We investigate the problem of maintaining the are labels in the suffix tree datastructure (Gusfield et al., 1992;Amir et al., 1994) when it undergoes string insertions and deletions. In current literature, this probl...
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We investigate the problem of maintaining the are labels in the suffix tree datastructure (Gusfield et al., 1992;Amir et al., 1994) when it undergoes string insertions and deletions. In current literature, this problem is solved either by a simple accounting strategy to obtain amortized bounds (Fiala and Green, 1989;Larson, 1996) or by a periodical suffix tree reconstruction to obtain worst-case bounds (according to the global rebuilding technique in Overmars, 1983). Unfortunately, the former approach is simple and space efficient at the cost of attaining amortized bounds for the single update;the latter is space consuming, in practice, because it needs to keep two extra suffix tree copies. In this paper, we obtain a simple realtime algorithm that achieves worst-case bounds and only requires small additional space (i.e., a bi-directional pointer per suffix tree label). We analyze it by introducing a combinatorial coloring problem on the suffix tree arcs. (C) 1998 - Elsevier Science B.V. All rights reserved.
Two vertices of an undirected graph are called k-edge-connected if there exist k edge-disjoint paths between them (equivalently, they cannot be disconnected by the removal of less than k edges from the graph). Equival...
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Two vertices of an undirected graph are called k-edge-connected if there exist k edge-disjoint paths between them (equivalently, they cannot be disconnected by the removal of less than k edges from the graph). Equivalence classes of this relation are called classes of k-edge-connectivity or k-edge-connected components. This paper describes graph structures relevant to classes of 4-edge-connectivity and traces their transformations as new edges are inserted into the graph. datastructures and an algorithm to maintain these classes incrementally are given. Starting with the empty graph, any sequence of q Same-4-Class? queries and it Insert-Vertex and lit Insert-Edge updates can be performed in O(q + m + ii log n total time. Each individual query requires O(1) time in the worst-case. In addition, an algorithm for maintaining the classes of k-edge-connectivity (k arbitrary) in a (k-1)-edge-connected graph is presented. Its complexity is O(q + m + n). with O(M + k(2)n log(n/k)) preprocessing, where M is the number of edges initially in the graph and n is the number of its vertices.
We describe a robust, dynamic algorithm to compute the arrangement of a set of line segments in the plane, and its implementation. The algorithm is robust because, following Greene(7) and Hobby,(11) it rounds the endp...
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We describe a robust, dynamic algorithm to compute the arrangement of a set of line segments in the plane, and its implementation. The algorithm is robust because, following Greene(7) and Hobby,(11) it rounds the endpoints and intersections of all line segments to representable points, but in a way that is globally topologically consistent. The algorithm is dynamic because, following Mulmuley,(16) it uses a randomized hierarchy of vertical cell decompositions to make locating points, and inserting and deleting line segments,, efficient. Our algorithm is novel because it marries the robustness of the Greene and Hobby algorithms with Mulmuley's dynamic algorithm in a way that preserves the desirable properties of each.
This paper proposes two new dynamically allocated datastructures for large and sparse matrices occurring in electric power system problems. The proposed datastructures have the features of optimizing memory requirem...
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This paper proposes two new dynamically allocated datastructures for large and sparse matrices occurring in electric power system problems. The proposed datastructures have the features of optimizing memory requirement and fast accessing of data. Their advantages as compared to classical methods will be discussed, and a tradeoff analysis between memory requirement and accessing time will be performed. It will be shown that improvement in both memory requirement and processing time can be achieved.
We consider the problem of maintaining on-line the triconnected components of a graph G. Let n be the current number of vertices of G. We present an O (rt)-space datastructure that supports insertions of vertices and...
