Flexible constrained sampling with guarantees for pattern mining

Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations when it comes to 1) flexibility in terms of quality measures and constraints that can be used, and/or 2) guarantees with respect to sampling accuracy. We therefore present Flexics, the first flexible pattern sampler that supports a broad class of quality measures and constraints, while providing strong guarantees regarding sampling accuracy. To achieve this, we leverage the perspective on pattern mining as a constraint satisfaction problem and build upon the latest advances in sampling solutions in SAT as well as existing pattern mining algorithms. Furthermore, the proposed algorithm is applicable to a variety of pattern languages, which allows us to introduce and tackle the novel task of sampling sets of patterns. We introduce and empirically evaluate two variants of Flexics: 1) a generic variant that addresses the well-known itemset sampling task and the novel pattern set sampling task as well as a wide range of expressive constraints within these tasks, and 2) a specialized variant that exploits existing frequent itemset techniques to achieve substantial speed-ups. Experiments show that Flexics is both accurate and efficient, making it a useful tool for pattern-based data exploration.Comment: Accepted for publication in Data Mining & Knowledge Discovery journal (ECML/PKDD 2017 journal track

Parallel local search for solving Constraint Problems on the Cell Broadband Engine (Preliminary Results)

We explore the use of the Cell Broadband Engine (Cell/BE for short) for combinatorial optimization applications: we present a parallel version of a constraint-based local search algorithm that has been implemented on a multiprocessor BladeCenter machine with twin Cell/BE processors (total of 16 SPUs per blade). This algorithm was chosen because it fits very well the Cell/BE architecture and requires neither shared memory nor communication between processors, while retaining a compact memory footprint. We study the performance on several large optimization benchmarks and show that this achieves mostly linear time speedups, even sometimes super-linear. This is possible because the parallel implementation might explore simultaneously different parts of the search space and therefore converge faster towards the best sub-space and thus towards a solution. Besides getting speedups, the resulting times exhibit a much smaller variance, which benefits applications where a timely reply is critical

Quiet Planting in the Locked Constraint Satisfaction Problems

We study the planted ensemble of locked constraint satisfaction problems. We describe the connection between the random and planted ensembles. The use of the cavity method is combined with arguments from reconstruction on trees and first and second moment considerations; in particular the connection with the reconstruction on trees appears to be crucial. Our main result is the location of the hard region in the planted ensemble. In a part of that hard region instances have with high probability a single satisfying assignment.Comment: 21 pages, revised versio

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