Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time. / Goranci, Gramoz; Henzinger, Monika; Thorup, Mikkel.
I: ACM Transactions on Algorithms, Bind 14, Nr. 2, 17, 2018.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time
AU - Goranci, Gramoz
AU - Henzinger, Monika
AU - Thorup, Mikkel
PY - 2018
Y1 - 2018
N2 - We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with O(log(3) n log log(2) n) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup (2007). It also stays in sharp contrast to a polynomial conditional lower bound for the fully dynamic weighted minimtun cut problem. Our algorithm is obtained by combining a sparsification technique of Kawarabayashi and Thorup (2015) or its recent improvement by Henzinger, Rao, and Wang (2017), and an exact incremental algorithm of Henzinger (1997). We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(n log n/epsilon(2)) space Monte Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithum maintains a (1 + epsilon)-approximation to the minimtun cut. The algorithum has O((alpha(n) log(3) n) / epsilon(2)) amortized update time and constant query time, where alpha(n) stands for the inverse of Ackermann function.
AB - We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with O(log(3) n log log(2) n) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup (2007). It also stays in sharp contrast to a polynomial conditional lower bound for the fully dynamic weighted minimtun cut problem. Our algorithm is obtained by combining a sparsification technique of Kawarabayashi and Thorup (2015) or its recent improvement by Henzinger, Rao, and Wang (2017), and an exact incremental algorithm of Henzinger (1997). We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(n log n/epsilon(2)) space Monte Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithum maintains a (1 + epsilon)-approximation to the minimtun cut. The algorithum has O((alpha(n) log(3) n) / epsilon(2)) amortized update time and constant query time, where alpha(n) stands for the inverse of Ackermann function.
KW - Minimum cut
KW - edge connectivity
KW - space-efficient dynamic graph algorithms
U2 - 10.1115/3174803
DO - 10.1115/3174803
M3 - Journal article
VL - 14
JO - ACM Transactions on Algorithms
JF - ACM Transactions on Algorithms
SN - 1549-6325
IS - 2
M1 - 17
ER -
ID: 202484882