TY - GEN
T1 - All-Pairs Max-Flow is no Harder than Single-Pair Max-Flow
T2 - 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023
AU - Abboud, Amir
AU - Li, Jason
AU - Panigrahi, Debmalya
AU - Saranurak, Thatchaphol
N1 - Publisher Copyright: © 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - A Gomory-Hu tree (also called a cut tree) succinctly represents (s, t) min-cuts (and therefore, (s, t) max-flow values) of all pairs of vertices s, t in an undirected graph. In this paper, we give an m1+o(1)-time algorithm for constructing a Gomory-Hu tree for a graph with m edges. This shows that the all-pairs max-flows problem has the same running time as the single-pair max-flow problem, up to a subpolynomial factor. Prior to our work, the best known Gomory-Hu tree algorithm was obtained in recent work by Abboud et al. (FOCS 2022) and requires Õ(n2) time for a graph with n vertices. Our result marks a natural culmination of over 60 years of research into the all-pairs maxflows problem that started with Gomory and Hu's pathbreaking result introducing the Gomory-Hu tree in 1961.
AB - A Gomory-Hu tree (also called a cut tree) succinctly represents (s, t) min-cuts (and therefore, (s, t) max-flow values) of all pairs of vertices s, t in an undirected graph. In this paper, we give an m1+o(1)-time algorithm for constructing a Gomory-Hu tree for a graph with m edges. This shows that the all-pairs max-flows problem has the same running time as the single-pair max-flow problem, up to a subpolynomial factor. Prior to our work, the best known Gomory-Hu tree algorithm was obtained in recent work by Abboud et al. (FOCS 2022) and requires Õ(n2) time for a graph with n vertices. Our result marks a natural culmination of over 60 years of research into the all-pairs maxflows problem that started with Gomory and Hu's pathbreaking result introducing the Gomory-Hu tree in 1961.
UR - http://www.scopus.com/inward/record.url?scp=85177769242&partnerID=8YFLogxK
U2 - 10.1109/FOCS57990.2023.00137
DO - 10.1109/FOCS57990.2023.00137
M3 - منشور من مؤتمر
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 2204
EP - 2212
BT - Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023
PB - IEEE Computer Society
Y2 - 6 November 2023 through 9 November 2023
ER -