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DTSTART:20250101T000000
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DTSTART;TZID=Asia/Seoul:20260127T163000
DTEND;TZID=Asia/Seoul:20260127T173000
DTSTAMP:20260416T075602
CREATED:20251015T110913Z
LAST-MODIFIED:20260106T021752Z
UID:11724-1769531400-1769535000@dimag.ibs.re.kr
SUMMARY:Daniel Dadush\, A Strongly Polynomial Algorithm for Linear Programs with at Most Two Non-Zero Entries per Row or Column
DESCRIPTION: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. Primal and dual feasibility were shown by Végh (MOR ’17) and Megiddo (SICOMP ’83) respectively. 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. Our approach is based on the recent primal-dual interior point method (IPM) due to Allamigeon\, Dadush\, Loho\, Natura and Végh (FOCS ’22). The number of iterations needed by the IPM is bounded\, up to a polynomial factor in the number of inequalities\, by 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 applying a reduction of Hochbaum (ORL ’04)\, the same bound applies to any linear program with at most two non-zeros per column or per row \nJoint work with Zhuan Khye Koh (Boston U)\, Bento Natura (Columbia)\, Neil Olver (LSE)\, and László A. Végh (Bonn).
URL:https://dimag.ibs.re.kr/event/2026-01-27/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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