Implementation of Finite Lattices in VLSI for Fault-State Encoding in High-Speed Networks

  • Andreas C. Döring
  • Gunther Lustig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1800)


In this paper the propagation of information about fault states and its implementation in high-speed networks is discussed. The algebraic concept of a lattice (partial ordered set with supremum and infimum) is used to describe the necessary operation. It turns out that popular algorithms can be handled this way. Using the properties of lattices efficient implementation options can be found.


Fault State Fault Region Boolean Lattice Finite Lattice Bottom Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AGSY94]
    James D. Allen, Patrick T. Gaughan, David E. Schimmel, and Sudhakar Yalamanchili. Ariadne — an adaptive router for fault-tolerant multicomputers. In Proceedings of the 21st Annual International Symposium on Computer Architecture, pages 278–288, Chicago, Illinois, April 18–21, 1994. IEEE Computer Society TCCA and ACM SIGARCH.Google Scholar
  2. [BCF+95] Nanette J. Boden, Danny Cohen, Robert E. Felderman, Alan E. Kulawik, Charles L. Seitz, Jakov N. Seizovic, and Wen-King Su. Myrinet: A gigabit-per-second local-area network. IEEE Micro, 15(1), February 1995.Google Scholar
  3. [CA95]
    Chris M. Cunningham and Dimiter R. Avresky. Fault-Tolerant Adaptive Routing for Two-Dimensional Meshes. In Proceedings of the First International Symposium on High-Performance Computer Architecture, pages 122–131, Raleigh, North Carolina, January 1995. IEEE Computer Society.Google Scholar
  4. [CS90]
    Ming-Syan Chen and Kang G. Shin. Depth-First Search Approach for Fault-Tolerant Routing in Hypercube Multicomputers. IEEE Transactions on Parallel and Distributed Systems, 1(2):152–159, April 1990.CrossRefMathSciNetGoogle Scholar
  5. [CW96]
    Ge-Ming Chiu and Shui-Pan Wu. A Fault-Tolerant Routing Strategy in Hypercube Multicomputers. IEEE Transactions on Computers, 45(2):143–155, February 1996.zbMATHCrossRefGoogle Scholar
  6. [DOL98]
    A. C. Döring, W. Obelöer, and G. Lustig. Programming and Implementation of Reconfigurable Routers. In Proc. Field Programmable Logic and Applications. 8th International Workshop, FPL’ 98, volume 1482 of Lecture Notes in Computer Science, pages 500–504, 1998.Google Scholar
  7. [DOLM98]
    Andreas C. Döring, Wolfgang Obelöer, Gunther Lustig, and Erik Maehle. A Flexible Approach for a Fault-Tolerant Router. In Proc. Parallel and Distributed Processing-Proceedings of 10 IPPS/SPDP’ 98 Workshops, volume 1388 of Lecture Notes in Computer Science, pages 693–713, 1998.Google Scholar
  8. [Kyu79]
    Shoji Kyuno. An Inductive Algorithm to Construct Finite Lattices. Mathematics of Computation, 33(145):409–421, January 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [TW98]
    Ming-Jer Tsai and Sheng-De Wang. A fully adaptive routing algorithm. IEEE Transactions on Parallel and Distributed Systems, 9(2):163–174, February 1998.CrossRefGoogle Scholar
  10. [Wu98]
    Jie Wu. Adaptive Fault-Tolerant Routing in Cube-Based Multicomputers Using Safety Vectors. IEEE Transactions on Parallel and Distributed Systems, 9(4):321–334, April 1998.CrossRefGoogle Scholar
  11. [Xil98]
    Xilinx, Inc. XC4000XV Family Field Programmable Gate Arrays. Data Sheet, May 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Andreas C. Döring
    • 1
  • Gunther Lustig
    • 1
  1. 1.Institut für Technische InformatikMedizinische Universität zu LübeckLübeckGermany

Personalised recommendations