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41
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 520 (40 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straightline, polyline, visibility), and update the drawing in a smooth way.
Randomized Search Trees
 ALGORITHMICA
, 1996
"... We present a randomized strategy for maintaining balance in dynamically changing search trees that has optimal expected behavior. In particular, in the expected case a search or an update takes logarithmic time, with the update requiring fewer than two rotations. Moreover, the update time remains ..."
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Cited by 139 (1 self)
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We present a randomized strategy for maintaining balance in dynamically changing search trees that has optimal expected behavior. In particular, in the expected case a search or an update takes logarithmic time, with the update requiring fewer than two rotations. Moreover, the update time remains logarithmic, even if the cost of a rotation is taken to be proportional to the size of the rotated subtree. Finger searches and splits and joins can be performed in optimal expected time also. We show that these results continue to hold even if very little true randomness is available, i.e. if only a logarithmic number of truely random bits are available. Our approach generalizes naturally to weighted trees, where the expected time bounds for accesses and updates again match the worst case time bounds of the best deterministic methods. We also discuss ways of implementing our randomized strategy so that no explicit balance information is maintained. Our balancing strategy and our alg...
An Optimal Algorithm for Closest Pair Maintenance
 Discrete Comput. Geom
, 1995
"... Given a set S of n points in kdimensional space, and an L t metric, the dynamic closest pair problem is defined as follows: find a closest pair of S after each update of S (the insertion or the deletion of a point). For fixed dimension k and fixed metric L t , we give a data structure of size O(n) ..."
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Cited by 35 (0 self)
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Given a set S of n points in kdimensional space, and an L t metric, the dynamic closest pair problem is defined as follows: find a closest pair of S after each update of S (the insertion or the deletion of a point). For fixed dimension k and fixed metric L t , we give a data structure of size O(n) that maintains a closest pair of S in O(logn) time per insertion and deletion. The running time of algorithm is optimal up to constant factor because \Omega\Gammaaus n) is a lower bound, in algebraic decisiontree model of computation, on the time complexity of any algorithm that maintains the closest pair (for k = 1). The algorithm is based on the fairsplit tree. The constant factor in the update time is exponential in the dimension. We modify the fairsplit tree to reduce it. 1 Introduction The dynamic closest pair problem is one of the very wellstudied proximity problem in computational geometry [6, 1720, 22, 2426, 2831]. We are given a set S of n points in kdimensional space...
Efficient treebased revocation in groups of lowstate devices
 In Proceedings of Crypto ’04, volume 2204 of LNCS
, 2004
"... Abstract. We study the problem of broadcasting confidential information to a collection of n devices while providing the ability to revoke an arbitrary subset of those devices (and tolerating collusion among the revoked devices). In this paper, we restrict our attention to lowmemory devices, that i ..."
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Cited by 33 (1 self)
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Abstract. We study the problem of broadcasting confidential information to a collection of n devices while providing the ability to revoke an arbitrary subset of those devices (and tolerating collusion among the revoked devices). In this paper, we restrict our attention to lowmemory devices, that is, devices that can store at most O(log n) keys. We consider solutions for both zerostate and lowstate cases, where such devices are organized in a tree structure T. We allow the group controller to encrypt broadcasts to any subtree of T,evenifthetreeisbasedonanmultiway organizational chart or a severely unbalanced multicast tree. 1
Searching dynamic point sets in spaces with bounded doubling dimension
 In The thirtyeighth annual ACM symposium on Theory of computing (STOC
, 2006
"... We present a new data structure that facilitates approximate nearest neighbor searches on a dynamic set of points in a metric space that has a bounded doubling dimension. Our data structure has linear size and supports insertions and deletions in O(log n) time, and finds a (1 + ɛ)approximate neares ..."
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Cited by 29 (8 self)
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We present a new data structure that facilitates approximate nearest neighbor searches on a dynamic set of points in a metric space that has a bounded doubling dimension. Our data structure has linear size and supports insertions and deletions in O(log n) time, and finds a (1 + ɛ)approximate nearest neighbor in time O(log n) +(1/ɛ) O(1). The search and update times hide multiplicative factors that depend on the doubling dimension; the space does not. These performance times are independent of the aspect ratio (or spread) of the points. Categories and Subject Descriptors: F.2.2 [Nonnumerical Algorithms and Problems]:Sorting and searching, computations on discrete structures; E.1 [Data Structures]:Graphs and networks, trees.
