Efficient construction of unit circular-arc models

  • Authors:

  • Min Chih Lin;Jayme L. Szwarcfiter

  • Affiliations:

  • Universidad de Buenos Aires, Buenos Aires, Argentina;Universidade Federal do Rio de Janeiro, RJ, Brasil

  • Venue:
  • SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
  • Year:
  • 2006

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Abstract

In a recent paper, Durán, Gravano, McConnell, Spinrad and Tucker described an algorithm of complexity O(n2) for recognizing whether a graph G with n vertices is a unit circular-arc (UCA) graph. Furthermore the following open questions were posed in the above paper: (i) Is it possible to construct a UCA model for G in polynomial time? (ii) Is it possible to construct a model, whose extremes of the arcs correspond to integers of polynomial size? (iii) If (ii) is true, could such a model be constructed in polynomial time? In the present paper, we describe a characterization of UCA graphs which leads to linear time algorithms for recognizing UCA graphs and constructing UCA models. Furthermore, we construct models whose extreme of the arcs correspond to integers of size O(n). The proposed algorithms provide positive answers to the three above questions.