81 citations · 403 across the 47 of their papers we have counts for
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The complexity of the normal surface solution space
Benjamin A. Burton
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important a…
Searching a bitstream in linear time for the longest substring of any given density
Benjamin A. Burton
Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an al…
The Weber-Seifert dodecahedral space is non-Haken
Benjamin A. Burton, J. Hyam Rubinstein, Stephan Tillmann
In this paper we settle Thurston's old question of whether the Weber-Seifert dodecahedral space is non-Haken, a problem that has been a benchmark for progress in computational 3-ma…
Quadrilateral-octagon coordinates for almost normal surfaces
Benjamin A. Burton
Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional…
Converting between quadrilateral and standard solution sets in normal surface theory
Benjamin A. Burton
The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a hig…