A unified approach to dynamic point location, ray shooting, and shortest paths in planar maps
 SIAM Journal on Computing
, 1996
"... Abstract. We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map dX/ [ with n vertices and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in A4. The space re ..."
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Cited by 24 (8 self)
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Abstract. We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map dX/ [ with n vertices and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in A4. The space requirement is O(n log n). Pointlocation queries take time O(log n). Rayshooting and shortestpath queries take time O(log n) (plus O(k) time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take O(log n) time (amortized for vertex updates). This is the first polylogtime dynamic data structure for shortestpath and rayshooting queries. It is also the first dynamic pointlocation data structure for connected planar maps that achieves optimal query time. Key words, point location, ray shooting, shortest path, computational geometry, dynamic algorithm
Methods for Achieving Fast Query Times in Point Location Data Structures
, 1997
"... Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data struc ..."
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Cited by 20 (1 self)
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Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data structures can be constructed so as to achieve O(log n) query times. But applications, such as those common in geographic information systems, motivate a reexamination of this problem with the goal of improving query times further while also simplifying the methods needed to achieve such query times. In this paper we perform such a reexamination, focusing on the issues that arise in three different classes of pointlocation query sequences: ffl sequences that are reasonably uniform spatially and temporally (in which case the constant factors in the query times become critical), ffl sequences that are nonuniform spatially or temporally (in which case one desires data structures that adapt to s...
Dynamic and I/OEfficient Algorithms for Computational Geometry and Graph Problems: Theoretical and Experimental Results
, 1995
"... As most important applications today are largescale in nature, highperformance methods are becoming indispensable. Two promising computational paradigms for largescale applications are dynamic and I/Oefficient computations. We give efficient dynamic data structures for several fundamental proble ..."
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Cited by 18 (4 self)
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As most important applications today are largescale in nature, highperformance methods are becoming indispensable. Two promising computational paradigms for largescale applications are dynamic and I/Oefficient computations. We give efficient dynamic data structures for several fundamental problems in computational geometry, including point location, ray shooting, shortest path, and minimumlink path. We also develop a collection of new techniques for designing and analyzing I/Oefficient algorithms for graph problems, and illustrate how these techniques can be applied to a wide variety of specific problems, including list ranking, Euler tour, expressiontree evaluation, leastcommon ancestors, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation. Finally, we present an extensive experimental study comparing the practical I/O efficiency of four algorithms for the orthogonal s...
Dynamization of the Trapezoid Method for Planar Point Location in Monotone Subdivisions
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY AND APPLICATIONS
, 1992
"... 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. Poi ..."
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Cited by 16 (5 self)
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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(logn) time, while updates take O(log² n) time (amortized for vertex insertion/deletion and worstcase for the others). The space requirement is O(n log n). This is the first fully dynamic point location data structure for monotone subdivisions that achieves optimal query time.
A Dynamic Lookup Scheme for Bursty Access Patterns
, 2001
"... The problem of fast address lookup is crucial to routing and thus has received considerable attention. Most of the work in this field has focused on improving the speed of individual accesses  independent from the underlying access pattern. Recently, Gupta et al. [1] proposed an efficient data str ..."
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Cited by 15 (0 self)
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The problem of fast address lookup is crucial to routing and thus has received considerable attention. Most of the work in this field has focused on improving the speed of individual accesses  independent from the underlying access pattern. Recently, Gupta et al. [1] proposed an efficient data structure to exploit the bias in access pattern. This technique achieves faster lookups for more frequently accessed keys while bounding the worst case lookup time; in fact it is (near) optimal under constraints on worst case performance. However, it needs to be rebuilt periodically to reflect the changes in access patterns, which can be inefficient for bursty environments. In this paper we introduce a new dynamic data structure to exploit biases in the access pattern, which tend to change dynamically. Recent work shows that there are many circumstances under which access patterns change quickly [2], [3]. Our data structure, which we call the Biased Skip List (BSL), has a selfupdate mechanism which reflects the changes in the access patterns efficiently and immediately, without any need for rebuilding. It improves throughput while keeping the worst case access time bounded by that of the fastest (unbiased) schemes. We demonstrate the practicality of BSL by experiments on data with varying degrees of burstiness. I.