Fully-dynamic min-cut

We show that we can maintain up to polylogarithmic edge connectivity for a fully-dynamic graph in ~O(pn) time per edge insertion or deletion. Within logarithmic factors, this matches the best time bound for 1-edge connectivity. Previously, no o(n) bound was known for edge connectivity above 3, and even for 3-edge connectivity, the best update time was O(n2=3), dating back to FOCS'92. Our algorithm maintains a concrete min-cut in terms of a pointer to a tree spanning one side of the cut plus ability to list the cut edges in O(logn) time per edge. By dealing with polylogarithmic edge connectivity, we immediately get a sampling based expected factor (1 + o(1)) approximation to general edge connectivity in ~O(pn) time per edge insertion or deletion. This algorithm also maintains a pointer to one side of a min-cut, but if we want to list the cut edges in O(logn) time per edge, the update time increases to ~O(pm).

• Type: Conference
• Year: 2001
• Where: STOC
• Authors: Mikkel Thorup
• Keywords: Algorithms, Cut Plus Ability, Polylogarithmic Edge Connectivity, STOC 2001, Update Time Increases