Irina Kostitsyna

Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

A geometric graph is angle-monotone if every pair of vertices has a path between them that—after some rotation—is x- and y-monotone. Angle-monotone graphs are \(\sqrt{2}\)-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized angle-monotone—specifically, we prove that the half-\(\theta _6\)-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex s to any vertex t whose length is within \(1 + \sqrt{2}\) times the Euclidean distance from s to t. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.

Algorithmic Traffic Abstraction and its Application to NextGen Generic Airspace

We develop traffic abstraction algorithms that, given a set of 4D Trajectories (4DTs), extract the traffic structure in terms of standard flows and critical points (conflict and merge points). We demonstrate the application of our techniques to enable the NextGen generic airspace concept. We also analyze historical demand data to evaluate the level of abstraction underlying the en-route traffic within high-altitude sectors. Finally, we compare the structure of historical traffic to user preferred, wind optimal futuristic trajectories.

On Minimizing Crossings in Storyline Visualizations

In a storyline visualization, we visualize a collection of interacting characters e.g., in a movie, play, etc. by x-monotone curves that converge for each interaction, and diverge otherwise. Given a storyline with n characters, we show tight lower and upper bounds on the number of crossings required in any storyline visualization for a restricted case. In particular, we show that if 1 each meeting consists of exactly two characters and 2 the meetings can be modeled as a tree, then we can always find a storyline visualization with

Simple wriggling is hard unless you are a fat hippo

On\log n

Single-player and two-player buttons & scissors games

crossings. Furthermore, we show that there exist storylines in this restricted case that require

Scandinavian thins on top of cake: on the smallest one-size-fits-all box

\varOmega n\log n