We present a parallel AND/OR Branch-and-Bound scheme that uses the power of a computational grid to push the boundaries of feasibility for combinatorial optimization. Two variants of the scheme are described, one of which aims to use machine learning techniques for parallel load balancing. In-depth analysis identifies two inherent sources of parallel search space redundancies that, together with general parallel execution overhead, can impede parallelization and render the problem far from embarrassingly parallel. We conduct extensive empirical evaluation on hundreds of CPUs, the first of its kind, with overall positive results. In a significant number of cases parallel speedup is close to the theoretical maximum and we are able to solve many very complex problem instances orders of magnitude faster than before; yet analysis of certain results also serves to demonstrate the inherent limitations of the approach due to the aforementioned redundancies.

In empirical studies we observed that caching can have very little impact in reducing the search effort in Branch and Bound search over context-minimal OR spaces. For example, in one of the problem domains used in our experiments we reduce only by 1% the number of nodes expanded when using caching in context-minimal OR spaces. By contrast, we reduce by 74% the number of nodes expanded when using caching in context-minimal AND/OR spaces on the same instances. In this work we document this unexpected empirical finding and provide explanations for the phenomenon.

MOTIVATION: The use of dense single nucleotide polymorphism (SNP) data in genetic linkage analysis of large pedigrees is impeded by significant technical, methodological and computational challenges. Here we describe Superlink-Online SNP, a new powerful online system that streamlines the linkage analysis of SNP data. It features a fully integrated flexible processing workflow comprising both well-known and novel data analysis tools, including SNP clustering, erroneous data filtering, exact and approximate LOD calculations and maximum-likelihood haplotyping. The system draws its power from thousands of CPUs, performing data analysis tasks orders of magnitude faster than a single computer. By providing an intuitive interface to sophisticated state-of-the-art analysis tools coupled with high computing capacity, Superlink-Online SNP helps geneticists unleash the potential of SNP data for detecting disease genes. RESULTS: Computations performed by Superlink-Online SNP are automatically parallelized using novel paradigms, and executed on unlimited number of private or public CPUs. One novel service is large-scale approximate Markov Chain-Monte Carlo (MCMC) analysis. The accuracy of the results is reliably estimated by running the same computation on multiple CPUs and evaluating the Gelman-Rubin Score to set aside unreliable results. Another service within the workflow is a novel parallelized exact algorithm for inferring maximum-likelihood haplotyping. The reported system enables genetic analyses that were previously infeasible. We demonstrate the system capabilities through a study of a large complex pedigree affected with metabolic syndrome. AVAILABILITY: Superlink-Online SNP is freely available for researchers at http://cbl-hap.cs.technion.ac.il/superlink-snp. The system source code can also be downloaded from the system website. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Vol. 29, No. 2, 2013, pp. 197–205 doi:10.1093/bioinformatics/bts658 The publishers regret that the author affiliations for this paper should appear as follows: Mark Silberstein1,2, Omer Weissbrod1,*, Lars Otten3, Anna Tzemach1, Andrei Anisenia1,4, Oren Shtark1, Dvir Tuberg1, Eddie Galfrin1, Irena Gannon1, Adel Shalata5,6,7, Zvi U. Borochowitz5,8, Rina Dechter3, Elizabeth Thompson9 and Dan Geiger1 1Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, 2Department of Computer Science, University of Texas at Austin, Austin, TX, USA, 3Donald Bren School of Information and Computer Sciences, UC Irvine, CA, USA, 4Department of Computer Science, University of Ottawa, Ottawa, Canada, 5The Simon Winter Institute for Human Genetics, Bnai-Zion Medical Center, Haifa, Israel, 6Research and Development Center, The Galilee Society, Shefa-Amr, Israel, 7Holy Family Hospital, Nazareth, Israel, 8The Rappaport Faculty of Medicine and Research Institute, Technion-Israel Institute of Technology, Haifa, Israel and 9Department of Statistics, University of Washington, Seattle, WA, USA

We study iterative randomized greedy algorithms for generating (elimination) orderings with small induced width and state space size — two parameters known to bound the complexity of inference in graphical models. We propose and implement the Iterative Greedy Variable Ordering (IGVO) algorithm, a new variant within this algorithm class. An empirical evaluation using different ranking functions and conditions of randomness, demonstrates that IGVO finds significantly better orderings than standard greedy ordering implementations when evaluated within an anytime framework. Additional order of magnitude improvements are demonstrated on a multi-core system, thus further expanding the set of solvable graphical models. The experiments also confirm the superiority of the MinFill heuristic within the iterative scheme.

One popular and efficient scheme for solving exactly combinatorial optimization problems over graphical models is depth-first Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This paper 1) analyzes and demonstrates this inherent conflict between effective exploitation of problem decomposition (through AND/OR search spaces) and the anytime behavior of depth-first search (DFS), 2) presents a first scheme to address this issue while maintaining desirable DFS memory properties, 3) analyzes and demonstrates its effectiveness. Our work is applicable to any problem that can be cast as search over an AND/OR search space.

The recently introduced notion of hypertree width has been shown to provide a broader characterization of tractable constraint and probabilistic networks than the tree width. This paper demonstrates empirically that in practice the bounding power of the tree width is still superior to the hypertree width for many benchmark instances of both probabilistic and deterministic networks.