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Simultaneous representation of interval and interval-containment orders

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We characterize the polysemic interval pairs—pairs of posets that admit simultaneous interval and interval-containment representations—and present algorithms to recoginze them and construct polysemic interval representations.

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  1. 1.

    Dushnik, B. and Miller, E. W. (1941) Partially ordered sets, Amer. J. Math. 63, 600–610.

  2. 2.

    Even, S. and Itai, A. (1971) Queues, Stacks and Graphs, in Theory of Machines and Computations, Z.Kohavi and A.Paz (eds), Academic Press, New York, pp. 71–86.

  3. 3.

    Fishburn, P. C. (1985) Interval Orders and Interval Graphs.: A Study of partially Ordered Sets, John Wiley, New York.

  4. 4.

    Golumbic, M. C. (1980) Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York.

  5. 5.

    Golumbic, M. C. and Shamir, R. (1993) Complexity and algorithms for reasoning about time: A graph theoretic approach, J. Assoc. Comput. Mach. 40(5), 1108–1133.

  6. 6.

    Kendall, D. G. (1969) Incidence matrices, interval graphs, and seriation in archaeology, Pacific J. Math. 28, 565–570.

  7. 7.

    Nökel, K. (1991) Temporally Distributed Symptoms in Technical Diagnosis, Lecture Notes in Artificial Intelligence, no. 517, Springer-Verlag, New York.

  8. 8.

    Papadimitriou, C. and Yannakakis, M. (1979) Scheduling interval ordered tasks, SIAM J. Comput. 8, 405–409.

  9. 9.

    Tanenbaum, P. J. (1995) On geometric representations of partially ordered sets Ph.D. Thesis, The Johns Hopkins University.

  10. 10.

    Tanenbaum, P. J. and Whitesides, S. (1996) Simultaneous dominance representation of multiple posets, Order 13, 351–364 (this issue).

  11. 11.

    Wiener, N. (1914) A contribution to the theory of relative position, Proc. Cambridge Philos. Soc. 17, 441–449.

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This work, supported in part by NSF grant CCR-9300079, also appears in the author's doctoral thesis [9], written at the Johns Hopkins University under the supervision of Professors Edward R. Scheinerman and Michael T. Goodrich.

Communicated by I. Rival

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Tanenbaum, P.J. Simultaneous representation of interval and interval-containment orders. Order 13, 339–350 (1996). https://doi.org/10.1007/BF00405593

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Mathematics Subject Classifications (1991)

  • 06A07
  • 68U05

Key words

  • polysemy
  • interval orders
  • interval containment orders