How to Assemble Tree Machines
Name
MIT-LCS-TM-255.pdf
Size
4.35 MB
Format
Adobe PDF
Checksum (MD5)
0c0e5d80f3f0844fab31da05f95392e4
Author(s)
Bhatt, Sandeep Nautam
Leiserson, Charles E.
Date Issued
March 1984
Series/Report no.
MIT-LCS-TM-255
Abstract
Many researchers have proposed that ensembles of processing elements be organized as trees. This paper explores how large tree machines can be assembled efficiently from smaller components. A principal constraint considered is the limited number of external connections from an integrated circuit chip. We also explore the emerging capabilities of restructurable VLSI which allows a chip to be customized after fabrication. We give a linear-area chip of m processors and only four off-chip connections which can be used as the sole building block to construct an arbirtarily large complete binary tree. We also present a restructurable linear-areas layout of m processors with O(lg m) pins that can realize an arbitrary binary tree of any size. This layout is based on a solution to the graph-theoretic problem: Given a tree in which each vertex is either black or white, determine how many edges need to be cut in order to bisect the tree into equal-size components, each containing exactly half the black and half the white vertices. These ideas extend to more general graphs using separator theoerems and bifurcators.
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