# Parallel and fast sequential algorithms for undirected edge connectivity augmentation

@article{Benczr1999ParallelAF,
title={Parallel and fast sequential algorithms for undirected edge connectivity augmentation},
author={Andr{\'a}s A. Bencz{\'u}r},
journal={Mathematical Programming},
year={1999},
volume={84},
pages={595-640}
}
• A. Benczúr
• Published 1 April 1999
• Computer Science, Mathematics
• Mathematical Programming
1,E2,..., such that ⋃i≤τEi optmially increases the connectivity by τ, for any integer τ. The main result of the paper is that this sequence of edge sets can be divided into O(n) groups such that within one group, all Ei are basically the same. Using this result, we improve on the running time of edge connectivity augmentation, as well as we give the first parallel (RNC) augmentation algorithm. We also present new efficient subroutines for finding the so-called extreme sets and the cactus…
2 Citations

### Primal-dual approach for directed vertex connectivity augmentation and generalizations

• Mathematics, Computer Science
SODA '05
• 2005
This work presents a combinatorial algorithm for the general problem that includes directed vertex or S - T connectivity augmentation and uses a primal-dual scheme for finding covers of partially ordered sets that satisfy natural abstract properties.

## References

SHOWING 1-10 OF 40 REFERENCES

### Successive edge-connectivity augmentation problems

• Mathematics, Computer Science
Math. Program.
• 1999
The augmentation algorithm of A. Frank can be used to solve the corresponding Successive Edge-Augmentation Problem and implies (a stronger version of) the Successive Augmentation Property, even for some non-uniform demands.

### Augmenting Graphs to Meet Edge-Connectivity Requirements

• A. Frank
• Mathematics
SIAM J. Discret. Math.
• 1992
A min-max formula is derived for $\gamma$ and a polynomial time algorithm to compute it is described, and the directed counterpart of the problem is solved and is shown to be NP-complete.

### A matroid approach to finding edge connectivity and packing arborescences

• H. Gabow
• Computer Science, Mathematics
STOC '91
• 1991
An algorithm that finds k edge-disjoint arborescences on a directed graph in time O(kmn + k3n2)2 is presented, based on two theorems of Edmonds that link these two problems and show how they can be solved.

### The minimum augmentation of any graph to a K-edge-connected graph

• Mathematics, Computer Science
Networks
• 1989
A good characterization and good algorithm are obtained for augmenting G0 to a K-edge-connected graph and applications are suggested in designing a reliable network aiming at the most effective use of exising network.

### Augmenting hypergraphs by edges of size two

• Mathematics
Math. Program.
• 1999
This work gives a good characterization for the minimum number of edges of size two whose addition to a given hypergraph H makes it k-edge-connected, and describes a strongly polynomial algorithm to find both a minimum cardinality augmentation, and a minimum cost augmentation.

### A Fast Algorithm for Optimally Increasing the Edge Connectivity

• Computer Science, Mathematics
SIAM J. Comput.
• 1997
The solution is particularly simple, it runs in O(nm) time, and it is a natural generalization of the algorithm in [K. Eswaran and R. Tarjan, SIAM J. Comput., 5 (1976), pp. 653--665] for the case where $\lambda+\delta =2$.

### A representation of cuts within 6/5 times the edge connectivity with applications

• A. Benczúr
• Computer Science
Proceedings of IEEE 36th Annual Foundations of Computer Science
• 1995
This paper gives an O(n/sup 2/)-sized planar geometric representation for all edge cuts with capacity less than 6/5c, and shows that in algorithms based on edge splitting, computing this representation O(log n) times substitute for one, or sometimes even /spl Omega/(n), u-/spl nu/ mincut computations can lead to significant savings.

### Representing and Enumerating Edge Connectivity Cuts in RNC

• Computer Science