1 / 13

Depth-Bounded Communication Complexity for Distributed Computation

This project investigates the depth-bounded communication complexity in distributed computation, focusing on minimizing communication for two physically separated parties engaged in a computation task within specified depth limits. It highlights the importance of localizing computation tasks in system-on-chip designs to mitigate long-distance communication costs. The project reviews prior work in communication complexity, introduces new problem formulations, and categorizes various combinational and sequential instances. Future work is suggested, exploring effective techniques and potential formulations.

albany
Télécharger la présentation

Depth-Bounded Communication Complexity for Distributed Computation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Depth-Bounded Communication Complexity for Distributed Computation Student: Jie-Hong Jiang Mentor: Prof. Robert Brayton EE249 Class Project 12/3/2002

  2. Motivation • In system-on-chip design, computation tasks may be localized in some particular locations (e.g. analog/digital separations) • Avoid long distance (delay) communication • An embedded system interacts with its environment, which may span over a large area • Localize computation tasks • Communication costs among different locations may be quite high (due to implementation, noise, delay, etc.) • Minimize communication links and depths

  3. Problem formulation • Given a computation task T(I,O) , two physically separated parties A(I1,O1) and B(I2,O2) want to fulfill task T using minimum amount of communication within a specified depth • Assume X1  X2 = X and X1  X2 = , where X = {I, O}

  4. Prior work • Communication complexity has been intensively studied in the community of theoretical computer science since 1979 • Yao’s formulation is the most well-studied • Assume the two parties in communication have unbounded computation power • Use protocol tree to represent the communication behavior • The height of tree = bits communicated

  5. What has been missing ? • Communication depths • Sharing of communication links

  6. Categorization • Combinational instances with one-sided outputs, i.e. (O1= O, O2= ) • Combinational instances with two-sided outputs, i.e. (O1, O2) • Sequential instances (finite-state machines)

  7. Combinational instance: One-sided output (O1= O, O2= ) • Reduce functional matrix representation • Merge identical rows and columns • Equivalent communication complexity analysis • Use multi-valued representation for multi-output functions

  8. Combinational instance: One-sided output (O1= O, O2= ) • Communication depths should be captured in embedded system design • Assume the two parties in communication have unbounded computation power. This is fine even for combinational implementations.

  9. Combinational instance: One-sided output (O1= O, O2= ) • Slicing functional matrices vs. building protocol trees • Limited alternating communication • Lower bounds • Depth-1, lg (#column) • Depth-k, minall protocol { i=1,…,k lg (max #branch at level i) }

  10. Combinational instance: Two-sided output (O1, O2) • Reduce functional matrix representation • Use multi-valued representation for multi-output functions row merging column merging

  11. Combinational instance: Two-sided output (O1, O2) • Sharing communication links may result in combinational cycles • Sometimes is essential to achieve minimum communication • Might possibly have ambiguous causalities (cause bi-stable, oscillation behaviors)

  12. Sequential instance • Degenerate state equivalence relation between two parties in communication • Take advantage of this partial information to reduce interaction • Compute partial information by Galois connection • Approximate by combinational techniques

  13. Conclusions and future work • We give a formulation for the analysis of the depth-bounded communication complexity problem • Effective techniques need to be explored • Language equation formulation ? • Game-theoretic formulation ? • Nash equilibrium may not even be local optimal for selfish row and column players • Cooperative games

More Related