51 citations · 301 across the 17 of their papers we have counts for
9 papers · 1 filter
Improved upper bounds in the moving sofa problem
Yoav Kallus, Dan Romik
The moving sofa problem, posed by L. Moser in 1966, asks for the planar shape of maximal area that can move around a right-angled corner in a hallway of unit width. It is known tha…
Locally optimal 2-periodic sphere packings
Alexei Andreanov, Yoav Kallus
The sphere packing problem is an old puzzle. We consider packings with m spheres in the unit cell (m-periodic packings). For the case m = 1 (lattice packings), Voronoi proved there…
The local optimality of the double lattice packing
Yoav Kallus, Wöden Kusner
This paper introduces a technique for proving the local optimality of packing configurations. Applying this technique to a general convex polygon, we prove that the construction of…
Pessimal packing shapes
Yoav Kallus
We address the question of which convex shapes, when packed as densely as possible under certain restrictions, fill the least space and leave the most empty space. In each differen…
When is the ball a local pessimum for covering?
Yoav Kallus
We consider the problem of identifying the worst point-symmetric shape for covering n-dimensional Euclidean space with lattice translates. Here we focus on the dimensions where the…
The 3-ball is a local pessimum for packing
Yoav Kallus
It was conjectured by Ulam that the ball has the lowest optimal packing fraction out of all convex, three-dimensional solids. Here we prove that any origin-symmetric convex solid o…