[1]

Alfred V. Aho, Jeffrey E. Hopcroft, and John D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley series in computer science and information processing. Addison-Wesley Publishing Company, Michigan University, 1st edition, 1974.

[2]

Lluís Alemany-Puig and Ramon Ferrer-i-Cancho. Edge crossings in random linear arrangements. Journal of Statistichal Mechanics, 2020:023403, 2020.

[3]

Lluís Alemany-Puig and Ramon Ferrer-i-Cancho. Fast calculation of the variance of edge crossings. arXiv, 2021.

[4]

Lluís Alemany-Puig and Ramon Ferrer-i-Cancho. Linear-time calculation of the expected sum of edge lengths in planar linearizations of trees. Arxiv, 2022.

[5]

Lluís Alemany-Puig and Ramon Ferrer-i-Cancho. Linear-time calculation of the expected sum of edge lengths in projective linearizations of trees. Computational Linguistics, 48(3):491–516, 04 2022.

[6]

Lluís Alemany-Puig, Juan Luis Esteban, and Ramon Ferrer-i-Cancho. Minimum projective linearizations of trees in linear time. Information Processing Letters, 174:106204, 2022.

[7]

Lluís Alemany-Puig, Juan Luis Esteban, and Ramon Ferrer-i-Cancho. On The Maximum Linear Arrangement Problem for Trees. arXiv, 2023.

[8]

Lluís Alemany-Puig, Juan Luis Esteban, and Ramon Ferrer-i-Cancho. The maximum linear arrangement problem for trees under projectivity and planarity. Information Processing Letters, 183:106400, 2024.

[9]

Lluís Alemany-Puig. Edge crossings in linear arrangements: from theory to algorithms and applications.. Master Thesis (M. Sc.), 2019.

[10]

Lluís Alemany-Puig. Theory, Algorithms and Applications of Arrangements of Graphs: Generation, Expectation and Optimization. PhD thesis, Universitat Politécnica de Catalunya – Barcelonatech, 2024.

[11]

Mark Anderson, David Vilares, and Carlos Gómez-Rodríguez. Artificially Evolved Chunks for Morphosyntactic Analysis. In Proceedings of the 18th International Workshop on Treebanks and Linguistic Theories (TLT, SyntaxFest 2019), pages 133–143, Paris, France, 08 2019. Association for Computational Linguistics.

[12]

Mark Anderson. An Unsolicited Soliloquy on Dependency Parsing. PhD thesis, Universidade da Coruña, 2021.

[13]

Patrick Bennett, Sean English, and Maria Talanda-Fisher. Weighted Turán problems with applications. Discrete Mathematics, 342:2165–2172, 8 2019.

[14]

Terry Beyer and Sandra Mitchell Hedetniemi. Constant Time Generation of Rooted Trees. SIAM Journal on Computing, 9(4):706–712, 1980.

[15]

Fan R. K. Chung. On optimal linear arrangements of trees. Computers & Mathematics with Applications, 10(1):43–60, 1984.

[16]

Charles J. Colbourn and Kellogg S. Booth. Linear Time Automorphism Algorithms for Trees, Interval Graphs, and Planar Graphs. SIAM Journal on Computing, 10(1):203–225, 1981.

[17]

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. The MIT Press, Cambridge, MA, USA, 2nd edition, 2001.

[18]

Matt DeVos and Kathryn Nurse. A Maximum Linear Arrangement Problem on Directed Graphs. arXiv, 2018.

[19]

Juan Luis Esteban and Ramon Ferrer-i-Cancho. A Correction on Shiloach's Algorithm for Minimum Linear Arrangement of Trees. SIAM Journal on Computing, 46(3):1146–1151, 2017.

[20]

Ramon Ferrer-i-Cancho, Carlos Gómez-Rodríguez, and Juan Luis Esteban. Are crossing dependencies really scarce? Physica A: Statistical Mechanics and its Applications, 493:311–329, 2018.

[21]

Ramon Ferrer-i-Cancho. Euclidean distance between syntactically linked words. Physical Review E, 70(5):5, 2004.

[22]

Ramon Ferrer-i-Cancho. A stronger null hypothesis for crossing dependencies. EPL (Europhysics Letters), 108(5):58003, 12 2014.

[23]

Ramon Ferrer-i-Cancho. The sum of edge lengths in random linear arrangements. Journal of Statistichal Mechanics, 2019(5):053401, 2019.

[24]

Richard Futrell, Kyle Mahowald, and Edward Gibson. Large-scale evidence of dependency length minimization in 37 languages. Proceedings of the National Academy of Sciences, 112(33):10336–10341, 2015.

