TY - GEN
T1 - A faster algorithm for solving general LPs
AU - Jiang, Shunhua
AU - Song, Zhao
AU - Weinstein, Omri
AU - Zhang, Hengjie
N1 - Publisher Copyright: © 2021 ACM.
PY - 2021/6/15
Y1 - 2021/6/15
N2 - The fastest known LP solver for general (dense) linear programs is due to [Cohen, Lee and Song'19] and runs in O?(n? +n2.5-?/2 + n2+1/6) time. A number of follow-up works [Lee, Song and Zhang'19, Brand'20, Song and Yu'20] obtain the same complexity through different techniques, but none of them can go below n2+1/6, even if ?=2. This leaves a polynomial gap between the cost of solving linear systems (n?) and the cost of solving linear programs, and as such, improving the n2+1/6 term is crucial toward establishing an equivalence between these two fundamental problems. In this paper, we reduce the running time to O?(n? +n2.5-?/2 + n2+1/18) where ? and ? are the fast matrix multiplication exponent and its dual. Hence, under the common belief that ? ? 2 and ? ? 1, our LP solver runs in O?(n2.055) time instead of O?(n2.16).
AB - The fastest known LP solver for general (dense) linear programs is due to [Cohen, Lee and Song'19] and runs in O?(n? +n2.5-?/2 + n2+1/6) time. A number of follow-up works [Lee, Song and Zhang'19, Brand'20, Song and Yu'20] obtain the same complexity through different techniques, but none of them can go below n2+1/6, even if ?=2. This leaves a polynomial gap between the cost of solving linear systems (n?) and the cost of solving linear programs, and as such, improving the n2+1/6 term is crucial toward establishing an equivalence between these two fundamental problems. In this paper, we reduce the running time to O?(n? +n2.5-?/2 + n2+1/18) where ? and ? are the fast matrix multiplication exponent and its dual. Hence, under the common belief that ? ? 2 and ? ? 1, our LP solver runs in O?(n2.055) time instead of O?(n2.16).
KW - Convex optimization
KW - Dynamic data-structure
KW - Linear programming
UR - http://www.scopus.com/inward/record.url?scp=85108159337&partnerID=8YFLogxK
U2 - 10.1145/3406325.3451058
DO - 10.1145/3406325.3451058
M3 - منشور من مؤتمر
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 823
EP - 832
BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
A2 - Khuller, Samir
A2 - Williams, Virginia Vassilevska
T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Y2 - 21 June 2021 through 25 June 2021
ER -