Faster Algorithms for Edge Connectivity via Random 2-Out Contractions

by   Mohsen Ghaffari, et al.

We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We demonstrate the power of our new approach by obtaining better algorithms for sequential, distributed, and parallel models of computation. Our end results include the following randomized algorithms for computing edge connectivity with high probability: – Two sequential algorithms with complexities O(m log n) and O(m+n log^3 n). These improve on a long line of developments including a celebrated O(m log^3 n) algorithm of Karger [STOC'96] and the state of the art O(m log^2 n (loglog n)^2) algorithm of Henzinger et al. [SODA'17]. Moreover, our O(m+n log^3 n) algorithm is optimal whenever m = Ω(n log^3 n). Within our new time bounds, whp, we can also construct the cactus representation of all minimal cuts. – An Õ(n^0.8 D^0.2 + n^0.9) round distributed algorithm, where D denotes the graph diameter. This improves substantially on a recent breakthrough of Daga et al. [STOC'19], which achieved a round complexity of Õ(n^1-1/353D^1/353 + n^1-1/706), hence providing the first sublinear distributed algorithm for exactly computing the edge connectivity. – The first O(1) round algorithm for the massively parallel computation setting with linear memory per machine.


page 1

page 2

page 3

page 4


Near-Optimal Distributed Computation of Small Vertex Cuts

We present near-optimal algorithms for detecting small vertex cuts in th...

Distributed Edge Connectivity in Sublinear Time

We present the first sublinear-time algorithm for a distributed message-...

Improved Deterministic Connectivity in Massively Parallel Computation

A long line of research about connectivity in the Massively Parallel Com...

Provably-Efficient and Internally-Deterministic Parallel Union-Find

Determining the degree of inherent parallelism in classical sequential a...

A Randomized Algorithm for Edge-Colouring Graphs in O(m√(n)) Time

We present a simple randomized algorithm to edge-colour arbitrary simple...

Dynamic constant time parallel graph algorithms with sub-linear work

The paper proposes dynamic parallel algorithms for connectivity and bipa...

Planar Diameter via Metric Compression

We develop a new approach for distributed distance computation in planar...

Please sign up or login with your details

Forgot password? Click here to reset