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Hypergraph traversal revisited: Cost measures and dynamic algorithms

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

Directed hypergraphs are used in several applications to model different combinatorial structures. A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. A hyperpath, similarly to the notion of path in directed graphs, consists of a connection among nodes using hyperarcs. Unlike paths in graphs, however, hyperpaths are suitable of many different definitions of measure, corresponding to different concepts arising in various applications. In this paper we consider the problem of finding optimal hyperpaths according to several measures. We also provide results that may shed some light on the intrinsic complexity of finding optimal hyperpaths.

Work supported in part by EU ESPRIT Long Term Research Project ALCOM-IT under contract no. 20244.

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References

  1. P. Alimonti, E. Feuerstein, and U. Nanni. Linear time algorithms for liveness and boundedness in conflict-free petri nets. In 1st Latin American Theoretical Informatics, volume 583, pages 1–14. Lecture Notes in Computer Science, Springer-Verlag, 1992.

    Google Scholar 

  2. G. Ausiello, A. D'Atri, and D. Saccà. Graph algorithms for functional dependency manipulation. Journal of the ACM, 30:752–766, 1983.

    Article  MATH  Google Scholar 

  3. G. Ausiello, A. D'Atri, and D. Saccà. Minimal representation of directed hypergraphs. SIAM Journal on Computing, 15:418–431, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Ausiello, R. Giaccio. On-line algorithms for satisfiability formulae with uncertainty. Theoretical Computer Science 171:3–24, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Ausiello, R. Giaccio, G. F. Italiano, and U. Nanni. Optimal traversal of directed hypergraphs. Manuscript, 1997.

    Google Scholar 

  6. G. Ausiello and G. F. Italiano. Online algorithms for polynomially solvable satisfiability problems. Journal of Logic Programming, 10:69–90, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. Ausiello, G. F. Italiano, and U. Nanni. Dynamic maintenance of directed hypergraphs. Theoretical Computer Science, 72(2–3):97–117, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34:596–615, 1987.

    Article  MathSciNet  Google Scholar 

  9. G. Gallo, G. Longo, S. Nguyen, and S. Pallottino. Directed hypergraphs and applications. Discrete Applied Mathematics 42 (1993) 177–201.

    Article  MATH  MathSciNet  Google Scholar 

  10. G. Gallo and G. Rago. A hypergraph approach to logical inference for Datalog formulae. Technical Report 28/90, Dip. di Informatica, Univ. of Pisa, Italy, 1990.

    Google Scholar 

  11. G. F. Italiano and U. Nanni. On line maintenance of minimal directed hypergraphs. In 3rd Italian Conf. on Theoretical Computer Science, pages 335–349. World Scientific Co., 1989.

    Google Scholar 

  12. D. E. Knuth. A generalization of Dijkstra's algorithm. Information Processing Letters, 6(1):1–5, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. B. Miltersen. On-line reevaluation of functions. Technical Report DAIMI PB-380, Comp. Sci. Dept., Aarhus University, January 1992.

    Google Scholar 

  14. S. Nguyen and S. Pallottino. Hyperpaths and shortest hyperpaths. Combinatorial Optimization, 1403:258–271, 1989.

    MATH  MathSciNet  Google Scholar 

  15. G. Ramalingam and T. Reps, An Incremental Algorithm for a Generalization of the Shortest Path Problem, Journal of Algorithms, 21:267–305, 1996.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Italy

    Giorgio Ausiello & Umberto Nanni

  2. Dipartimento di Matematica Applicata ed Informatica, Università “Ca' Foscari” di Venezia, Italy

    Giuseppe F. Italiano

Authors
  1. Giorgio Ausiello
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  2. Giuseppe F. Italiano
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  3. Umberto Nanni
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Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Ausiello, G., Italiano, G.F., Nanni, U. (1998). Hypergraph traversal revisited: Cost measures and dynamic algorithms. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055754

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  • DOI: https://doi.org/10.1007/BFb0055754

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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