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cs.DS2026
Finding Short Paths on Simple Polytopes
Alexander E. Black, Raphael Steiner
We prove that computing a shortest monotone path to the optimum of a linear program over a simple polytope is NP-hard, thus resolving a 2022 open question of De Loera, Kafer, and S…
cs.DS2025
Short circuit walks in fixed dimension
Alexander E. Black, Christian Nöbel, Raphael Steiner
Circuit augmentation schemes are a family of combinatorial algorithms for linear programming that generalize the simplex method. To solve the linear program, they construct a so-ca…
cs.DS2025
Beyond Smoothed Analysis: Analyzing the Simplex Method by the Book
Eleon Bach, Alexander E. Black, Sophie Huiberts +1
Narrowing the gap between theory and practice is a longstanding goal of the algorithm analysis community. To further progress our understanding of how algorithms work in practice,…