Book ChapterDOI
Cache Oblivious Minimum Cut
Barbara Geissmann,Lukas Gianinazzi +1 more
- pp 285-296
Reads0
Chats0
TLDR
This work shows how to compute the minimum cut of a graph cache-efficiently using a cache oblivious algorithm and a simpler one that incurs cache misses.Abstract:
We show how to compute the minimum cut of a graph cache-efficiently. Let B be the width of a cache line and M be the size of the cache. On a graph with V vertices and E edges, we give a cache oblivious algorithm that incurs \(O(\lceil \frac{E}{B} (\log ^4 E) \log _{M/B} E\rceil )\) cache misses and a simpler one that incurs \(O(\lceil \frac{V^2}{B} \log ^3 V\rceil )\) cache misses.read more
Citations
More filters
Proceedings ArticleDOI
Communication-avoiding parallel minimum cuts and connected components
TL;DR: Novel scalable parallel algorithms for finding global minimum cuts and connected components, which are important and fundamental problems in graph processing, and an approximate variant of the minimum cut algorithm, which approximates the exact solutions well while using a fractions of cores in a fraction of time are provided.
Proceedings ArticleDOI
Parallel Minimum Cuts in Near-linear Work and Low Depth
TL;DR: This work presents the first near-linear work and poly-logritharithmic depth algorithm for computing a minimum cut in a graph, while previous parallel algorithms withpoly-logarithic depth required at least quadratic work in the number of vertices.
Posted Content
A Simple Algorithm for Minimum Cuts in Near-Linear Time
TL;DR: A self-contained version of Karger's algorithm is given with a new procedure, which produces a minimum cut on an m-edge, n-vertex graph in O(m \log^3 n) time with high probability, matching the complexity ofKarger's approach.
Proceedings ArticleDOI
Parallel Minimum Cuts in Near-linear Work and Low Depth
TL;DR: In this article, the authors presented a near-linear work and poly-logarithmic depth algorithm for computing a minimum cut in a graph, while previous parallel algorithms with poly logarithm-depth required at least quadratic work in the number of vertices.
Journal ArticleDOI
Parallel Minimum Cuts in Near-linear Work and Low Depth
TL;DR: In this paper, the authors presented a near-linear work and poly-logarithmic depth algorithm for computing a minimum cut in an undirected graph with O(m log 4 n) work and O(log 3 n) depth.
References
More filters
Journal ArticleDOI
The input/output complexity of sorting and related problems
Alok Aggarwal,S. Vitter Jeffrey +1 more
TL;DR: Tight upper and lower bounds are provided for the number of inputs and outputs (I/OS) between internal memory and secondary storage required for five sorting-related problems: sorting, the fast Fourier transform (FFT), permutation networks, permuting, and matrix transposition.
Journal ArticleDOI
A data structure for dynamic trees
TL;DR: An O(mn log n)-time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse graphs.
Journal ArticleDOI
A simple min-cut algorithm
Mechthild Stoer,Frank Wagner +1 more
TL;DR: An algorithm for finding the minimum cut of an undirected edge-weighted graph that has a short and compact description, is easy to implement, and has a surprisingly simple proof of correctness.
Book
On Finding Lowest Common Ancestors: Simplification and Parallelization
Baruch Schieber,Uzi Vishkin +1 more
TL;DR: A linear time and space preprocessing algorithm that enables us to answer each query in $O(1)$ time, as in Harel and Tarjan, which has the advantage of being simple and easily parallelizable.
Journal ArticleDOI
A new approach to the minimum cut problem
David R. Karger,Clifford Stein +1 more
TL;DR: A randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability with a significant improvement over the previous time bounds based on maximum flows.