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https://doi.org/10.1007/978-3-031-06007-6We discuss connections between sorting algorithms and graph theory. Taking a graph-theoretic view of sorting, we motivate generalizations of the problem of serial sorting, and describe recent results on parallel sorting, and sorting in rounds, which depend on deep graph-theoretic results.

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Graphs and Order978-94-009-5315-4Series ISSN 1389-2185

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Comparability Graphsts about comparability graphs. We ignore algorithmic aspects of comparability graphs because they are the subject of Möhring [1985]..The characterization problem for comparability graphs was considered first. The same characterization is given in Ghouila-Houri [1962] and in Gilmore and Hoffman [1964

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Algorithmic Aspects of Comparability Graphs and Interval Graphs graphs and partial orders both for theoretical investigations on their structural properties, and the development of efficient algorithmic methods for otherwise NP-hard combinatorial (optimization) problems on partial orders and their comparability graphs..The first part of the paper gives a survey

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The Information Theoretic Bound for Problems on Ordered Sets and Graphsps needed in worst case, where a step consists of a comparison of two elements . and . (this comparison is denoted .). The result of each comparison reduces the set of possible orderings of . to one of two sets: those in which . < . and those in which . < .. Since it is possible that the larger of t

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