Planar Straight-Line Embedding of Double-Tree Scan Architecture on a Rectangular Grid

Abstract

Double-tree-scan (DTS) is a new scan-path architecture that is deemed to be suitable for low-power testing of VLSI circuits. A full DTS resembles two complete k-level (k > 0) binary trees whose leaf nodes are merged pair-wise, and thus consists of exactly N$_{k}$ = 3 × 2$^{k}$ − 2 nodes. In this paper, the problem of planar straight-line embedding of a graph on a rectangular grid is investigated and an O(N$_{k}$) time algorithm for drawing it, is described. The embedding requires at most 2N$_{k}$ grid points, with an aspect ratio lying between 1 and f. Next, techniques of embedding a partial DTS is considered when the number of nodes n ≠ 3 × 2$^{k}$ − 2, for some k. Layouts of double-tree scan-paths for some benchmark circuits are also presented to demonstrate the results.