Continuous Yao Graphs
In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points $S⊂ ℝ^2$ and an angle $0 < Θ łeq 2π$, …
Theta-3 is connected
In this paper, we show that the $Θ$-graph with three cones is connected. We also provide an alternative proof of the connectivity of …
New and Improved Spanning Ratios for Yao Graphs
For a set of points in the plane and a fixed integer $k > 0$, the Yao graph $Y_k$ partitions the space around each point into $k$ …
Necklaces, Convolutions, and X + Y
We give subquadratic algorithms that, given two necklaces each with $n$ beads at arbitrary positions, compute the optimal rotation of …
Sum of Squared Edges for MST of a Point Set in a Unit Square
Non-crossing Matchings of Points with Geometric Objects
Cannibal Animal Games: a new variant of Tic-Tac-Toe
Colorful Strips
Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing …
Matching Points with Things
Relaxed Gabriel Graphs
The Distance Geometry of Music
We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of …
Reconstructing Points on a Circle from Labeled Distances
Convergence of the shadow sequence of inscribed polygons
A Pumping Lemma for Homometric Rhythms
Evenness preserving operations on musical rhythms
Vertex Pops and Popturns
On Rolling Cube Puzzles
We analyze the computational complexity of various rolling cube puzzles.
Deflating The Pentagon
Geometric properties of musical rhythms
Curves in the Sand: Algorithmic Drawing
The Distance Geometry of Deep Rhythms and Scales
Hamiltonian Cycles in Sparse Vertex-Adjacency Duals
Orderly Broadcasting in a 2D Torus