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Threshold graphs and synchronization protocols

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Combinatorics and Computer Science (CCS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1120))

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Abstract

This paper is a survey on the synchronization of a system of cooperating processes, when the mutual exclusion graph model and the semaphores are used. Threshold graphs and PVchunk semaphores are explained. Matroidal and matrogenic graphs are presented and their synchronization with a constant number of semaphores for each process are pointed out. Threshold dimension of a graph is explained and a sketched proof of its NP-completeness for k≥3 and of the polynomiality for k=2 is provided.

The interest in characterizing new classes of graphs not 2-threshold, but synchronizable with a constant number of semaphores, is shown.

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References

  1. Eisenberg M. A. and McGuire M. R. Further comments on Dijkstra's concurrent programming control problem. Comm. ACM, 15(11), 1972.

    Google Scholar 

  2. V. Chvátal and P. L. Hammer. Aggregation of inequalities in integer programming. Ann. Disc. Math., 1:145–162, 1977.

    Google Scholar 

  3. S. De Agostino and R. Petreschi. Parallel recognition algorithms for graphs with restricted neighbourhoods. Int. J. of Foundations of Comp. Sci., 1(2):123–130, 1990.

    Article  Google Scholar 

  4. S. De Agostino and R. Petreschi. On PVchunk operations and matrogenic graphs. Int. J. of Foundations of Comp. Sci., 3(1):11–20, 1992.

    Article  Google Scholar 

  5. E. W. Dijkstra. Cooperating sequential processes. In F. Genuys, editor, Programming Languages. Academic Press, New York, 1968.

    Google Scholar 

  6. Burns J. E. Symmetry in systems of asynchronous processes. In Proc. 22nd Annual Symp. on Foundations of Computer Science, pages 164–174, 1981.

    Google Scholar 

  7. Knuth D. E. Additional comments on a problem in concurrent programming control. Comm. ACM, 9(5):321–322, 1966.

    Article  Google Scholar 

  8. P. C. Fishburn. Interval Orders and Interval Graphs. Wiley, New York, 1985.

    Google Scholar 

  9. P. C. Fishburn. Intransitive indifference with unequal indifference intervals. Journal of Math. Psych., 7:144–149, 70.

    Google Scholar 

  10. S. Földes and P. L. Hammer. On a class of matroid-producing graphs. Colloq. Math. Soc. J. Bolyai (Combinatorics), 18:331–352, 1978.

    Google Scholar 

  11. De Bruijn J. G. Additional comments on a problem in concurrent programming control. Comm. ACM, 10(3):137–138, 1967.

    Article  Google Scholar 

  12. Le Lann G. Distributed systems, towards a formal approach. In IFIP Congress, pages 155–160, 1977.

    Google Scholar 

  13. Ricart G. and Agrawala A. K. An optimal algorithm for mutual exclusion in computer networks. Comm. ACM, 24(1):9–17, 1981. Corrigendum in Comm. ACM, 24 (9).

    Article  Google Scholar 

  14. Ricart G. and Agrawala A. K. Author's response to ‘on mutual exclusion in computer networks’ by carvalho and roucariol. Comm. ACM, 26(2):147–148, 1983.

    Google Scholar 

  15. M. R. Garey and D. S. Johnson. Computers and intractability. A guide to the theory of NP-completeness. W. H. Freeman and Co., San Francisco, 1979.

    Google Scholar 

  16. P. C. Gilmore and A. J. Hoffman. A characterization of comparability graphs and of interval graphs. Canad. J. Math., 16:539–548, 1964.

    Google Scholar 

  17. P. B. Henderson and Y. Zalkstein. A graph-theoretic characterization of the PVchunk class of synchronising primitives. SIAM J. Comput., 6(1):88–108, 1977.

    Article  Google Scholar 

  18. Suzuki I. and Kasami T. An optimality theory for mutual exclusion algorithms in computer networks. In Proc. of the 3rd Int. Conf. On Distributed Computing Systems, pages 365–370, Miami, 1982.

    Google Scholar 

  19. T. Ibaraki and U. N. Peled. Sufficient conditions for graphs to have threshold number 2. In P. Hansen, editor, Studies on Graphs and Discrete Programming, pages 241–268. Nort-Holland Publishing Company, Amsterdam, 1981.

