Minimum Cut Linear Arrangement of p-q Dags for VLSI Layout of Adder Trees

Kazuyoshi TAKAGI  Naofumi TAKAGI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.5   pp.767-774
Publication Date: 1999/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
graph algorithm,  minimum cut linear arrangement,  VLSI layout,  adder tree,  multiplier,  

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Two algorithms for minimum cut linear arrangement of a class of graphs called p-q dags are proposed. A p-q dag represents the connection scheme of an adder tree, such as Wallace tree, and the VLSI layout problem of a bit slice of an adder tree is treated as the minimum cut linear arrangement problem of its corresponding p-q dag. One of the two algorithms is based on dynamic programming. It calculates an exact minimum solution within nO(1) time and space, where n is the size of a given graph. The other algorithm is an approximation algorithm which calculates a solution with O(log n) cutwidth. It requires O(n log n) time.