Giuseppe F. Italiano, Alberto Marchetti Spaccamela, and Umberto Nanni. Dynamic data structures for series parallel digraphs. In Proc. First WADS,  Home/Search   Document Not in Database   Summary   Related Articles   Check

....only if 9w 2 V : u T w w S v: It is by no means clear that one can handle the existential quantifier over the vertices V of the graph in logarithmic time. Indeed, note that our algorithm is unable to identify such a w, it merely verifies its existence. Other Classes of Graphs. Italiano et al. [37] present a dynamic reachability algorithm for series parallel digraphs; apart from these and the class studied in the present paper, no other class of digraphs is known to the author that allows fully dynamic reachability algorithms within polylogarithmic time bounds. The only other nontrivial ....

Giuseppe F. Italiano, Alberto Marchetti Spaccamela, and Umberto Nanni. Dynamic data structures for series parallel digraphs. In Proc. First WADS,

....insert and delete operations on G without violating its topology. For the query operation, observe that j M i=1 x i = 1 v 1 OE v 0 j 1 ; j = 1; n: Thus a lower bound on the Prefix Problem implies a lower bound on the Transitive Closure Problem. 2.4. Related work. Italiano et al. [7] present a dynamic reachability algorithm for series parallel digraphs; apart from these and the class studied in the present paper, no other class of digraphs is known to the author that allows fully dynamic reachability algorithms within polylogarithmic time bounds. The only other nontrivial ....

Giuseppe F. Italiano, Alberto Marchetti Spaccamela, and Umberto Nanni, Dynamic data structures for series parallel digraphs, Proc. First Workshop on Algorithms and Data Structures (WADS) (F. Dehne, J.-R. Sack, and N. Santoro, eds.), Lecture Notes in Computer Science, vol. 382, Springer Verlag, Berlin, 1989, pp. 352--373.

....al. 12] give an algorithm that runs in time O(log n) In the directed case, planarity gives an O(n 2=3 log n) algorithm due to Subramanian [40] For DC algorithms in the directed case, we must restrict even further: Italiano et al. present an O(logn) solution for series parallel digraphs, see [23]; Tamassia and Preparata [42] achieve the same bound for another class (see Section 3.2) Recently, Miltersen and Subramanian [32] have studied classes that give rise to sub logarithmic complexity. They get tight bounds of Theta(log log n= log log log n) for (directed and undirected) bounded ....

....graphs investigated in [21] has the merit of being sufficiently general to admit a strong lower bound, which to my knowledge is not the case for any other DC algorithms. The reader 9 Authors Upper bound Lower bound Miltersen and Subramanian [32] Theta(log log n= log log log n) Italiano et al. [23] O(logn) Preparata and Tamassia [42] O(logn) Tamassia and Tollis [43] O(logn) Husfeldt [21] O(logn) Omega Gamma358 n= log log n) Subramanian [40] O(n 2=3 log n) Omega Gamma368 n= log log n) Table II.2. Restricted versions of Dynamic Transitive Closure. is invited to check carefully that ....

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Giuseppe F. Italiano, Alberto Marchetti Spaccamela, and Umberto Nanni, Dynamic data structures for series parallel digraphs, Proc. First Workshop on Algorithms and Data Structures (WADS) (F. Dehne, J.-R. Sack, and N. Santoro, eds.), Lecture Notes in Computer Science, vol. 382, Springer Verlag, Berlin, 1989, pp. 352--373.

....the present problem have been studied by Tamassia and Preparata [20] who consider the case where the source and the sink remain on the same face, and Tamassia and Tollis [21] who allow the source and the sink to be on di#erent faces but modify the repertory of update operations. Italiano et al. [11] present a dynamic reachability algorithm for series parallel digraphs. Papers by Bodlaender [3] and Cohen et al. 4] extend this to graphs of tree width two and three, respectively. Apart from these and the class studied in the present paper, no other class of digraphs is known to the author ....

....Apart from these and the class studied in the present paper, no other class of digraphs is known to the author that allows fully dynamic reachability algorithms within polylogarithmic time bounds. It is easy to see that the##e#2 n log log n) lower bound applies to the problems studied in [3, 4, 11, 18]. For the problems in [20, 21] no better bound than ##an# log n log log log n) is known to the author; this bound can be proved using techniques from [2, 13, 23] see also [14] Other dynamic problems on planar st graphs are studied in [1] and [19] Reference [20] contains pointers to a vast ....

Giuseppe F. Italiano, Alberto Marchetti Spaccamela, and Umberto Nanni. Dynamic data structures for series parallel digraphs. In Proc. First Workshop on Algorithms and Data Structures (WADS), volume 382 of Lecture Notes in Computer Science, pages 352--373. Springer Verlag, Berlin, 1989.

....e is currently a spanning edge, and if so, which tree it belongs to. Dynamic problems on graphs have been extensively studied. Several algorithms have been proposed for maintaining fundamental structural information about dynamic graphs, such as connectivity [9, 10, 15, 24, 26] transitive closure [17, 18, 19, 20, 21, 34, 23], and shortest paths [1, 8, 25, 28, 34] Dynamic planar graphs arise in communication networks, graphics, and VLSI design, and they occur in algorithms that build planar subdivisions such as Voronoi diagrams. Algorithms have been proposed for maintaining the embedding of a planar graph [29] and ....

G. F. Italiano, A. M. Spaccamela, and U. Nanni. Dynamic data structures for series parallel digraphs. In Proc. Workshop on Algorithms and Data Structures, (WADS 89), Lecture Notes in Computer Science, vol. 382, pages 352--372. Springer-Verlag, Berlin, 1989.

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