M. Rauch Henzinger. Fully dynamic cycle-equivalence in graphs. In Shafi Goldwasser, editor, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 744--757, Los Alamitos, CA, USA, November 1994. IEEE Computer Society Press.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of this work will appear in [14] 1 Fully dynamic algorithms tend to involve complicated data structures and are quite difficult to implement. The deterministic fully dynamic algorithms for 2 edge connectivity (given in [3] 2 vertex connectivity (given in [10] and cycle equivalence (given in [8]) are good examples of this. The randomized fully dynamic algorithms for 2 edge connectivity (given in [9, 15] and 2 vertex connectivity (given in [11] are pretty involved too. In fact, the 2 vertex connectivity algorithm of [11] does not work for some graphs in which the maximum degree is ....

....undirected graph are cycle equivalent iff the set of cycles that contain e 1 is exactly the same as the set of cycles that contain e 2 . Finding the cycle equivalence classes is central to several compilation problems. See [12, 20, 6] for some applications of cycle equivalence. As mentioned in [8], dynamic algorithms for this problem can speed up incremental compilers. No special purpose incremental or backtracking algorithms are known for this problem. The only dynamic algorithms known for handling an incremental or a backtracking sequence of updates are the fully dynamic algorithms. A ....

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M. Rauch Henzinger. Fully dynamic cycle equivalence in graphs. In Proceedings of 35th Symposium on Foundations of Computer Science, pages 744--755, 1994.

....answering a query. For the dynamic connectivity problem, for example, a query takes two nodes u and v as its arguments and returns True , if there is a path connecting u and v in the current graph. The field of dynamic graph algorithms has been a blossoming field of research in the last years [4, 9, 11, 13, 14, 15, 17, 19, 31, 33], motivated by theoretical and practical questions (see for instance [29] However, despite this blend of theoretical and practical interests, we are aware of no implementations and experimental studies in this field. In this paper, we aim at bridging this gap by studying the practical properties ....

M. R. Henzinger. Fully dynamic cycle equivalence in graphs. Proc. 35th IEEE Symp. Foundations of Computer Science (1994), 744--755.

....cardinality. In the case of maximum matching a query outputs a current maximum matching. Alternatively, a query could also be: Is the edge e in the current graph in the current maximum matching Recently, a lot of work has been done on dynamic algorithms for various connectivity proper ties [10, 11, 12, 13, 16, 24, 25, 26]. The current best deterministic bound for maintaining connected or 2 edge connected components of a graph is O(x ) 10] The best randomized algorithm achieves O(1 3 resp. O(1 4 per update [17] It is an open problem if the connected or 2 edge con nected components of a graph can be ....

M. Rauch Henzinger. Fully dynamic cycle equivalence in graphs. In Proc. 25th Syrup. on Foundations of Computer Science, pages 744 755, 1994.

....Award. y Department of Computer Science, University of Victoria, Victoria, BC. Email: val csr.uvic.ca. This research was supported by an NSERC Grant. 1 Throughout the paper the logarithms are base 2. Previous Work. In recent years a lot of work has been done in fully dynamic algorithms (see [1, 3, 4, 6, 7, 8, 10, 11, 12, 15, 16, 18] for connectivity related work in undirected graphs) There is also a large body of work for restricted classes of graphs and for insertions only algorithms. Currently the best time bounds for fully dynamic algorithms in undirected n node graphs are: O( p n) per update for a minimum spanning ....

.... in undirected n node graphs are: O( p n) per update for a minimum spanning forest [3] O( p n) per update and O(1) per query for connectivity [3] O( p n log n) per update and O(log 2 n) per query for cycle equivalence ( Does the removal of the given 2 edges disconnect the graph ) [11]; O( p n) per update and O(1) per query for bipartiteness ( Is the graph bipartite ) 3] There is a lower bound in the cell probe model of Omega Gamma 32 n= log log n) on the amortized time per operation for all these problems which applies to randomized algorithms [9, 11, 13] If deletions ....

[Article contains additional citation context not shown here]

M. R. Henzinger, "Fully Dynamic Cycle-Equivalence in Graphs", Proc. 35th Symp. on Foundations of Computer Science, 1994, 744--755.

....cardinality. In the case of maximum matching a query outputs a current maximum matching. Alternatively, a query could also be: Is the edge e in the current graph in the current maximum matching Recently, a lot of work has been done on dynamic algorithms for various connectivity properties [10, 11, 12, 13, 18, 27, 28, 29]. The current best deterministic bound for maintaining connected or 2 edge connected components of a graph is O( p n) 10] The best randomized algorithm achieves O(log 2 n) resp. O(log 3 n) per update [17] It is an open problem if the connected or 2 edge connected components of a graph ....

M. Rauch Henzinger. Fully dynamic cycle equivalence in graphs. In Proc. 35th Symp. on Foundations of Computer Science, pages 744 -- 755, 1994.

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M. Rauch Henzinger. Fully dynamic cycle-equivalence in graphs. In Shafi Goldwasser, editor, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 744--757, Los Alamitos, CA, USA, November 1994. IEEE Computer Society Press.

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