Solving Stable Matching Problems via Cooperative Parallel Local Search

International audienceStable matching problems and its variants have several practical applications, like the Hospital/Residents problem, stable roommates problem or bipartite market sharing. An important generalization problem is the SMTI which allows for incompleteness and ties in the user's preference lists. Finding a maximal size stable matching for SMTI is compu-tationally difficult. We developed a Local Search method to solve SMTI using the Adaptive Search algorithm and present experimental evidence that this approach is much more efficient than state-of-the-art exact and approximate methods (in terms of both computational effort required and quality of solution). We also tried a parallel version of our algorithm. For this we reused the Cooperative Parallel Local Search framework (CPLS) we designed. CPLS is a highly parametric framework for the execution in parallel of local search solvers allowing them to cooperate though communication. The cooperative parallel version of our local search algorithm improves performance so much that very large and hard instances can be solved quickly

Towards Next Generation Sequential and Parallel SAT Solvers

This thesis focuses on improving the SAT solving technology. The improvements focus on two major subjects: sequential SAT solving and parallel SAT solving. To better understand sequential SAT algorithms, the abstract reduction system Generic CDCL is introduced. With Generic CDCL, the soundness of solving techniques can be modeled. Next, the conflict driven clause learning algorithm is extended with the three techniques local look-ahead, local probing and all UIP learning that allow more global reasoning during search. These techniques improve the performance of the sequential SAT solver Riss. Then, the formula simplification techniques bounded variable addition, covered literal elimination and an advanced cardinality constraint extraction are introduced. By using these techniques, the reasoning of the overall SAT solving tool chain becomes stronger than plain resolution. When using these three techniques in the formula simplification tool Coprocessor before using Riss to solve a formula, the performance can be improved further. Due to the increasing number of cores in CPUs, the scalable parallel SAT solving approach iterative partitioning has been implemented in Pcasso for the multi-core architecture. Related work on parallel SAT solving has been studied to extract main ideas that can improve Pcasso. Besides parallel formula simplification with bounded variable elimination, the major extension is the extended clause sharing level based clause tagging, which builds the basis for conflict driven node killing. The latter allows to better identify unsatisfiable search space partitions. Another improvement is to combine scattering and look-ahead as a superior search space partitioning function. In combination with Coprocessor, the introduced extensions increase the performance of the parallel solver Pcasso. The implemented system turns out to be scalable for the multi-core architecture. Hence iterative partitioning is interesting for future parallel SAT solvers. The implemented solvers participated in international SAT competitions. In 2013 and 2014 Pcasso showed a good performance. Riss in combination with Copro- cessor won several first, second and third prices, including two Kurt-Gödel-Medals. Hence, the introduced algorithms improved modern SAT solving technology

The Eureka Programming Model for Speculative Task Parallelism

In this paper, we describe the Eureka Programming Model (EuPM) that simplifies the expression of speculative parallel tasks, and is especially well suited for parallel search and optimization applications. The focus of this work is to provide a clean semantics for, and efficiently support, such "eureka-style" computations (EuSCs) in general structured task parallel programming models. In EuSCs, a eureka event is a point in a program that announces that a result has been found. A eureka triggered by a speculative task can cause a group of related speculative tasks to become redundant, and enable them to be terminated at well-defined program points. Our approach provides a bound on the additional work done in redundant speculative tasks after such a eureka event occurs. We identify various patterns that are supported by our eureka construct, which include search, optimization, convergence, and soft real-time deadlines. These different patterns of computations can also be safely combined or nested in the EuPM, along with regular task-parallel constructs, thereby enabling high degrees of composability and reusability. As demonstrated by our implementation, the EuPM can also be implemented efficiently. We use a cooperative runtime that uses delimited continuations to manage the termination of redundant tasks and their synchronization at join points. In contrast to current approaches, EuPM obviates the need for cumbersome manual refactoring by the programmer that may (for example) require the insertion of if checks and early return statements in every method in the call chain. Experimental results show that solutions using the EuPM simplify programmability, achieve performance comparable to hand-coded speculative task-based solutions and out-perform non-speculative task-based solutions

A review of literature on parallel constraint solving

As multicore computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint algorithms are amenable to parallelisation; whether to use shared memory or distributed computation; whether to use static or dynamic decomposition; and how to best exploit portfolios and cooperating search. We review the literature, and see that we can sometimes do quite well, some of the time, on some instances, but we are far from a general solution. Yet there seems to be little overall guidance that can be given on how best to exploit multicore computers to speed up constraint solving. We hope at least that this survey will provide useful pointers to future researchers wishing to correct this situation

Quantum and Classical Multilevel Algorithms for (Hyper)Graphs

Combinatorial optimization problems on (hyper)graphs are ubiquitous in science and industry. Because many of these problems are NP-hard, development of sophisticated heuristics is of utmost importance for practical problems. In recent years, the emergence of Noisy Intermediate-Scale Quantum (NISQ) computers has opened up the opportunity to dramaticaly speedup combinatorial optimization. However, the adoption of NISQ devices is impeded by their severe limitations, both in terms of the number of qubits, as well as in their quality. NISQ devices are widely expected to have no more than hundreds to thousands of qubits with very limited error-correction, imposing a strict limit on the size and the structure of the problems that can be tackled directly. A natural solution to this issue is hybrid quantum-classical algorithms that combine a NISQ device with a classical machine with the goal of capturing “the best of both worlds”. Being motivated by lack of high quality optimization solvers for hypergraph partitioning, in this thesis, we begin by discussing classical multilevel approaches for this problem. We present a novel relaxation-based vertex similarity measure termed algebraic distance for hypergraphs and the coarsening schemes based on it. Extending the multilevel method to include quantum optimization routines, we present Quantum Local Search (QLS) – a hybrid iterative improvement approach that is inspired by the classical local search approaches. Next, we introduce the Multilevel Quantum Local Search (ML-QLS) that incorporates the quantum-enhanced iterative improvement scheme introduced in QLS within the multilevel framework, as well as several techniques to further understand and improve the effectiveness of Quantum Approximate Optimization Algorithm used throughout our work