### Abstract

This paper considers two-dimensional (2-D) retiming, which is the problem of retiming circuits that operate on 2-D signals. We begin by discussing two types of parallelism available in 2-D data processing, which we call inter-iteration parallelism and inter-operation parallelism. We then present two novel techniques for 2-D retiming that can be used to extract inter-operation parallelism. These two techniques are designed to minimize the amount of memory required to implement a 2-D data-flow graph while maintaining a desired clock rate for the circuit. The first technique is based on an integer linear programming (ILP) formulation of the problem, and is called ILP 2-D retiming. This technique considers the entire 2-D retiming problem as a whole, but long central processing unit times are required if the circuit is large. The second technique, called orthogonal 2-D retiming, is a linear programming formulation which is derived by partitioning ILP 2-D retiming into two parts called s- and a-retiming. This technique finds a solution in polynomial time and is much faster than the ILP 2-D retiming technique, but the two sub-problems (s- and a-retiming) can give results which are not compatible with one another. To solve this incompatibility problem, a variation of orthogonal 2-D retiming called integer orthogonal 2-D retiming is developed. This technique runs in polynomial time and the s-retiming and a-retiming steps are guaranteed to give compatible results. We show that the techniques presented in this paper can result in memory hardware savings of 50% compared to previously published 2-D retiming techniques.

Original language | English (US) |
---|---|

Pages (from-to) | 198-211 |

Number of pages | 14 |

Journal | IEEE Transactions on Very Large Scale Integration (VLSI) Systems |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1999 |

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*IEEE Transactions on Very Large Scale Integration (VLSI) Systems*,

*7*(2), 198-211. https://doi.org/10.1109/92.766747

**Two-dimensional retiming.** / Denk, Tracy C.; Parhi, Keshab K.

Research output: Contribution to journal › Article

*IEEE Transactions on Very Large Scale Integration (VLSI) Systems*, vol. 7, no. 2, pp. 198-211. https://doi.org/10.1109/92.766747

}

TY - JOUR

T1 - Two-dimensional retiming

AU - Denk, Tracy C.

AU - Parhi, Keshab K

PY - 1999/1/1

Y1 - 1999/1/1

N2 - This paper considers two-dimensional (2-D) retiming, which is the problem of retiming circuits that operate on 2-D signals. We begin by discussing two types of parallelism available in 2-D data processing, which we call inter-iteration parallelism and inter-operation parallelism. We then present two novel techniques for 2-D retiming that can be used to extract inter-operation parallelism. These two techniques are designed to minimize the amount of memory required to implement a 2-D data-flow graph while maintaining a desired clock rate for the circuit. The first technique is based on an integer linear programming (ILP) formulation of the problem, and is called ILP 2-D retiming. This technique considers the entire 2-D retiming problem as a whole, but long central processing unit times are required if the circuit is large. The second technique, called orthogonal 2-D retiming, is a linear programming formulation which is derived by partitioning ILP 2-D retiming into two parts called s- and a-retiming. This technique finds a solution in polynomial time and is much faster than the ILP 2-D retiming technique, but the two sub-problems (s- and a-retiming) can give results which are not compatible with one another. To solve this incompatibility problem, a variation of orthogonal 2-D retiming called integer orthogonal 2-D retiming is developed. This technique runs in polynomial time and the s-retiming and a-retiming steps are guaranteed to give compatible results. We show that the techniques presented in this paper can result in memory hardware savings of 50% compared to previously published 2-D retiming techniques.

AB - This paper considers two-dimensional (2-D) retiming, which is the problem of retiming circuits that operate on 2-D signals. We begin by discussing two types of parallelism available in 2-D data processing, which we call inter-iteration parallelism and inter-operation parallelism. We then present two novel techniques for 2-D retiming that can be used to extract inter-operation parallelism. These two techniques are designed to minimize the amount of memory required to implement a 2-D data-flow graph while maintaining a desired clock rate for the circuit. The first technique is based on an integer linear programming (ILP) formulation of the problem, and is called ILP 2-D retiming. This technique considers the entire 2-D retiming problem as a whole, but long central processing unit times are required if the circuit is large. The second technique, called orthogonal 2-D retiming, is a linear programming formulation which is derived by partitioning ILP 2-D retiming into two parts called s- and a-retiming. This technique finds a solution in polynomial time and is much faster than the ILP 2-D retiming technique, but the two sub-problems (s- and a-retiming) can give results which are not compatible with one another. To solve this incompatibility problem, a variation of orthogonal 2-D retiming called integer orthogonal 2-D retiming is developed. This technique runs in polynomial time and the s-retiming and a-retiming steps are guaranteed to give compatible results. We show that the techniques presented in this paper can result in memory hardware savings of 50% compared to previously published 2-D retiming techniques.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032678804&partnerID=8YFLogxK

U2 - 10.1109/92.766747

DO - 10.1109/92.766747

M3 - Article

VL - 7

SP - 198

EP - 211

JO - IEEE Transactions on Very Large Scale Integration (VLSI) Systems

JF - IEEE Transactions on Very Large Scale Integration (VLSI) Systems

SN - 1063-8210

IS - 2

ER -