Remarks on some concurrency measures

  • M. Habib
  • M. Morvan
  • J. X. Rampon
Multiprocessor Systems And Concurrency
Part of the Lecture Notes in Computer Science book series (LNCS, volume 484)


The aim of the present work is to bring together problems and new results (namely vector clock labelling introduced by Fidge [1988] and Mattern [1989], concurrency measures proposed by Charron-Bost [1989] and Fidge [1989]) in concurrency theory with old and new results developped in computational order theory (interval orders, lattice of maximal antichains, minimax antichains). We hope that this approach will be fruitful in both domains, for example we discuss some new measures and their associated computational complexity, that can be of some interest.


concurrency parallelism distributed computations partial orders interval orders antichains computational complexity disgraphs 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. M. Aigner, "Combinatorial Theory", Springer-Verlag, 1979.Google Scholar
  2. M.D. Atkinson, "The complexity of Orders", in Algorithms and Order, (I. Rival, ed.) Kluwer Acad. Publ., Dordrecht (1989) 195–230.Google Scholar
  3. V. Bouchitté, M. Habib, "The calculation of invariants for ordered sets", in Algorithms and Order, (I. Rival, ed.) Kluwer Acad. Publ., Dordrecht (1989) 231–279.Google Scholar
  4. K.M. Chandy, L. Lamport, "Distributed snapshots: determining global states of distributed systems", in ACM Trans on Computer Systems, vol. 3, No1 (1985) 63–75.Google Scholar
  5. B. Charron-Bost, "Combinatorics and geometry of consistent cuts: application to concurrency theory", Rapport de Recherche de l'Ecole Normale Supérieure, Paris, Liens No89-3, avril 89.Google Scholar
  6. B. Charron-Bost, "Mesures de la concurrence et du parallélisme des calculs répartis", Thèse de Doctorat, Université Paris VII, 1989.Google Scholar
  7. D.G. Corneil, Y. Perl, "Clustering and domination in perfect graphs", Discrete Applied Math. (1984).Google Scholar
  8. S.A. Cook, "The complexity of theorem proving procedures", Proc. 3rd Ann. ACM Symp. on Theory of Computing (1971) 151–158.Google Scholar
  9. R.P. Dilworth, "Some combinatorial problems on partially ordered sets", in R. Bellman, M. Hall (ed.), Combinatorial Analysis, Proc. Symp. Appl. Math., vol. 10, AMS, Providence (1960) 85–90.Google Scholar
  10. J. Fidge, "Timestamps in message-passing systems that preserve the partial ordering", Proc. 11th Australian Computer Science Conference (1988) p. 56–66.Google Scholar
  11. J. Fidge, "A simple run-time concurrency measure", preprint 1989.Google Scholar
  12. P.C. Fishburn, "Interval orders and interval graphs", Wiley, 1985.Google Scholar
  13. M.R. Garey, D.S. Johnson, "Computers and intractability: a guide to the theory of NP-completeness", Freeman, 1979.Google Scholar
  14. M.C. Golumbic, "Algorithmic graph theory and perfect graphs", Academic Press, New-York, 1980.Google Scholar
  15. M.C. Golumbic, "Interval graphs and related topics", Discrete Mathematics 55 (1985) 113–121.Google Scholar
  16. P. Grillet, "Maximal chains and antichains", Fund. Math. 65 (1969), 157–167.Google Scholar
  17. M. Habib, R. Jegou, "N-free posets as generalizations of series-parallel posets", Discret Appl. Math. 12(3) (1985), 279–291.Google Scholar
  18. M. Habib, M. Morvan, J.X. Rampon, "About minimal interval order extensions", Research Report CRIM, No84, juin 90.Google Scholar
  19. J.M. Helary, N. Plouzeau, M. Raynal, "A characterization of a particular class of distributed snapshots", in Proc. of Int. Conf. on Computing and Information (ICCC'89), Toronto, North-Holland (1989) 23–27.Google Scholar
  20. T. Hiraguchi, "On the dimension of partially ordered sets", Sci. Rep. Kanazawa Univ. 4 (1955) 77–94.Google Scholar
  21. D. Kelly, W.T. Trotter, "Dimension theory for ordered sets", in "Ordered sets", I. Rival ed., D. Reidel Publishing Company (1982) 171–211.Google Scholar
  22. N. Korte, R.H. Möhring, "An incremental linear-time algorithm to recognize intervals graphs", SIAM Journal of Computing 18 (1989) 68–81.Google Scholar
  23. L. Lamport, "Time, clock and the ordering of the events in a distributed system", Comm. of the ACM 21:7 (1978) 551–565.Google Scholar
  24. B. Leclerc, B. Monjardet, "Orders ‘C.A.C.'", Fund. Math. 79 (1973), 11–22.Google Scholar
  25. Ma, J. Spinrad, "Avoiding matrix multiplication" same issue.Google Scholar
  26. F. Mattern, "Virtual time and global states of distributed systems", in Parallel and Distributed Algorithms, M. Cosnard et al. (Ed.), Elsevier Science Publications (North-Holland), (1989) 215–226.Google Scholar
  27. F. Mattern, "Asynchronous distributed termination — parallel and symmetric solutions with echo algorithms", Algorithmica (1990) 5: 325–340.Google Scholar
  28. R.H. Möhring, "Algorithmic aspects of comparability graphs and interval graphs", in Graphs and Order (I. Rival, ed.) D. REIDEL, Dordrecht (1985) 41–102.Google Scholar
  29. R.H. Möhring, "Computationally tractable classes of ordered sets", in Algorithms and Order, (I. Rival, ed.), Kluwer Acad. Publ., Dordrecht, (1989) 105–193.Google Scholar
  30. D.S. Parker, et al., "Detection of mutual inconsistency in distributed systems", IEEE Transactions on Software Engineering, vol. SE-9, No3, May (1983) 240–246.Google Scholar
  31. J.S. Provan and M.O. Ball, "The complexity of counting cuts and of computing the probability that a graph is connected", SIAM J. Comput. 12, 777–788 (1983).Google Scholar
  32. K. Reuter, "The jump number and the lattice of maximal antichains", preprint Darmstadt, 1989, to appear in Discrete mathematics.Google Scholar
  33. I. Rival, "Optimal linear extensions by interchanging chains", Proc. Amer. Math. Soc. 89 (1982), 387–394.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • M. Habib
    • 1
  • M. Morvan
    • 1
  • J. X. Rampon
    • 1
  1. 1.C.R.I.M., (CNRS & Université de Montpellier II)MontpellierFrance

Personalised recommendations