T. S. Hsu and V. Ramachandran, Finding a smallest augmentation to biconnect a graph, SIAM Journal on Computing, 22 (1993), pp. 889912.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for both graphs and directed graphs are referred to [F 94] Let us focus on node connectivity augmentation problems: given a graph, increase the node connectivitytok by adding the minimum number of new edges. The case k =2was solved by Eswaran Tarjan [ET 76] and later Hsu Ramachandran [HR 93] gave a linear time algorithm. The case k =3was solved byWatanabe Nakamura [WN 90] and a linear time algorithm was given by Hsu Ramachandran [HR 91] The case k =4was solved by Hsu [H 95] using an O(jEj n log n) time algorithm, and earlier Hsu [H 92] gave an almost linear time ....

T. Hsu and V. Ramachandran, "Finding a smallest augmentation to biconnect a graph," SIAM J. Computing 22( 889--912.

....directed graphs are referred to [F 94] Let us focus on node connectivity augmentation problems: given an (undirected) graph, increase the node connectivity to k 0 by adding the minimum number of new edges. The case k 0 = 2 was solved by Eswaran Tarjan [ET 76] and later Hsu Ramachandran [HR 93] gave a linear time algorithm. The case k 0 = 3 was solved by Watanabe Nakamura [WN 90] and a linear time algorithm was given by Hsu Ramachandran [HR 91] The case k 0 = 4 was solved by Hsu [H 95] using an O(jEj n log n) time algorithm, and earlier Hsu [H 92] gave an almost linear time ....

T. Hsu and V. Ramachandran, "Finding a smallest augmentation to biconnect a graph," SIAM J. Computing 22 (1993), 889--912.

....graphs and directed graphs are referred to [F 94] Let us focus on node connectivity augmentation problems: given a graph, increase the node connectivity to k 0 by adding the minimum number of new edges. The case k 0 = 2 was solved by Eswaran Tarjan [ET 76] and later Hsu Ramachandran [HR 93] gave a linear time algorithm. The case k 0 = 3 was solved by Watanabe Nakamura [WN 90] and a linear time algorithm was given by Hsu Ramachandran [HR 91] The case k 0 = 4 was solved by Hsu [H 95] using an O(jEj n log n) time algorithm, and earlier Hsu [H 92] gave an almost ....

T. Hsu and V. Ramachandran, "Finding a smallest augmentation to biconnect a graph," SIAM J. Computing 22 (1993), 889--912.

....basic DFS approach of [ET76] to generalize the technique to work for any k. Eswaran and Tarjan solved the case of increasing connectivity from 1 to 2 in their seminal paper, where the problem was first introduced. For the case of vertex connectivity, for k = 2; 3 the best algorithms are due to [ET76, RG77, HR91b] and [HR91a] respectively. A more general edge connectivity problem was considered by Frank [Fr92] when the feasibility graph is a clique, and shown to be solvable in polynomial time. Specifically, one is required to find a minimum spanning subgraph where specific connectivity requirements are ....

T. S. Hsu and V. Ramachandran, "On finding a smallest augmentation to biconnect a graph," 2 nd Annual International Symposium on Algorithms, Springer Verlag LNCS 557, pp. 326--335, (1991).

....needed to biconnect an undirected graph and proved that the lower bound can always be achieved. Rosenthal and Goldner [RG77] developed a lineartime sequential algorithm for finding a smallest biconnectivity augmentation; however, the algorithm in [RG77] contains an error. Hsu and Ramachandran [HR93] gave a corrected linear time sequential algorithm. An O(log 2 n) time parallel algorithm on an EREW PRAM using a linear number of processors for this problem was also given in Hsu and Ramachandran [HR93] Fern andez Baca and Williams [FBW89] considered the smallest augmentation problem for ....

....augmentation; however, the algorithm in [RG77] contains an error. Hsu and Ramachandran [HR93] gave a corrected linear time sequential algorithm. An O(log 2 n) time parallel algorithm on an EREW PRAM using a linear number of processors for this problem was also given in Hsu and Ramachandran [HR93]. Fern andez Baca and Williams [FBW89] considered the smallest augmentation problem for reaching biconnectivity on hierarchically defined graphs. This version of the augmentation problem has applications in VLSI circuit design. They obtained a polynomial time algorithm for the above problem. ....

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T.-s. Hsu and V. Ramachandran. On finding a smallest augmentation to biconnect a graph. SIAM J. Comput., 22(5):889--912, 1993.

....biconnect an undi 19 rected graph and proved that the lower bound can always be achieved. Rosenthal and Goldner [RG77] developed a linear time sequential algorithm for finding a smallest augmentation to biconnect a graph; however, the algorithm in [RG77] contains an error. Hsu and Ramachandran [HR91b] gave a corrected linear time sequential algorithm. An O(log 2 n) time parallel algorithm on an EREW PRAM using a linear number of processors for this problem was also given in Hsu and Ramachandran [HR91b] We will describe the above two algorithms in Chapter 3. Fern andez Baca and Williams ....

....a graph; however, the algorithm in [RG77] contains an error. Hsu and Ramachandran [HR91b] gave a corrected linear time sequential algorithm. An O(log 2 n) time parallel algorithm on an EREW PRAM using a linear number of processors for this problem was also given in Hsu and Ramachandran [HR91b] We will describe the above two algorithms in Chapter 3. Fern andez Baca and Williams [FBW89] considered the smallest augmentation problem for reaching 2 edge connectivity, biconnectivity, and strong connectivity on hierarchically defined graphs. This version of the augmentation problem has ....

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T.-s. Hsu and V. Ramachandran. On finding a smallest augmentation to biconnect a graph. In Proc. 2nd Annual Int'l Symp. on Algorithms, volume LNCS #557, pages 326--335. Springer-Verlag, 1991. SIAM J. Comput., to appear.

.... properly setting G, H 1 and H 2 , our augmentation algorithm also subsumes several existing optimal algorithms for graph augmentation, including those for 2 edge connecting a vertex subset [29] 2 edge connecting a whole graph [3] biconnecting a vertex subset [29] and biconnecting a whole graph [12, 23]. The main result of this paper is formally stated in the following theorem. Theorem 1.1 Given G, H 1 and H 2 , the smallest bi level augmentation problem can be solved in optimal linear time. Before proving this theorem in x4 through x6, we give some key definitions in x2 and solve application ....

....nc(G) 2. A singular block consisted of a strict cut vertex is a strict cut 2 block. Given two subsets of vertices H 1 and H 2 in G = V; E) G is bi level connected with respect to H 1 and H 2 , if H 1 is biconnected and H 2 is 2 edge connected. Most of the definitions given here can be found in [1, 8, 11, 12]. 3 Motivations By properly choosing G, H 1 and H 2 , we can use our augmentation algorithm to solve several optimization problems for protecting sensitive information in cross tabulated tables [6, 7, 17, 15, 16, 20] and for improving the reliability of communication networks [5, 13, 24] 3.1 ....

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T.-s. Hsu and V. Ramachandran. On finding a smallest augmentation to biconnect a graph. SIAM J. Comput., 22(5):889--912, 1993.

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T. S. Hsu and V. Ramachandran, Finding a smallest augmentation to biconnect a graph, SIAM Journal on Computing, 22 (1993), pp. 889912.

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