Abstract
AbstractWe give a randomized algorithm that finds a minimum cut in an undirected weighted m-edge n-vertex graph G with high probability in $$O(m \log ^2 n)$$
O
(
m
log
2
n
)
time. This is the first improvement to Karger’s celebrated $$O(m \log ^3 n)$$
O
(
m
log
3
n
)
time algorithm from 1996. Our main technical contribution is a deterministic $$O(m \log n)$$
O
(
m
log
n
)
time algorithm that, given a spanning tree T of G, finds a minimum cut of G that 2-respects (cuts two edges of) T.
Funder
Israel Science Foundation
Publisher
Springer Science and Business Media LLC
Reference44 articles.
1. Abboud, A., Krauthgamer, R., Li, J., Panigrahi, D., Saranurak, T., Trabelsi, O.: Breaking the cubic barrier for all-pairs max-flow: Gomory-hu tree in nearly quadratic time. In 63rd FOCS, pp. 884–895 (2022)
2. Alstrup, S., Holm, J., Lichtenberg, K.D., Thorup, M.: Maintaining information in fully dynamic trees with top trees. ACM Trans. Algorithms 1(2), 243–264 (2005)
3. Bhardwaj, N., Lovett, A.M., Sandlund, B.: A simple algorithm for minimum cuts in near-linear time. In 17th SWAT, vol. 162, pp. 12(18), 1–12 (2020)
4. Brodal, G.S., Fagerberg, R., Pedersen, C.N.S.: Computing the quartet distance between evolutionary trees in time $${O}(n \log ^2 n)$$. In 12th ISAAC, pp. 731–742 (2001)
5. Chen, L., Kyng, R., Liu, Y.P., Peng, R., Gutenberg, M.P., Sachdeva, S.: Maximum flow and minimum-cost flow in almost-linear time. In 63rd FOCS, pp. 612–623 (2022)