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Found 8 papers, 2 papers with code
The expected sum of edge lengths in planar linearizations of trees. Theory and applications
In the domain of applications, we derive a $O(n)$-time algorithm to calculate the expected value of the sum of edge lengths.
The Maximum Linear Arrangement Problem for trees under projectivity and planarity
In the projective variant for rooted trees, arrangements have to be planar and the root of the tree cannot be covered by any edge.
The Linear Arrangement Library. A new tool for research on syntactic dependency structures
One of the main concerns in this field is the statistical patterns of syntactic dependency structures.
Linear-time calculation of the expected sum of edge lengths in random projective linearizations of trees
Thus far, the expectation of the sum of dependency distances in random projective shufflings of a sentence has been estimated approximately with a Monte Carlo procedure whose cost is of the order of $Rn$, where $n$ is the number of words of the sentence and $R$ is the number of samples; it is well known that the larger $R$, the lower the error of the estimation but the larger the time cost.
Minimum projective linearizations of trees in linear time
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.
The optimality of syntactic dependency distances
Here we recast the problem of the optimality of the word order of a sentence as an optimization problem on a spatial network where the vertices are words, arcs indicate syntactic dependencies and the space is defined by the linear order of the words in the sentence.
Fast calculation of the variance of edge crossings in random arrangements
The crossing number of a graph $G$, $\mathrm{cr}(G)$, is the minimum number of edge crossings arising when drawing a graph on a certain surface.
Computation Discrete Mathematics Data Structures and Algorithms Combinatorics
