm Selection for Pseudo-Boolean Optimization with Given Computational Time Limits

Machine learning (ML) techniques have been proposed to automatically select the best solver from a portfolio of solvers, based on predicted performance. These techniques have been applied to various problems, such as Boolean Satisfiability, Traveling Salesperson, Graph Coloring, and others. These methods, known as meta-solvers, take an instance of a problem and a portfolio of solvers as input. They then predict the best-performing solver and execute it to deliver a solution. Typically, the quality of the solution improves with a longer computational time. This has led to the development of anytime selectors, which consider both the instance and a user-prescribed computational time limit. Anytime meta-solvers predict the best-performing solver within the specified time limit. Constructing an anytime meta-solver is considerably more challenging than building a meta-solver without the "anytime" feature. In this study, we focus on the task of designing anytime meta-solvers for the NP-hard optimization problem of Pseudo-Boolean Optimization (PBO), which generalizes Satisfiability and Maximum Satisfiability problems. The effectiveness of our approach is demonstrated via extensive empirical study in which our anytime meta-solver improves dramatically on the performance of Mixed Integer Programming solver Gurobi, which is the best-performing single solver in the portfolio. For example, out of all instances and time limits for which Gurobi failed to find feasible solutions, our meta-solver identified feasible solutions for 47% of these