Exploiting parallelism is a key strategy for speeding up computation. However, on hard combinatorial problems, such a strategy has been surprisingly challenging due to the intricate variable interactions.We introduce a novel way in which parallelism can be used to exploit hidden structure of hard combinatorial problems. Our approach complements divide-and-conquer and portfolio approaches. We evaluate our approach on the minimum set basis problem: a core combinatorial problem with a range of applications in optimization, machine learning, and system security. We also highlight a novel sustainability related application, concerning the discovery of new materials for renewable energy sources such as improved fuel cell catalysts.

Many state-of-the-art algorithms for solving hard combinatorial problems in artificial intelligence (AI) include elements of stochasticity that lead to high variations in runtime, even for a fixed problem instance. Knowledge about the resulting runtime distributions (RTDs) of algorithms on given problem instances can be exploited in various meta-algorithmic procedures, such as algorithm selection, portfolios, and randomized restarts. Previous work has shown that machine learning can be used to individually predict mean, median and variance of RTDs. To establish a new state-of-the-art in predicting RTDs, we demonstrate that the parameters of an RTD should be learned jointly and that neural networks can do this well by directly optimizing the likelihood of an RTD given runtime observations. In an empirical study involving five algorithms for SAT solving and AI planning, we show that neural networks predict the true RTDs of unseen instances better than previous methods, and can even do so when only few runtime observations are available per training instance.

Exploiting parallelism is a key strategy for speeding up computation. However, on hard combinatorial problems, such a strategy has been surprisingly challenging due to the intricate variable interactions. In this paper we introduce a novel way in which parallelism can be used to exploit hidden structure of hard combinatorial problems, orthogonal to divide-and-conquer and portfolio approaches. We demonstrate the success of this approach on the minimal set basis problem, which has a wide range of applications e.g., in optimization, machine learning, and system security. We also show the effectiveness of our approach on a related application problem from materials discovery. In our approach, a large number of smaller sub-problems are identified and solved concurrently. We then aggregate the information from those solutions, and use this information to initialize the search of a global, complete solver. We show that this strategy leads to a significant speed-up over a sequential approach since the aggregated sub-problem solution information often provides key structural insights to the complete solver. Our approach also greatly outperforms state-of-the-art incomplete solvers in terms of solution quality. Our work opens up a novel angle for using parallelism to solve hard combinatorial problems.

A key strategy for speeding up computation is to run in parallel on multiple cores. However, on hard combinatorial problems, exploiting parallelism has been surprisingly challenging. It appears that traditional divide-and-conquer strategies do not work well, due to the intricate non-local nature of the interactions between the problem variables. In this paper, we introduce a novel way in which parallelism can be used to exploit hidden structure of hard combinatorial problems. We demonstrate the success of this approach on minimal set basis problem, which has a wide range of applications in machine learning and system security, etc. We also show the effectiveness on a related application problem from materials discovery. In our approach, a large number of smaller sub-problems are identified and solved concurrently. We then aggregate the information from those solutions, and use this to initialize the search of a global, complete solver. We show that this strategy leads to a significant speed-up over a sequential approach. The strategy also greatly outperforms state-of-the-art incomplete solvers in terms of solution quality. Our work opens up a novel angle for using parallelism to solve hard combinatorial problems.