Abstract
The first linear algorithm for recognizing interval graphs was presented by Booth and Leuker[4] in 1976. The first phase of this algorithm finds a perfect elimination scheme and determines all maximal cliques A 1,..., A s , of a given graph using the fact that interval graphs are a proper subclass of chordal graphs. This part is based on a lexicographic breadth first search (for short lexBFS) which is also used in other areas such as scheduling problems [18][5]. In the second phase the PQ-tree data structure is used to get a representation of all possible consecutive arrangements of all maximal cliques A 1,..., A s . Korte and Möhring[13], 1989, improved this algorithm by a more adaptive version of PQ-trees, so called MPQ-trees, for the second phase. In this paper we show a new solution of the second phase by repeated use of lexBFS, which produces a linear arrangement of the maximal cliques A 1,..., A s , if there is one.
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© 1991 Springer-Verlag Berlin Heidelberg
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Simon, K. (1991). A new simple linear algorithm to recognize interval graphs. In: Bieri, H., Noltemeier, H. (eds) Computational Geometry-Methods, Algorithms and Applications. CG 1991. Lecture Notes in Computer Science, vol 553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54891-2_22
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DOI: https://doi.org/10.1007/3-540-54891-2_22
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