94 citations · 361 across the 25 of their papers we have counts for
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The Least Spanning Area of a Knot and the Optimal Bounding Chain Problem
Nathan M. Dunfield, Anil N. Hirani
Two fundamental objects in knot theory are the minimal genus surface and the least area surface bounded by a knot in a 3-dimensional manifold. When the knot is embedded in a genera…
Cohomologous Harmonic Cochains
Anil N. Hirani, Kaushik Kalyanaraman, Han Wang +1
We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also u…
Least Squares Ranking on Graphs
Anil N. Hirani, Kaushik Kalyanaraman, Seth Watts
Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge valu…
Optimal Homologous Cycles, Total Unimodularity, and Linear Programming
Tamal K. Dey, Anil N. Hirani, Bala Krishnamoorthy
Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given…