Parallel ear decomposition search (EDS) and st-numbering in graphs
Theoretical Computer Science
Time-optimal leader election in general networks
Journal of Parallel and Distributed Computing
Introduction to algorithms
How to find biconnected components in distributed networks
Journal of Parallel and Distributed Computing
Improved algorithms for graph four-connectivity
Journal of Computer and System Sciences
Reducing edge connectivity to vertex connectivity
ACM SIGACT News
An introduction to parallel algorithms
An introduction to parallel algorithms
Finding triconnected components by local replacement
SIAM Journal on Computing
Randomized algorithms
An optimal randomised logarithmic time connectivity algorithm for the EREW PRAM
Journal of Computer and System Sciences
Sub-linear distributed algorithms for sparse certificates and biconnected components
Journal of Algorithms
A SubLinear Time Distributed Algorithm for Minimum-Weight Spanning Trees
SIAM Journal on Computing
Fast distributed construction of small k-dominating sets and applications
Journal of Algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Optimal randomized EREW PRAM algorithms for finding spanning forests
Journal of Algorithms
Nearest common ancestors: a survey and a new distributed algorithm
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Parallel Integer Sorting Is More Efficient Than Parallel Comparison Sorting on Exclusive Write PRAMs
SIAM Journal on Computing
Proceedings of the Ninth Conference on Foundations of Software Technology and Theoretical Computer Science
Graph Theory With Applications
Graph Theory With Applications
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
A faster distributed protocol for constructing a minimum spanning tree
Journal of Computer and System Sciences
A Simple 3-Edge-Connected Component Algorithm
Theory of Computing Systems
Echo Algorithms: Depth Parallel Operations on General Graphs
IEEE Transactions on Software Engineering
Network synchronization with polylogarithmic overhead
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
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We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph. In the model of distributed computing in a graph G = (V, E) with O(log |V|)-bit messages, our approach yields faster algorithms for several problems. The diameter of G is denoted by D, and the maximum degree by Δ. We obtain simple O(D)-time distributed algorithms to find all cut edges, 2-edge-connected components, and cut pairs, matching or improving upon previous time bounds. Under natural conditions these new algorithms are universally optimal—that is, a Ω(D)-time lower bound holds on every graph. We obtain a O(D+Δ/log |V|)-time distributed algorithm for finding cut vertices; this is faster than the best previous algorithm when Δ, D = O(&sqrt;|V|). A simple extension of our work yields the first distributed algorithm with sub-linear time for 3-edge-connected components. The basic distributed algorithms are Monte Carlo, but they can be made Las Vegas without increasing the asymptotic complexity. In the model of parallel computing on the EREW PRAM, our approach yields a simple algorithm with optimal time complexity O(log V) for finding cut pairs and 3-edge-connected components.