We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a non-split link due to [2, 3]. Building on this and using the chirality of torus knots and ...
Let d and t be fixed positive integers, and let denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem ...
This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without ...
We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...
We study the impact of metric constraints on the realizability of planar graphs. Let G be a subgraph of a planar graph H (where H is the "host" of G). The graph G is free in H if for every choice of positive lengths for the edges of G, the host H has a pla ...
We present a novel method for building a multiresolution representation of large digital surface models. The surface points coincide with the nodes of a planar graph which can be processed using a critically sampled, invertible lifting scheme. To drive the ...
Artists and architects often need to handle multiple constraints during design of physical constructions. We define a performative constraint as any constraint on design that is tied to the performance of the model--either during fabrication, construction, ...
Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, an ...
The Hanani--Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generali ...
