Implementation Techniques for Fast OBDD Dynamic Variable Reordering

Hiroshige FUJII

Implementation Techniques for Fast OBDD Dynamic Variable Reordering

Hiroshige FUJII

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Ordered binary decision diagrams (OBDDs) have been widely used in many CAD applications as efficient data structures for representing and manipulating Boolean functions. For the efficient use of the OBDD, it is essential to find a good variable order, because the size of the OBDD heavily depends on its variable order. Dynamic variable reordering is a promising solution to the variable ordering problem of the OBDD. Dynamic variable reordering with the sifting algorithm is especially effective in minimizing the size of the OBDD and reduces the need to find a good initial variable order. However, it is very time-consuming for practical use. In this paper, we propose two new implementation techniques for fast dynamic variable reordering. One of the proposed techniques reduces the number of variable swaps by using the lower bound of the OBDD size, and the other accelerates the variable swap itself by recording the node states before the swap and the pivot nodes of the swap. By using these new techniques, we have achieved the speed-up ranging from 2.5 to 9.8 for benchmark circuits. These techniques have reduced the disadvantage of dynamic variable reordering and have made it more attractive for users.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E78-A No.12 pp.1729-1734

Publication Date: 1995/12/25

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Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)

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Hiroshige FUJII, "Implementation Techniques for Fast OBDD Dynamic Variable Reordering" in IEICE TRANSACTIONS on Fundamentals, vol. E78-A, no. 12, pp. 1729-1734, December 1995, doi: .
Abstract: Ordered binary decision diagrams (OBDDs) have been widely used in many CAD applications as efficient data structures for representing and manipulating Boolean functions. For the efficient use of the OBDD, it is essential to find a good variable order, because the size of the OBDD heavily depends on its variable order. Dynamic variable reordering is a promising solution to the variable ordering problem of the OBDD. Dynamic variable reordering with the sifting algorithm is especially effective in minimizing the size of the OBDD and reduces the need to find a good initial variable order. However, it is very time-consuming for practical use. In this paper, we propose two new implementation techniques for fast dynamic variable reordering. One of the proposed techniques reduces the number of variable swaps by using the lower bound of the OBDD size, and the other accelerates the variable swap itself by recording the node states before the swap and the pivot nodes of the swap. By using these new techniques, we have achieved the speed-up ranging from 2.5 to 9.8 for benchmark circuits. These techniques have reduced the disadvantage of dynamic variable reordering and have made it more attractive for users.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e78-a_12_1729/_p

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@ARTICLE{e78-a_12_1729,
author={Hiroshige FUJII, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Implementation Techniques for Fast OBDD Dynamic Variable Reordering},
year={1995},
volume={E78-A},
number={12},
pages={1729-1734},
abstract={Ordered binary decision diagrams (OBDDs) have been widely used in many CAD applications as efficient data structures for representing and manipulating Boolean functions. For the efficient use of the OBDD, it is essential to find a good variable order, because the size of the OBDD heavily depends on its variable order. Dynamic variable reordering is a promising solution to the variable ordering problem of the OBDD. Dynamic variable reordering with the sifting algorithm is especially effective in minimizing the size of the OBDD and reduces the need to find a good initial variable order. However, it is very time-consuming for practical use. In this paper, we propose two new implementation techniques for fast dynamic variable reordering. One of the proposed techniques reduces the number of variable swaps by using the lower bound of the OBDD size, and the other accelerates the variable swap itself by recording the node states before the swap and the pivot nodes of the swap. By using these new techniques, we have achieved the speed-up ranging from 2.5 to 9.8 for benchmark circuits. These techniques have reduced the disadvantage of dynamic variable reordering and have made it more attractive for users.},
keywords={},
doi={},
ISSN={},
month={December},}

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TY - JOUR
TI - Implementation Techniques for Fast OBDD Dynamic Variable Reordering
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1729
EP - 1734
AU - Hiroshige FUJII
PY - 1995
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E78-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 1995
AB - Ordered binary decision diagrams (OBDDs) have been widely used in many CAD applications as efficient data structures for representing and manipulating Boolean functions. For the efficient use of the OBDD, it is essential to find a good variable order, because the size of the OBDD heavily depends on its variable order. Dynamic variable reordering is a promising solution to the variable ordering problem of the OBDD. Dynamic variable reordering with the sifting algorithm is especially effective in minimizing the size of the OBDD and reduces the need to find a good initial variable order. However, it is very time-consuming for practical use. In this paper, we propose two new implementation techniques for fast dynamic variable reordering. One of the proposed techniques reduces the number of variable swaps by using the lower bound of the OBDD size, and the other accelerates the variable swap itself by recording the node states before the swap and the pivot nodes of the swap. By using these new techniques, we have achieved the speed-up ranging from 2.5 to 9.8 for benchmark circuits. These techniques have reduced the disadvantage of dynamic variable reordering and have made it more attractive for users.
ER -