## Optimal Bi-Level Augmentation for Selectively Enhancing Graph Connectivity with Applications (1996)

Venue: | in Proc. 2nd International Symp. on Computing and Combinatorics, vol. LNCS #1090 |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Hsu96optimalbi-level,

author = {Tsan-sheng Hsu and Ming-Yang Kao},

title = {Optimal Bi-Level Augmentation for Selectively Enhancing Graph Connectivity with Applications},

booktitle = {in Proc. 2nd International Symp. on Computing and Combinatorics, vol. LNCS #1090},

year = {1996},

pages = {169--178},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Our main problem is abstracted from several optimization problems for protecting information in cross tabulated tables and for improving the reliability of communication networks. Given an undirected graph G and two vertex subsets H 1 and H 2 , the smallest bi-level augmentation problem is that of adding to G the smallest number of edges such that G contains two internally vertex-disjoint paths between every pair of vertices in H 1 and two edge-disjoint paths between every pair of vertices in H 2 . We give a data structure to represent essential connectivity information of H 1 and H 2 simultaneously. Using this data structure, we solve the bi-level augmentation problem in O(n + m) time, where n and m are the numbers of vertices and edges in G. Our algorithm can be parallelized to run in O(log 2 n) time using n +m processors on an EREW PRAM. By properly setting G, H 1 and H 2 , our augmentation algorithm also subsumes several existing optimal algorithms for graph augmentation. 1 Int...