Distributed Minimum Cut Approximation

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We present two randomized approximation algorithms that both run in a standard synchronous message passing model where in each round, O(log n) bits can be transmitted over every edge (a.k.a. the CONGEST model). The first algorithm is based on a simple and new approach for analyzing random edge sampling, which we call random layering technique. For any any weighted graph and any ∈ (0, 1), the algorithm finds a cut of size at most O( −1 λ) in O(D) + ˜O(n1/2+ ) rounds, where λ is the minimum-cut size and the ˜O-notation hides poly-logarithmic factors in n. In addition, using the outline of a centralized algorithm due to Matula [SODA ’93], we present a randomized algorithm to compute a cut of size at most (2 + )λ in ˜O((D + √ n)/ 5 ) rounds for any > 0. The time complexities of our algorithms almost match the ˜Ω(D + √ n) lower bound of Das Sarma et al. [STOC ’11], thus lead...

• Type: Journal
• Year: 2013
• Where: WDAG
• Authors: Mohsen Ghaffari, Fabian Kuhn
• Keywords: Algorithms, WDAG 2013