Dec 7th 14:15

Neil Olver (LSE): A strongly polynomial algorithm for linear programs with at most two non-zero entries per row or column

Abstract: We give a strongly polynomial algorithm for minimum cost generalized flow, and hence for optimizing any linear program with at most two non-zero entries per row, or at most two non-zero entries per column. Our result can be viewed as progress towards understanding whether all linear programs can be solved in strongly polynomial time, also referred to as Smale's 9th problem.<br><br> Our approach is based on the recent primal-dual interior point method (IPM) due to Allamigeon, Dadush, Loho, Natura and Végh (FOCS '22). They show that the number of iterations needed by the IPM can be bounded in terms of the straight line complexity of the central path; roughly speaking, this is the minimum number of pieces of any piecewise linear curve that multiplicatively approximates the central path. As our main contribution, we show that the straight line complexity of any minimum cost generalized flow instance is polynomial in the number of arcs and vertices. By a reduction of Hochbaum, the same bound applies to any linear program with at most two non-zeros per column or per row. Further, we demonstrate how to handle initialization, and how to ensure that the bit complexity of each iterate remains bounded during the execution of the algorithm.<br><br>Joint work with Daniel Dadush, Zhuan Khye Koh, Bento Natura and László Végh.

Dec 21st 14:15

Talk (Hannah Tillmann-Morris)

Jan 11th 14:15

Talk (Ansgar Freyer)

Jan 18th 14:15

Talk (Matthias Schymura)

Jan 25th 14:15


Feb 1st 14:15

Talk (Sophie Huiberts)

Feb 8th 14:15

Talk (Eva Philippe)