D. Eppstein, Z. Galil, G. F. Italiano, and T. H. Spencer. Separator based sparsification I: Planarity testing and minimum spanning trees. Journal of Computer and System Science, 52(1):3--27, 1996. http://www.unisa.it/ gfi.dir/Papers/sparse.ps.Z.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(or equivalently where to put an inserted edge in the rotations of the two incident vertices) because otherwise it may be very time consuming to recompute a planar embedding. In a sense this difficulties can be seen in the fully dynamic planarity problem: here every operation needs n) time [EGIS96] whereas the biconnectivity problem in plane graphs needs only time O(log n) See also the article of Tamassia [Tam96] 21 provide an algorithm that has amortized running time of O(log n) per update, O(1) worst case time per query and uses linear space. Alternatively the amortized running ....

D. Eppstein, Z. Galil, G. F. Italiano, and T. H. Spencer. Separator based sparsification I: Planarity testing and minimum spanning trees. Journal of Computer and System Science, 52(1):3--27, 1996. http://www.unisa.it/ gfi.dir/Papers/sparse.ps.Z.

....general graphs, it seemed unlikely that it could be used to speed up algorithms for special families of graphs that are already sparse, such as planar graphs. However, algorithms for planar graphs are especially important, as these graphs arise frequently in applications. In the companion paper [11] we developed a new, general technique for dynamic planar graph problems, based upon the notion of compressed certificates, which have both fewer edges and fewer vertices than the original graph. We expanded the notion of certificate to a definition for graphs in which a subset of the vertices is ....

....edge insertions and deletions, with queries that test whether the graph is currently planar or whether a potential new edge would violate planarity. In this paper we extend these ideas in several ways. Our first constribution is to adapt separator based sparsification from the companion paper [11] to work on more general certificates and properties. Namely, we extend the notion of compressed certificates to properties that can be defined with respect to a particular pair of vertices rather than on the whole graph. We refer to these as local certificates as opposed to global certificates. ....

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D. Eppstein, Z. Galil, G. F. Italiano, and T. H. Spencer, Separator based sparsification I: Planarity testing and minimum spanning trees, J. Comput. System Sci., Special issue on STOC 93, 52 (1996), pp. 3--27.

....logarithm by reducing the number of vertices as well as the number of edges in the recursive subproblems. # 2.2. Separator Based Sparsification Certificates We applied sparsification to speed up our kinetic algorithms for general graphs. We now similarly apply separator based sparsification [12] to speed up our algorithms for planar graphs and for minor closed graph families. The basic idea of this approach is to divide the graph into two subgraphs by a separator, a small set X of vertices shared by both subgraphs, so that each subgraph has only a constant fraction of the original ....

D. Eppstein, Z. Galil, G. F. Italiano, and T. H. Spencer. Separator based sparsification I: planarity testing and minimum spanning trees. J. Computing & Systems Sciences, 52 (1996), 3--27.

....URL: http: www.info.uniroma2.it italiano . Part of this work was done while visiting the Max Planck Institut fur Informatik, Im Stadtwald, 66123 Saarbrucken, Germany. 1 Introduction In the last years research in dynamic graph algorithms has been a blossoming field (see e.g. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24]) The main dynamic model that has been considered in the literature is the following. We are given a graph G = V; E) and we wish to maintain some property P in G during edge deletions and edge insertions. We refer to this as the dynamic edge model . If the graph represents a communication ....

....O(log n) time) However, since switching a vertex on or off could cause as many as Theta(n) edges to be deleted or inserted, each vertex update could require O(n log n) time in the worst case. In this paper, we show how to adapt the separator based sparsification technique of Eppstein et al. [5, 6] to this problem, and give algorithms and data structures for solving the problem in O(log 3 n) amortized time per insert, delete, switch on, switch off, and query operations over sequences of Omega Gamma n) operations. This improves sharply on previous approaches. Our algorithms exploit ....

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D. Eppstein, Z. Galil, G. F. Italiano, T. H. Spencer. Separator based sparsification I: planarity testing and minimum spanning trees. Journal of Computer and System Science, Special issue of STOC'93, 52, no. 1 (1996), 3--27.

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