Minimum Monotone Spanning Trees
Emilio Di Giacomo, Walter Didimo, Eleni Katsanou, Lena Schlipf,, Antonios Symvonis, Alexander Wolff

TL;DR
This paper introduces a new class of monotone spanning trees constrained by a set of directions, providing polynomial-time algorithms for their computation and analyzing their structural properties.
Contribution
It characterizes ${\
Findings
Polynomial-time algorithms for fixed number of directions
Existence of high-degree vertices in minimum ${\
paper_type
Abstract
Computing a Euclidean minimum spanning tree of a set of points is a seminal problem in computational geometry and geometric graph theory. We combine it with another classical problem in graph drawing, namely computing a monotone geometric representation of a given graph. More formally, given a finite set of points in the plane and a finite set of directions, a geometric spanning tree with vertex set is -monotone if, for every pair of vertices of , there exists a direction for which the unique path from to in is monotone with respect to . We provide a characterization of -monotone spanning trees. Based on it, we show that a -monotone spanning tree of minimum length can be computed in polynomial time if the number of directions is fixed, both when (i) the set of…
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Optical Network Technologies · Interconnection Networks and Systems
