81 citations · 403 across the 47 of their papers we have counts for
5 papers · 1 filter
The Pachner graph and the simplification of 3-sphere triangulations
Benjamin A. Burton
It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need…
Optimising a nonlinear utility function in multi-objective integer programming
Melih Ozlen, Meral Azizoğlu, Benjamin A. Burton
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updat…
A tree traversal algorithm for decision problems in knot theory and 3-manifold topology
Benjamin A. Burton, Melih Ozlen
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly de…
Projective geometry and the outer approximation algorithm for multiobjective linear programming
Benjamin A. Burton, Melih Ozlen
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as…
Maximal admissible faces and asymptotic bounds for the normal surface solution space
Benjamin A. Burton
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dim…