arXiv subjects

Vincent Bian

Publications and source records attributed to Vincent Bian.

3 recordsLinked to original sources

arXiv2023

Improving the Runtime of Algorithmic Polarization of Hidden Markov Models

We improve the runtime of the linear compression scheme for hidden Markov sources presented in a 2018 paper of Guruswami, Nakkiran, and Sudan. Under the previous scheme, compressing a message of length $n$ takes $O(n \log n)$ runtime, and decompressing takes $O(n^{1 + δ})$ runtime for any fixed $δ> 0.$ We present how to improve the runtime of the decoding scheme to $O(n \log n)$ by caching intermediate results to avoid repeating computation.

cs.IT↗

arXiv2021

Edge-Unfolding Prismatoids: Tall or Rectangular Base

We show how to edge-unfold a new class of convex polyhedra, specifically a new class of prismatoids (the convex hull of two parallel convex polygons, called the top and base), by constructing a nonoverlapping "petal unfolding" in two new cases: (1) when the top and base are sufficiently far from each other; and (2) when the base is a rectangle and all other faces are nonobtuse triangles. The latter result extends a previous result by O'Rourke that the petal unfolding of a prismatoid avoids overlap when the base is a triangle (possibly obtuse) and all other faces are nonobtuse triangles. We also illustrate the difficulty of extending this result to a general quadrilateral base by giving a counterexample to our technique.

cs.CG↗

arXiv2018

Special Configurations in Anchored Rectangle Packings

Given a finite set S in $[0,1]^2$ including the origin, an anchored rectangle packing is a set of non-overlapping rectangles in the unit square where each rectangle has a point of S as its left-bottom corner and contains no point of S in its interior. Allen Freedman conjectured in the 1960's one can always find an anchored rectangle packing with total area at least $1/2$. We verify the conjecture for point configurations whose relative positions belong to certain classes of permutations.

math.CO↗