[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/aeg/wpaper/2010-18.html
   My bibliography  Save this paper

Classification and Traversal Algorithmic Techniques for Optimization Problems on Directed Hyperpaths

Author

Listed:
  • Giorgio Ausiello

    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

  • Giuseppe F. Italiano

    (Dipartimento di Informatica, Sistemi e Produzione, Universita' di Roma Tor Vergata", via del Politecnico 1, 00133, Roma, Italy.)

  • Luigi Laura

    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

  • Umberto Nanni

    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

  • Fabiano Sarracco

    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

Abstract
Directed hypergraphs are used in several applications to model different combinatorial struc- tures. 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, which have been used in a wide set of applications. Not surprisingly, depending on the considered measure function the cost of finding optimal hyperpaths may range from NP-hard to linear time. A first solution for finding optimal hyperpaths in case of a superior functions (SUP) can be found in a seminal work by Knuth [Knu77], which generalizes Dijkstra's Algorithm [Dij59] to deal with a grammar problem. This solution is further extended by Ramalingam and Reps [RR96] to deal with weakly superior functions (WSUP). Dijkstra's priority queue can find optimal paths or hyperpaths if the measure function complies two hypotheses: it is monotone with respect to all its arguments and (multidimensional) triangle inequality holds. We show that monotonicity - alone - is sufficient to guarantee interesting properties, and to make some optimization algorithms effective. Hence we introduce the generalized superior function (GSUP), and consider the symmetrical classes of inferior functions, giving rise to a hierarchy of classes of optimization problems on directed hypergraphs. After showing that some measure functions might induce cycles in optimal hyperpaths, we come up to another taxonomy of measure functions, based on the structure of the optimal hyperpaths they determine, and relate the two hierarchies. Finally we introduce a general algorithmic pattern for the single-source optimal hyperpath problem encompassing existing and new algorithms, and compare their effectiveness in various cases, including the case of optimal cyclic hyperpaths.

Suggested Citation

  • Giorgio Ausiello & Giuseppe F. Italiano & Luigi Laura & Umberto Nanni & Fabiano Sarracco, 2010. "Classification and Traversal Algorithmic Techniques for Optimization Problems on Directed Hyperpaths," DIS Technical Reports 2010-18, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    • Handle: RePEc:aeg:wpaper:2010-18
    as

    Download full text from publisher

    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/wpaper/2010-18.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Paola Alimonti & Esteban Feuerstein & Luigi Laura & Umberto Nanni, 2010. "Linear Time Analysis of Properties of Conflict-Free and General Petri nets," DIS Technical Reports 2010-09, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aeg:wpaper:2010-18. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Antonietta Angelica Zucconi (email available below). General contact details of provider: https://edirc.repec.org/data/dirosit.html .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.