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A Cleanup on Transitive Orientation
 In Orders, Algorithms, and Applications (ORDAL 94), Lecture Notes in Comput. Sci. 831
, 1994
"... . In the past, different authors developed distinct approaches to the problem of transitive orientation. This also resulted in different ideas and different theorems which seem unrelated. In this paper we show the connections between these theories and present a new algorithm to recognize a comparab ..."
Abstract

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. In the past, different authors developed distinct approaches to the problem of transitive orientation. This also resulted in different ideas and different theorems which seem unrelated. In this paper we show the connections between these theories and present a new algorithm to recognize a comparability graph. A comparability graph is an undirected graph G = (V; E), jV j = n, jEj = m, in which every edge may be assigned a direction so that the resulting digraph is a partial order. To the best of our knowledge, literature so far knows mainly two solutions for this problem. The first solution is due to Golumbic [7] and computes a Gdecomposition recursively. This is a partition of the edges into socalled implication classes which define a transitive orientation. This algorithm runs in time O(n \Delta m). The resulting orientation is transitive if the algorithm terminates successfully. The second solution with running time O(n 2 ) was given by Spinrad [11]. This algorithm computes a...