Journal and book chapter submissions
Fast Schulze voting using quickselect.
A. Arora,
D. Eppstein, and
R. L. Huynh.
arXiv:2411.18790.
We show how to determine the outcome of a Schulze method election, from an input consisting of an \(m\times m\) array of pairwise margins of victory, in time \(O(m^2\log m)\). The algorithm uses random pivoting like that of quickselect.
Entropy-bounded computational geometry made easier and sensitive to sortedness.
D. Eppstein,
M. T. Goodrich,
A. M. Illickan, and
C. A. To.
arXiv:2508.20489.
Proc. 37th
Canadian Conference on Computational Geometry, 2025,
pp. 53–61.
We define a notion of structural entropy of point sets under which a set has low entropy when it can be covered by few disjoint triangles that are either entirely under the hull of the input or presorted, and show that we can find the hull in time sensitive to this entropy. Generalizations of the same technique apply to geometric maxima, lower envelopes, and visibility polygons.