Computational complexity analysis of determinant decision diagram

Authors:
Guoyong Shi
Affiliations:
School of Microelectronics, Shanghai Jiao Tong University, Shanghai, China
Venue:
IEEE Transactions on Circuits and Systems II: Express Briefs
Year:
2010

Citing 7
Cited 2

Graph-Based Algorithms for Boolean Function Manipulation

IEEE Transactions on Computers
Zero-suppressed BDDs for set manipulation in combinatorial problems

DAC '93 Proceedings of the 30th international Design Automation Conference
Fast Analog Circuit Synthesis Using Multiparameter Sensitivity Analysis Based on Element-Coefficient Diagrams

ISVLSI '05 Proceedings of the IEEE Computer Society Annual Symposium on VLSI: New Frontiers in VLSI Design
Symbolic analysis of analog circuits containing voltage mirrors and current mirrors

Analog Integrated Circuits and Signal Processing
Canonical symbolic analysis of large analog circuits with determinant decision diagrams

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Hierarchical symbolic analysis of analog integrated circuits via determinant decision diagrams

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient approximation of symbolic expressions for analog behavioral modeling and analysis

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

A simple implementation of determinant decision diagram

Proceedings of the International Conference on Computer-Aided Design
A survey on binary decision diagram approaches to symbolic analysis of analog integrated circuits

Analog Integrated Circuits and Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

A determinant decision diagram (DDD) uses a binary decision diagram (BDD) to calculate a determinant symbolically, which is then applied for symbolic circuit analysis. The efficiency of such a technique is determined mainly by a symbol ordering scheme. Finding an optimal symbol order is an nondeterministic polynomial-time hard problem in the practice of BDD. So far, it is unknown what an optimal order is for a general sparse matrix. This brief shows that a row-wise (or column-wise) order is an optimal BDD order for full matrices in the sense that the DDD graph constructed has the minimum number of vertices (i.e., the DDD size). The optimal DDD size is proven to be (n ċ 2n-1) for an n × n full matrix. This size provides a DDD complexity measure that has rarely been investigated in the literature.