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Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach

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Book cover Theoretical Computer Science (ICTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2202))

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Abstract

The purpose of this paper is twofold. First, we review several basic combinatorial problems that have been stated in terms of directed hypergraphs and have been studied in the literature in the framework of different application domains. Among them, transitive closure, transitive reduction, flow and cut problems, and minimum weight traversal problems. For such problems we illustrate some of the most important algorithmic results in the context of both static and dynamic applications. Second, we address a specific dynamic problem which finds several interesting applications, especially in the framework of knowledge representation: the maintenance of minimum weight hyperpaths under hyperarc weight increases and hyperarc deletions. For such problem we provide a new efficient algorithm applicable for a wide class of hyperpath weight measures.

Work partially supported by the ISTP rogramme of the EU under contract number IST-1999-14186 (ALCOM-FT).

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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 Proceedings of Latin American symposium on Theoretical INformatics (LATIN’92), volume 583 of Lecture Notes in Computer Science, pages 1–14. Springer-Verlag, 1992.

    Google Scholar 

  2. C. Alonso, B. Pulido, and G. G. Acosta. On line industrial diagnosis: an attempt to apply arti.cial intelligence techniques to process control. In 11th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems (IEA-98-AIE), volume 1415 of Lecture Notes in Artificial Intelligence, pages 804–813. Springer-Verlag, 1998.

    Google Scholar 

  3. H. R. Andersen. Model checking and boolean graphs. Theoretical Computer Science, 126(1):3–30, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Aráoz. Forward chaining is simple(x). Operations Research Letters, 26:23–26, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Ausiello, A. D’Atri, and D. Saccà. Graph algorithms for functional dependency manipulation. Journal of the ACM, 30(4):752–766, 1983.

    Article  MATH  Google Scholar 

  6. G. Ausiello, A. D’Atri, and D. Saccà. Minimal representation of directed hypergraphs. SIAM Journal on Computing, 15(2):418–431, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. Ausiello, P. G. Franciosa, D. Frigioni, and R. Giaccio. Decremental maintenance of minimum rank hyperpaths and minimum models of Horn formulæ. Technical Report ALCOMFT-TR-01-19, IST Programme of the EU IST-1999-14186 (ALCOM-FT), 2001. http://www.brics.dk/cgi-alcomft/db~state=reports.

  8. G. Ausiello and R. Giaccio. On-line algorithms for satis.ability problems with uncertainty. Theoretical Computer Science, 171(1-2):3–24, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  9. G. Ausiello and G. F. Italiano. On-line algorithms for polynomially solvable satisfiability problems. Journal of Logic Programming, 10(1/2/3-4):69–90, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  10. 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 

  11. G. Ausiello, G. F. Italiano, and U. Nanni. Optimal traversal of directed hypergraphs. Technical Report TR-92-073, International Computer Science Institute, Berkeley, CA, September 1992.

    Google Scholar 

  12. G. Ausiello, G. F. Italiano, and U. Nanni. Hypergraph traversal revisited: Cost measures and dynamic algorithms. In Symposium on Mathematical Foundations of Computer Science (MFCS’98), volume 1450 of Lecture Notes in Computer Science, pages 1–16. Springer-Verlag, 1998.

    Chapter  Google Scholar 

  13. C. Berge. Graphs and Hypergraphs. North-Holland, Amsterdam, The Netherlands, 1973.

    MATH  Google Scholar 

  14. C. Berge. Hypergraphs: combinatorics of finite sets. North-Holland, Amsterdam, The Netherlands, 1989.

    Book  MATH  Google Scholar 

  15. H. Boley. Directed recursive labelnode hypergraphs: A new representation language. Artificial Intelligence, 9(1):49–85, 1977.

    Article  MATH  Google Scholar 

  16. R. Cambini, G. Gallo, and M. G. Scutellà. Flows on hypergraphs. Mathematical Programming, 78:195–217, 1997.

    MathSciNet  Google Scholar 

  17. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to algorithms. MIT Press and McGraw-Hill Book Company, 1992.

