### Recent Submissions

• #### Map construction algorithms: a local evaluation through hiking data ﻿

(2020-02-26)
Article
Restricted access - publisher's policy
We study five existing map construction algorithms, designed and tested with urban vehicle data in mind, and apply them to hiking trajectories with different terrain characteristics. Our main goal is to better understand ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel graphs ﻿

(2020-08)
Article
Restricted access - publisher's policy
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape $$\mathcal {C}$$ . Let S be a point ...
• #### Convex quadrangulations of bichromatic point sets ﻿

(2020-06-05)
Article
Restricted access - publisher's policy
We consider quadrangulations of red and blue points in the plane where each face is convex and no edge connects two points of the same color. In particular, we show that the following problem is NP-hard: Given a finite set ...
• #### The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability ﻿

(2019-12-01)
Article
Open Access
We study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, ...
• #### Computing optimal shortcuts for networks ﻿

(Elsevier, 2019-11-16)
Article
Restricted access - publisher's policy
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received ...
• #### Region-based approximation of probability distributions (for visibility between imprecise points among obstacles) ﻿

(2019-07)
Article
Open Access
Let p and q be two imprecise points, given as probability density functions on R2 , and let O be a set of disjoint polygonal obstacles in R2 . We study the problem of approximating the probability that p and q can see each ...
• #### Capturing points with a rotating polygon (and a 3D extension) ﻿

(2019-04)
Article
Open Access
We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on ...
• #### Antimagic labelings of caterpillars ﻿

(2019-04-15)
Article
Open Access
A k-antimagic labeling of a graph G is an injection from E(G) to {1,2, ..., |E(G)|+k} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident ...
• #### A note on flips in diagonal rectangulations ﻿

(Chapman & Hall/CRC, 2018-11-09)
Article
Open Access
Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. ...
• #### On the complexity of barrier resilience for fat regions and bounded ply ﻿

(2018-06)
Article
Open Access
In the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions so ...
• #### Colored ray configurations ﻿

(2018-05)
Article
Open Access
We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We ...
• #### New results on production matrices for geometric graphs ﻿

(2018-07-01)
Article
Open Access
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of ...