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We consider the problem of maintaining on-line the triconnected components of a graph G. Let n be the current number of vertices of G. We present an O (rt)-space datastructure that supports insertions of vertices and edges, and queries of the type ''Are there three vertex-disjoint paths between vertices v(1) and v(2)?'' A sequence of k operations takes time O(k . alpha(k,n)) if G is biconnected (alpha(k,n) denotes the well-known Ackermann's function inverse), and time O(n log n + k) if G is not biconnected. Note that the bounds do not depend on the number of edges of G. We use the SPQR-tree, a versatile datastructure that represents the decomposition of a biconnected graph with respect to its triconnected components, and the BC-tree, which represents the decomposition of a connected graph with respect to its biconnected components.
A point location scheme is presented for a dynamic planar subdivision whose underlying graph is only required to be connected. The operations supported include: reporting the name of the region containing a query poin...
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A point location scheme is presented for a dynamic planar subdivision whose underlying graph is only required to be connected. The operations supported include: reporting the name of the region containing a query point, inserting/deleting an edge, and inserting/deleting/moving a degree-2 vertex. The scheme uses O(n) space, has a worst-case query time of O(log2 n), and a worst-case update time of O(log n), where n is the number of vertices currently in the subdivision. Insertion (respectively, deletion) of an arbitrary k-edge chain inside a region can be performed in O(k log(n + k)) (respectively, O(k log n)) time in worst-case. The scheme outperforms the solutions given in works by Fries, Mehlhorn, and Naeher and by Overmars and also handles more general subdivisions than the schemes given in works by Preparata and Tamassia. The result is based on a new solution to a dynamic visibility problem for a set of tine segments in the plane that are nonintersecting, except possibly at endpoints. The scheme is then extended to speed up the insertion/deletion of a k-edge monotone chain to O(log2 n log log n + k) time (or O(log n log log n + k) time for an alternative model of input), but at the expense of increasing the other time bounds slightly. Additional results include a generalization to subdivisions consisting of algebraic segments of bounded degree and a persistent scheme that allows point location queries in the past and updates in the present.
We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translat...
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We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O (log n) time, while updates take O (log(2) n) time (amortized for vertex insertion/deletion and worst-case for the other updates). The space requirement is O(n log n). This is the first fully dynamic point location datastructure for monotone subdivisions that achieves optimal query time.
We present a fully dynamic technique for point location in triangulations that allows a tradeoff between query and update time, and can be used in conjunction with any of the known static point location datastructure...
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We present a fully dynamic technique for point location in triangulations that allows a tradeoff between query and update time, and can be used in conjunction with any of the known static point location datastructures. Let S be a triangulation whose current number of vertices is n. We show that for any smooth nondecreasing integer function b(n) with 2 less-than-or-equal-to b(n) less-than-or-equal-to square-root-n, there exists a dynamic point location datastructure for S with space O(n), query time O(log2n)/log b(n)), and update time O((log2n)b(n)/log b(n).
We show that a planarst-graphG admits two total orders on the setV∪E ∪F, whereV, E, andF are respectively the set of vertices, edges, and faces ofG, with |V| =n. Assuming thatG is to be dynamically modified by means...
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We show that a planarst-graphG admits two total orders on the setV∪E ∪F, whereV, E, andF are respectively the set of vertices, edges, and faces ofG, with |V| =n. Assuming thatG is to be dynamically modified by means of insertions of edges and expansions of vertices (and their inverses), we exhibit anO(n)-space dynamic data structure for the maintenance of these orders such that an update can be performed in timeO(logn). The discovered structural properties of planarst-graphs provide a unifying theoretical underpinning for several applications, such as dynamic point location in planar monotone subdivisions, dynamic transitive-closure query in planarst-graphs, and dynamic contact-chain query in convex subdivisions. The presented techniques significantly outperform previously known solutions of the same problems.
A row displacement method compresses efficiently a sparse matrix into a one-dimensional array. The access time with this method isO(l), but the application was restricted to the static matrices. In order to extend the...
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A row displacement method compresses efficiently a sparse matrix into a one-dimensional array. The access time with this method isO(l), but the application was restricted to the static matrices. In order to extend the use of the row displacement method to the dynamic matrices, the algorithms for insertion and deletion are proposed and the effectivity is confirmed by theoretical and empirical observations.
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