    Google Scholar 

  20. Lamport L. A new solution of Dijkstra's concurrent programming problem. Comm. ACM, 17(8):453–455, 1974.

    Article  Google Scholar 

  21. Lamport L. Time, clocks and the ordering of events in a distributed system. Comm. ACM, 21(7):558–565, 1978.

    Article  Google Scholar 

  22. Peterson G. L. Myths about the mutual exclusion problem. Inf. Proc. Lett., 12(3):115–116, 1981.

    Article  Google Scholar 

  23. Peterson G. L. A new solution to Lamport's concurrent programming problem using shared variables. ACM Toplas, 5(1):56–65, 1983.

    Article  Google Scholar 

  24. Tze-Heng Ma. On the thresold dimension 2 graphs, manuscript, September 1993.

    Google Scholar 

  25. N. V. R. Mahadev and U. N. Peled. Threshold Graphs and Related Topics. Elsevier Publishers, 1995.

    Google Scholar 

  26. P. Marchioro, A. Morgana, R. Petreschi, and B. Simeone. Degree sequences of matrogenic graphs. Discrete Math., 51:47–61, 1984.

    Article  Google Scholar 

  27. Carvalho O. and Roucairol G. On mutual exclusion in computer networks. Comm. ACM, 26(2):146–147, 1983.

    Google Scholar 

  28. E. T. Ordman. Minimal threshold separators and memory requirements for synchronization. SIAM J. Comput., 18(1):152–165, 1989.

    Article  Google Scholar 

  29. J. Orlin. The minimal integral separator of a threshold graph. Ann. Disc. Math., 1:415–419, 1977.

    Google Scholar 

  30. U. N. Peled. Matroidal graphs. Discrete Math., 20:263–286, 1977.

    Google Scholar 

  31. Hehner E. C. R. and Shyamasundar R. K. An implementation of P and V. Inf. Proc. Lett., 12(4):196–198, 1981.

    Article  Google Scholar 

  32. Thomas Raschle and Klaus Simon. Recognition of graphs with threshold dimension two. In The 27th Annual ACM Symposium on Theory of Computing, Las Vegas, NE, 1995.

    Google Scholar 

  33. Thomas Raschle and Andrea Sterbini. 2-threshold graphs can be recognized in O(n3) time. Private communication.

    Google Scholar 

  34. Michel Raynal. Algorithms for mutual exclusion. North Oxford Academic, 1986.

    Google Scholar 

  35. Andrea Sterbini. 2-Thresholdness and its Implications: from the Synchronization with PV chunk to the Ibaraki-Peled Cojecture. PhD thesis, University of Rome ”La Sapienza”, 1994.

    Google Scholar 

  36. H. Vantilborgh and A. van Lamsweerde. On an extension of Dijkstra's semaphore primitives. Inform. Process. Lett., 1:181–186, 1972.

    Article  Google Scholar 

  37. Dijkstra E. W. Co-operating sequential processes. In F. Genuys, editor, Programming Languages, pages 43–112. Academic Press, New York, 1965.

    Google Scholar 

  38. Dijkstra E. W. Self-stabilizing systems in spite of distributed control. Comm. ACM, 17(11):643–644, 1974.

    Article  Google Scholar 

  39. Doran R. W. and Thomas L. K. Variants of the software solution to mutual exclusion. Inf. Proc. Lett., 10(4):206–208, 1980.

    Article  Google Scholar 

  40. Kessels J. L. W. Arbitration without common modifiable variables. Acta Informatica, 17:135–141, 1982.

    Article  Google Scholar 

  41. M. Yannakakis. The complexity of the partial order dimension problem. SIAM J. Algebraic Discrete Methods, 3(3):351–358, 1982.

    Google Scholar 

  42. K. Yue and R. T. Jacob. An efficient starvation-free semaphore solution for the graphical mutual exclusion problem. Comput. J., 34(4):345–349, 1991.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University ”La Sapienza”, Via Salaria, 113-00198, Rome, Italy

    Rossella Petreschi & Andrea Sterbini

Authors
  1. Rossella Petreschi
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  2. Andrea Sterbini
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Michel Deza Reinhardt Euler Ioannis Manoussakis

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© 1996 Springer-Verlag Berlin Heidelberg

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Petreschi, R., Sterbini, A. (1996). Threshold graphs and synchronization protocols. In: Deza, M., Euler, R., Manoussakis, I. (eds) Combinatorics and Computer Science. CCS 1995. Lecture Notes in Computer Science, vol 1120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61576-8_97

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  • DOI: https://doi.org/10.1007/3-540-61576-8_97

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61576-7

  • Online ISBN: 978-3-540-70627-4

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