Csaba
D. Tóth
Associate Professor
Department of Mathematics
California State University, Northridge
Room SN 434, 18111 Nordhoff St
Northridge, CA 913308313
Phone: (818) 6772826
cdtoth ♠ acm.org
Manuscripts

Maximum area axisaligned square packings,
 Hugo A. Akitaya, Matthew D. Jones, David Stalfa, and Csaba D. Tóth,
 manuscript, 2018.
 (abstract)
Given a point set S={s_{1},...,s_{n}} in the unit square U=[0,1]^{2}, an anchored square packing is a set of n interiordisjoint squares in U such that s_{i} is a corner of the ith square. The reach R(S) of S is the set of points that may be covered by such a packing (i.e., the union of all squares anchored at points in S).
It is shown that area(R(S))≥1/2 for every S⊂U, and this bound is the best possible.
The region R(S) can be computed in O(n log n) time. Finally, we show that finding a maximum area anchored square packing is NPcomplete. This is the first hardness proof for a square packing problem where the possible sizes of the squares are not part of the input.

On convex polygons in Cartesian products,
 JeanLou De Carufel, Adrian Dumitrescu, Wouter Meulemans, Tim Ophelders, Claire Pennarun, Csaba D. Tóth, and Sander Verdonschot,
 submitted, 2018.

Optimal cutting of a polygon by lasers,
 Esther Arkin, Peter Brass, Rathish Das, Jie Gao, Mayank Goswami, Joseph S.B. Mitchell, Valentin Polishchuk, and Csaba D. Tóth,
 in Abstracts of the 26th Fall Workshop on Computational Geometry (New York, NY, 2016).
Publications