Incremental Exact Min-Cut in Poly-logarithmic Amortized Update Time
We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with ~O(1) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup [Combinatorica 2007]. It also stays in sharp contrast to a polynomial conditional lower-bound for the fully-dynamic weighted minimum cut problem. Our algorithm is obtained by combining a recent sparsification technique of Kawarabayashi and Thorup [STOC 2015] and an exact incremental algorithm of Henzinger [J. of Algorithm 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 algorithm maintains a (1+epsilon)-approximation to the minimum cut. The algorithm has ~O(1) amortized update-time and constant query-time.
Dynamic Graph Algorithms
Minimum Cut
Edge Connectivity
46:1-46:17
Regular Paper
Gramoz
Goranci
Gramoz Goranci
Monika
Henzinger
Monika Henzinger
Mikkel
Thorup
Mikkel Thorup
10.4230/LIPIcs.ESA.2016.46
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