Breadth-first manipulation of SBDD of Boolean functions for vector processing

Ochi, Hiroyuki; Ishiura, Nagisa; Yajima, Shuzo

doi:10.1145/127601.127704

Cited by 40 publications

(26 citation statements)

References 5 publications

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“…This algorithm relies on a depth first traversal algorithm. In [22] a breadth first traversal algorithm with the same time bound is given.…”

Section: Obdds and Previous Resultsmentioning

confidence: 99%

“…This makes the previously developed breadth first algorithm [22] work in a levelwise manner. Implementing the algorithms they obtained runtime speedups of several hundreds compared to an implementation using depth first algorithms.…”

Section: Obdds and Previous Resultsmentioning

confidence: 99%

“…Very recently Ashar and Cheong [5] showed how to develop levelwise algorithms without introducing extra vertices, and conducted experiments which showed that on large OBDDs their algorithms outperform all other known algorithms. As the general idea (levelwise algorithms) are the same in [22] and [5], we will only consider the latter paper here. Finally, it should be mentioned that Klarlund and Rauhe in [16] report significant runtime improvements when working on OBDDs fitting in internal memory and using algorithms taking advantage of the blocked transport of data between cache and main memory.…”

Section: Obdds and Previous Resultsmentioning

confidence: 99%

“…If not the vertex is given a new unique label and inserted in the table. The implementations reported in [5,6,22,23] all use this general idea. From a theoretical point of view the table uses a lot of space, namely O(n · |G| 2 ), but using "lazy initialization" [2] the running time of the algorithm can be kept at O(|G|), as that is the number of entries in the table which is actually used.…”

Section: Reduce Algorithmsmentioning

confidence: 99%

“…Ordered BinaryDecision Diagrams (OBDDs) [7,8] are the state-of-the-art data structure for boolean function manipulation and they have been successfully used to solve problems from all of the above mentioned areas. There exist implementations of OBDD software packages for a number of sequential and parallel machines [5,6,22,23]. Even though there exist very different sized OBDD representations of the same boolean function, OBDDs in real applications tend to be very large.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The I/O-Complexity of Ordered Binary-Decision Diagram Manipulation

Arge¹

1996

BRICS

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Ordered Binary-Decision Diagrams (OBDD) are the state-of-theart data structure for boolean function manipulation and there exist several software packages for OBDD manipulation. OBDDs have been successfully used to solve problems in e.g. digital-systems design, verification and testing, in mathematical logic, concurrent system design and in artificial intelligence. The OBDDs used in many of these applications quickly get larger than the avaliable main memory and it becomes essential to consider the problem of minimizing the Input/Output (I/O) communication. In this paper we analyze why existing OBDD manipulation algorithms perform poorly in an I/O environment and develop new I/O-efficient algorithms. * An extended abstract version of this paper was presented at the Sixth International Symposium on Algorithms and Computation (ISAAC'95).

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“…This algorithm relies on a depth first traversal algorithm. In [22] a breadth first traversal algorithm with the same time bound is given.…”

Section: Obdds and Previous Resultsmentioning

confidence: 99%

Section: Obdds and Previous Resultsmentioning

confidence: 99%

Section: Obdds and Previous Resultsmentioning

confidence: 99%

Section: Reduce Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The I/O-Complexity of Ordered Binary-Decision Diagram Manipulation

Arge¹

1996

BRICS

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Memory optimization in function and set manipulation with BDDs

Cabodi¹,

Quer²,

Camurati³

1998

Softw: Pract. Exper.

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SUMMARYBinary Decision Diagrams (BDDs) are the state-of-the-art technique for many synthesis, verification and testing problems in CAD for VLSI. Many researchers proposed optimized BDD-based representations, but in many complex applications the (working) memory required is still too much. Virtual memory is no alternative solution, because if the working set size for a program is large and memory accesses are random, an extremely large number of page faults significantly modifies the performance of the software. This paper proposes a solution to this problem for a specific application, namely BDD-based exploration of large state spaces, an issue often found in CAD for VLSI. Our 'divide-and-conquer' approach for reachability analysis is based on decomposition of state sets carried out at different levels and on an effective use of mass memory. As a result, we are able to explore the state space of large Finite State Machines. At the same time, the technique we develop is orthogonal to a variety of symbolic techniques and graph manipulation procedures and it allows reducing complexity of very common operations. Experimental results, on well known synchronous benchmarks usually used in the field of CAD for VLSI, show that this approach is particularly effective on larger problems as decomposition decreases the amount of working memory, avoids page faulting and makes the overall process more efficient.

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Acceleration of relational database operations on vector processors

Meki

Kambayashi

2000

Syst. Comp. Jpn.

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With the expansion of the areas of database applications, the amount of data processed has become gigantic, and the demand for faster database systems has increasingly intensified. Thus, many efforts have been expended to execute database operations more efficiently using special hardware. However, for the cases in which mass-produced LSI cannot be used, cost has become excessive, and replacement methods have been sought. Vector processors have powerful pipeline operators and large-capacity main memories and have rapidly spread in recent years. In this paper, algorithms for relational database operations suitable for vector processors showing the characteristics of vector processors sufficiently are presented. This algorithm is based on the hash method, which is highly efficient when the capacity of the main memory is large, and it is shown that a rate of acceleration more than 10 times the average is obtained for representative relational database operations when this algorithm is executed on a vector processor. © 2000 Scripta Technica, Syst Comp Jpn, 31(8): 7988, 2000

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Breadth-first manipulation of SBDD of Boolean functions for vector processing

Cited by 40 publications

References 5 publications

The I/O-Complexity of Ordered Binary-Decision Diagram Manipulation

The I/O-Complexity of Ordered Binary-Decision Diagram Manipulation

Memory optimization in function and set manipulation with BDDs

Acceleration of relational database operations on vector processors

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