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Title: The cost of embedding


This report describes the cost of embedding and its implication for quantum computing.

  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Technical Report
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Computer Science; Mathematics

Citation Formats

Lemons, Nathan Wishard. The cost of embedding. United States: N. p., 2017. Web. doi:10.2172/1364582.
Lemons, Nathan Wishard. The cost of embedding. United States. doi:10.2172/1364582.
Lemons, Nathan Wishard. 2017. "The cost of embedding". United States. doi:10.2172/1364582.
title = {The cost of embedding},
author = {Lemons, Nathan Wishard},
abstractNote = {This report describes the cost of embedding and its implication for quantum computing.},
doi = {10.2172/1364582},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 6

Technical Report:

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  • Parallel computations often yield computation structures which are trees; the shape of such a tree evolves over time as the computation progresses. However, parallel computers are usually designed as networks of processors with fixed connections; it is therefore important to embed the dynamic structure of a computation efficiently in a fixed network. The authors consider the problem of dynamically embedding an evolving binary tree with, at most, N nodes in an N-node hypercube. They present a simple randomized algorithm which uses only local control and guarantees constant dilation, while maintaining constant load with high probability; this is the first load-balancingmore » algorithm that achieves constant dilation. They also prove that random solutions to this problem are highly desirable, by demonstrating that any deterministic embedding algorithm which maintains constant load must have omega (square root of log N) dilation.« less
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