Efficiently realizing interval sequences

Amotz Bar-Noy, Keerti Choudhary, David Peleg, Dror Rawitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider the problem of realizable interval-sequences. An interval sequence comprises of n integer intervals [ai, bi] such that 0 ≤ ai ≤ bi ≤ n − 1, and is said to be graphic/realizable if there exists a graph with degree sequence, say, D = (d1, . . ., dn) satisfying the condition ai ≤ di ≤ bi, for each i ∈ [1, n]. There is a characterisation (also implying an O(n) verifying algorithm) known for realizability of interval-sequences, which is a generalization of the Erdös-Gallai characterisation for graphic sequences. However, given any realizable interval-sequence, there is no known algorithm for computing a corresponding graphic certificate in o(n2) time. In this paper, we provide an O(n log n) time algorithm for computing a graphic sequence for any realizable interval sequence. In addition, when the interval sequence is non-realizable, we show how to find a graphic sequence having minimum deviation with respect to the given interval sequence, in the same time. Finally, we consider variants of the problem such as computing the most regular graphic sequence, and computing a minimum extension of a length p non-graphic sequence to a graphic one.

Original languageEnglish
Title of host publication30th International Symposium on Algorithms and Computation, ISAAC 2019
EditorsPinyan Lu, Guochuan Zhang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771306
StatePublished - Dec 2019
Externally publishedYes
Event30th International Symposium on Algorithms and Computation, ISAAC 2019 - Shanghai, China
Duration: 8 Dec 201911 Dec 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference30th International Symposium on Algorithms and Computation, ISAAC 2019


  • Graph realization
  • Graphic sequence
  • Interval sequence

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