Minimum projective linearizations of trees in linear time
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Cita com:
hdl:2117/354921
Tipus de documentArticle
Data publicació2022-03
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
ProjecteGESTION Y ANALISIS DE DATOS COMPLEJOS (AEI-TIN2017-89244-R)
SISTEMAS DE PRUEBA MAS ALLA DE RESOLUCION: ANALISIS TEORICO (AEI-PID2019-109137GB-C22)
SISTEMAS DE PRUEBA MAS ALLA DE RESOLUCION: ANALISIS TEORICO (AEI-PID2019-109137GB-C22)
Abstract
The Minimum Linear Arrangement problem (MLA) consists of finding a mapping π from vertices of a graph to distinct integers that minimizes {u,v}∈E |π(u) − π(v)|. In that setting, vertices are often assumed to lie on a horizontal line and edges are drawn as semicircles above said line. For trees, various algorithms are available to solve the problem in polynomial time in n = |V |. There exist variants of the MLA in which the arrangements are constrained. Iordanskii, and later Hochberg and Stallmann (HS), put forward O(n)-time algorithms that solve the problem when arrangements are constrained to be planar (also known as one-page book embeddings). We also consider linear arrangements of rooted
trees that are constrained to be projective (planar embeddings where the root is not covered by any edge). Gildea and Temperley (GT) sketched an algorithm for projective arrangements which they claimed runs in O(n) but did not provide any justification of its cost. In contrast, Park and Levy claimed that GT’s algorithm runs in O(n logdmax) where dmax is the maximum degree but did not provide sufficient detail. Here we correct an error in HS’s algorithm for the planar case, show its relationship with the projective case, and derive simple algorithms for the projective and planar cases that run without a doubt in O(n) time.
CitacióAlemany, L.; Esteban, J.L.; Ferrer-i-Cancho, R. Minimum projective linearizations of trees in linear time. "Information processing letters", Març 2022, vol. 174, article 106204, p. 1-7.
ISSN0020-0190
Versió de l'editorhttps://www.sciencedirect.com/science/article/pii/S0020019021001198
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