Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
M. Aigner, "Combinatorial Theory", Springer-Verlag, 1979.
M.D. Atkinson, "The complexity of Orders", in Algorithms and Order, (I. Rival, ed.) Kluwer Acad. Publ., Dordrecht (1989) 195–230.
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.
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.
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.
B. Charron-Bost, "Mesures de la concurrence et du parallélisme des calculs répartis", Thèse de Doctorat, Université Paris VII, 1989.
D.G. Corneil, Y. Perl, "Clustering and domination in perfect graphs", Discrete Applied Math. (1984).
S.A. Cook, "The complexity of theorem proving procedures", Proc. 3rd Ann. ACM Symp. on Theory of Computing (1971) 151–158.
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.
J. Fidge, "Timestamps in message-passing systems that preserve the partial ordering", Proc. 11th Australian Computer Science Conference (1988) p. 56–66.
J. Fidge, "A simple run-time concurrency measure", preprint 1989.
P.C. Fishburn, "Interval orders and interval graphs", Wiley, 1985.
M.R. Garey, D.S. Johnson, "Computers and intractability: a guide to the theory of NP-completeness", Freeman, 1979.
M.C. Golumbic, "Algorithmic graph theory and perfect graphs", Academic Press, New-York, 1980.
M.C. Golumbic, "Interval graphs and related topics", Discrete Mathematics 55 (1985) 113–121.
P. Grillet, "Maximal chains and antichains", Fund. Math. 65 (1969), 157–167.
M. Habib, R. Jegou, "N-free posets as generalizations of series-parallel posets", Discret Appl. Math. 12(3) (1985), 279–291.
M. Habib, M. Morvan, J.X. Rampon, "About minimal interval order extensions", Research Report CRIM, No84, juin 90.
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.
T. Hiraguchi, "On the dimension of partially ordered sets", Sci. Rep. Kanazawa Univ. 4 (1955) 77–94.
D. Kelly, W.T. Trotter, "Dimension theory for ordered sets", in "Ordered sets", I. Rival ed., D. Reidel Publishing Company (1982) 171–211.
N. Korte, R.H. Möhring, "An incremental linear-time algorithm to recognize intervals graphs", SIAM Journal of Computing 18 (1989) 68–81.
L. Lamport, "Time, clock and the ordering of the events in a distributed system", Comm. of the ACM 21:7 (1978) 551–565.
B. Leclerc, B. Monjardet, "Orders ‘C.A.C.'", Fund. Math. 79 (1973), 11–22.
Ma, J. Spinrad, "Avoiding matrix multiplication" same issue.
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.
F. Mattern, "Asynchronous distributed termination — parallel and symmetric solutions with echo algorithms", Algorithmica (1990) 5: 325–340.
R.H. Möhring, "Algorithmic aspects of comparability graphs and interval graphs", in Graphs and Order (I. Rival, ed.) D. REIDEL, Dordrecht (1985) 41–102.
R.H. Möhring, "Computationally tractable classes of ordered sets", in Algorithms and Order, (I. Rival, ed.), Kluwer Acad. Publ., Dordrecht, (1989) 105–193.
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.
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).
K. Reuter, "The jump number and the lattice of maximal antichains", preprint Darmstadt, 1989, to appear in Discrete mathematics.
I. Rival, "Optimal linear extensions by interchanging chains", Proc. Amer. Math. Soc. 89 (1982), 387–394.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Habib, M., Morvan, M., Rampon, J.X. (1991). Remarks on some concurrency measures. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1990. Lecture Notes in Computer Science, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53832-1_45
Download citation
DOI: https://doi.org/10.1007/3-540-53832-1_45
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53832-5
Online ISBN: 978-3-540-46310-8
eBook Packages: Springer Book Archive