    Google Scholar 

  18. J. de Kleer. An assumption based truth maintenance system. Artificial Intelligence, 28:127–162, 1986.

    Article  Google Scholar 

  19. W. F. Dowling and J. H. Gallier. Linear-time algorithms for testing the satis.ability of propositional horn formulæ. Journal of Logic Programming, 1(3):267–284, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  20. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34(3):596–615, 1987.

    Article  MathSciNet  Google Scholar 

  21. G. Gallo, C. Gentile, D. Pretolani, and G. Rago. Max horn SATan d the minimum cut problem in directed hypergraphs. Mathematical Programming, 80:213–237, 1998.

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  23. G. Gallo and G. Rago. A hypergraph approach to logical inference for datalog formulæ. Technical Report TR-28/90, Dipartimento di Informatica, Università di Pisa, Italy, 1990.

    Google Scholar 

  24. S. Gnesi, U. Montanari, and A. Martelli. Dynamic programming as graph searching: An algebraic approach. Journal of the ACM, 28(4):737–751, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  25. G. F. Italiano and U. Nanni. On-line maintenance of minimal directed hypergraphs. In Italian Conference on Theoretical Computer Science, pages 335–349, 1989.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  27. K. Konolige. Abductive theories in arti.cial intelligence. In Principles of Knowledge Representation, pages 129–152. CSLI Publications, 1996.

    Google Scholar 

  28. X. Liu and S. A. Smolka. Simple linear-time algorithms for minimal fixed points. In International Colloquium on Automata, Languages and Programming (ICALP’98), volume 1443 of Lecture Notes in Computer Science, pages 53–65. Springer-Verlag, 1998.

    Chapter  Google Scholar 

  29. D. Maier and J. D. Ullman. Connections in acyclic hypergraphs. In Symposium on Principles of Database Systems (PODS’82), pages 34–39. ACM Press, 1982.

    Google Scholar 

  30. A. Martelli and U. Montanari. Additive and/or graphs. In 3rd International Joint Conference on Artificial Intelligence (IJCAI’73), pages 1–11, 1973.

    Google Scholar 

  31. S. Nguyen and S. Pallottino. Hypergraphs and shortest hyperpaths. In Combinatorial Optimization, volume 1403 of Lecture Notes in Mathematics, pages 258–271. Springer-Verlag, 1986.

    Google Scholar 

  32. N. J. Nilsson. Problem solving methods in Artificial Intelligence. McGraw-Hill, New York, 1971.

    Google Scholar 

  33. D. Pretolani. Satisfiability and hypergraphs. Technical Report TD-12/93, Dipartimento di Informatica, Università di Pisa, Italy, 1993.

    Google Scholar 

  34. D. Pretolani. A directed hypergraph model for random time dependent shortest paths. European Journal of Operational Research, 123:315–324, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  35. G. Ramalingam and T. Reps. An incremental algorithm for a generalization of the shortest-path problem. Journal of Algorithms, 21(2):267–305, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  36. J. D. Ullman. Principles of Database Systems. Computer Science Press, 1982.

    Google Scholar 

  37. H. C. Yen. A unified approach for deciding the existence of certain Petri net paths. Information and Computation, 96(1):119–137, 1992.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    Giorgio Ausiello & Daniele Frigioni

  2. Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza”, Italy

    Paolo G. Franciosa

Authors
  1. Giorgio Ausiello
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  2. Paolo G. Franciosa
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  3. Daniele Frigioni
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Ausiello, G., Franciosa, P.G., Frigioni, D. (2001). Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach. In: Theoretical Computer Science. ICTCS 2001. Lecture Notes in Computer Science, vol 2202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45446-2_20

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  • DOI: https://doi.org/10.1007/3-540-45446-2_20

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  • Print ISBN: 978-3-540-42672-1

  • Online ISBN: 978-3-540-45446-5

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