[25]

Daniel Gildea and David Temperley. Optimizing Grammars for Minimum Dependency Length. In Proceedings of the 45th Annual Meeting of the Association of Computational Linguistics, pages 184–191, Prague, Czech Republic, 06 2007. Association for Computational Linguistics.

[26]

The GNU Multiple Precision Arithmetic Library. https://gmplib.org/. Accessed: 2020-03-24.

[27]

Carlos Gómez-Rodríguez, John Carroll, and David Weir. Dependency Parsing Schemata and Mildly Non-Projective Dependency Parsing. Computational Linguistics, 37(3):541–586, 2011.

[28]

Frank Harary and Allen J. Schwenk. The number of caterpillars. Discrete Mathematics, 6:359–365, 1973.

[29]

Frank Harary. Graph Theory. CRC Press, Boca Raton, FL, USA, 2nd edition, 1969.

[30]

Robert A. Hochberg and Matthias F. Stallmann. Optimal one-page tree embeddings in linear time. Information Processing Letters, 87(2):59–66, 2003.

[31]

Yingqi Jing and Haitao Liu. Mean hierarchical distance. Augmenting mean dependency distance. In Proceedings of the Third International Conference on Dependency Linguistics, pages 161–170, 2015.

[32]

Sylvain Kahane, Chunxiao Yan, and Marie-Amélie Botalla. What are the limitations on the flux of syntactic dependencies? Evidence from UD treebanks. In Proceedings of the Fourth International Conference on Dependency Linguistics, pages 73–82, 9 2017.

[33]

Richard M. Karp. Reducibility among Combinatorial Problems, pages 85–103. Springer US, Boston, MA, 1972.

[34]

Haitao Liu. Dependency direction as a means of word-order typology: a method based on dependency treebanks. Lingua, 120(6):1567–1578, 2010.

[35]

Ján Macutek, Radek Cech, and Marine Courtin. The Menzerath-Altmann law in syntactic structure revisited. In Proceedings of the Second Workshop on Quantitative Syntax (Quasy, SyntaxFest 2021), pages 65–73, Sofia, Bulgaria, 12 2021. Association for Computational Linguistics.

[36]

Luka Marohnić. Graph theory package for Giac/Xcas - Reference manual. https://usermanual.wiki/Document/graphtheoryusermanual.346702481/view, 2018. Accessed: 2020-01-13.

[37]

Spider Graph – Wolfram Math World. https://mathworld.wolfram.com/SpiderGraph.html. Accessed: 2022-10-04.

[38]

Albert Nijenhuis and Herbert S. Wilf. Combinatorial Algorithms: For Computers and Hard Calculators. Academic Press, Inc., Orlando, FL, USA, 2nd edition, 1978.

[39]

Kathryn Nurse. Maximum linear arrangement of directed graphs. Master's thesis, Simon Fraser University, 2019.

[40]

Richard Otter. Annals of Mathematics The Number of Trees. 49(3):583–599, 1948.

[41]

Heinz Prüfer. Neuer Beweis eines Satzes über Permutationen. Arch. Math. Phys, 27:742–744, 1918.

[42]

Giorgio Satta, Emily Pitler, Sampath Kannan, and Mitchell Marcus. Finding Optimal 1-Endpoint-Crossing Trees. In Transactions of the Association for Computational Linguistics, pages 13–24, 2013.

[43]

Yossi Shiloach. A Minimum Linear Arrangement Algorithm for Undirected Trees. SIAM Journal on Computing, 8(1):15–32, 1979.

[44]

N. J. A. Sloane. The On-line Encyclopedia of Integer Sequences - A000055 - Number of trees with n unlabeled nodes. https://oeis.org/A000055. Accessed: 2019-12-28.

[45]

N. J. A. Sloane. The On-line Encyclopedia of Integer Sequences - A000081 - Number of unlabeled rooted trees with n nodes (or connected functions with a fixed point). https://oeis.org/A000081. Accessed: 2019-03-31.

[46]

Neil James Alexander Sloane. The On-Line Encyclopedia of Integer Sequences - A338706 - Number of \(2\)-linear trees on \(n\) nodes. https://oeis.org/A338706, 1964-2022. Accessed: 2022-10-07.

[47]

Tanay Wakhare, Eric Wityk, and Charles R. Johnson. The proportion of trees that are linear. Discrete Mathematics, 343(10):112008, 2020.

[48]

Herbert S. Wilf. The uniform selection of free trees. Journal of Algorithms, 2:204–207, 1981.

[49]

Robert Alan Wright, Bruce Richmond, Andrew Odlyzko, and Brendan D. McKay. Constant Time Generation of Free Trees. SIAM Journal on Computing, 15:540–548, 05 1986.