Parallel disk-based computation for large, monolithic binary decision diagrams

Kunkle, Daniel; Slavici, Vlad; Cooperman, Gene

doi:10.1145/1837210.1837222

Cited by 13 publications

(14 citation statements)

References 34 publications

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“…Kunkle et al [19] converted the algorithm further to one based on latency-tolerant, Parallel BFS, well-suited for parallel disks. However, at that time, the considered algorithm was not known to be just an instance of a more general method.…”

Section: A General Methods For Migrating Recursive Algorithms From Thementioning

confidence: 99%

“…Some problems may allow representations in which nodes in the next frontier need not be compared to nodes from the previous frontiers [19]. In these problems, only subproblems at the same BFS level can be duplicates of one another.…”

Section: A General Methods For Migrating Recursive Algorithms From Thementioning

confidence: 99%

“…The following two general results form the basis of the conversion from a sequential, RAM-based, recursive computation (which uses a stack) to a parallel, external memory, nonrecursive computation (which uses the concept of a latencytolerant Parallel Queue, described for the case of a binary decision diagram package in [19,Section 4…”

Section: Related Workmentioning

confidence: 99%

“…An important part of many symbolic computations is working with very large graph-like data structures, that only fit on parallel disks: groups [25], binary decision diagrams [19] and others. Very large finite state automata are useful in many areas, within symbolic computations and outside of it, as discussed in Section 3.…”

Section: Introductionmentioning

confidence: 99%

“…When working with the above mentioned large graph-like data structures, techniques similar to dynamic programming are often employed (for example, see [19,25]). Migrating dynamic programming to parallel disks is described in Section 2.1 and in our parallel disk-based implementation of the 0-1 Knapsack problem in Section 4.…”

Section: Introductionmentioning

confidence: 99%

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An efficient programming model for memory-intensive recursive algorithms using parallel disks

Slavici

Kunkle

Cooperman

et al. 2012

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

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In order to keep up with the demand for solutions to problems with ever-increasing data sets, both academia and industry have embraced commodity computer clusters with locally attached disks or SANs as an inexpensive alternative to supercomputers. With the advent of tools for parallel disks programming, such as MapReduce, STXXL and Roomythat allow the developer to focus on higher-level algorithms -the programmer productivity for memory-intensive programs has increased many-fold. However, such parallel tools were primarily targeted at iterative programs.We propose a programming model for migrating recursive RAM-based legacy algorithms to parallel disks. Many memory-intensive symbolic algebra algorithms are most easily expressed as recursive algorithms. In this case, the programming challenge is multiplied, since the developer must re-structure such an algorithm with two criteria in mind: converting a naturally recursive algorithm into an iterative algorithm, while simultaneously exposing any potential data parallelism (as needed for parallel disks).This model alleviates the large effort going into the design phase of an external memory algorithm. Research in this area over the past 10 years has focused on per-problem solutions, without providing much insight into the connection between legacy algorithms and out-of-core algorithms. Our method shows how legacy algorithms employing recursion and non-streaming memory access can be more easily translated into efficient parallel disk-based algorithms.We demonstrate the ideas on a largest computation of its kind: the determinization via subset construction and minimization of very large nondeterministic finite set automata (NFA). To our knowledge, this is the largest subset construction reported in the literature. Determinization for large NFA has long been a large computational hurdle in the study of permutation classes defined by token passing networks. The programming model was used to design and implement an efficient NFA determinization algorithm that solves the next stage in analyzing token passing networks representing two stacks in series.

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Section: A General Methods For Migrating Recursive Algorithms From Thementioning

confidence: 99%

Section: A General Methods For Migrating Recursive Algorithms From Thementioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An efficient programming model for memory-intensive recursive algorithms using parallel disks

Slavici

Kunkle

Cooperman

et al. 2012

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

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HPC‐GAP: engineering a 21st‐century high‐performance computer algebra system

Behrends

Hammond

Janjić

et al. 2016

Concurrency and Computation

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SUMMARYSymbolic computation has underpinned a number of key advances in Mathematics and Computer Science. Applications are typically large and potentially highly parallel, making them good candidates for parallel execution at a variety of scales from multi-core to high-performance computing systems. However, much existing work on parallel computing is based around numeric rather than symbolic computations. In particular, symbolic computing presents particular problems in terms of varying granularity and irregular task sizes that do not match conventional approaches to parallelisation. It also presents problems in terms of the structure of the algorithms and data. This paper describes a new implementation of the free open-source GAP computational algebra system that places parallelism at the heart of the design, dealing with the key scalability and cross-platform portability problems. We provide three system layers that deal with the three most important classes of hardware: individual shared memory multi-core nodes, mid-scale distributed clusters of (multi-core) nodes and full-blown high-performance computing systems, comprising large-scale tightly connected networks of multi-core nodes. This requires us to develop new cross-layer programming abstractions in the form of new domain-specific skeletons that allow us to seamlessly target different hardware levels. Our results show that, using our approach, we can achieve good scalability and speedups for two realistic exemplars, on high-performance systems comprising up to 32 000 cores, as well as on ubiquitous multi-core systems and distributed clusters. The work reported here paves the way towards full-scale exploitation of symbolic computation by high-performance computing systems, and we demonstrate the potential with two major case studies.

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Adiar Binary Decision Diagrams in External Memory

Sølvsten

Pol

Jakobsen

et al. 2022

Lecture Notes in Computer Science

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We follow up on the idea of Lars Arge to rephrase the Reduce and Apply operations of Binary Decision Diagrams (BDDs) as iterative I/O-efficient algorithms. We identify multiple avenues to simplify and improve the performance of his proposed algorithms. Furthermore, we extend the technique to other common BDD operations, many of which are not derivable using Apply operations alone. We provide asymptotic improvements to the few procedures that can be derived using Apply.Our work has culminated in a BDD package named Adiar that is able to efficiently manipulate BDDs that outgrow main memory. This makes Adiar surpass the limits of conventional BDD packages that use recursive depth-first algorithms. It is able to do so while still achieving a satisfactory performance compared to other BDD packages: Adiar, in parts using the disk, is on instances larger than 9.5 GiB only 1.47 to 3.69 times slower compared to CUDD and Sylvan, exclusively using main memory. Yet, Adiar is able to obtain this performance at a fraction of the main memory needed by conventional BDD packages to function.

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Parallel disk-based computation for large, monolithic binary decision diagrams

Cited by 13 publications

References 34 publications

An efficient programming model for memory-intensive recursive algorithms using parallel disks

An efficient programming model for memory-intensive recursive algorithms using parallel disks

HPC‐GAP: engineering a 21st‐century high‐performance computer algebra system

Adiar Binary Decision Diagrams in External Memory

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