Results 1  10
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113
New Data Structures for Orthogonal Range Searching
, 2001
"... We present new general techniques for static orthogonal range searching problems intwo and higher dimensions. For the general range reporting problem in R 3, we achieve query time O(log n + k) using space O(n log1+ " n), where n denotes the number of storedpoints and k the number of point ..."
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Cited by 81 (2 self)
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We present new general techniques for static orthogonal range searching problems intwo and higher dimensions. For the general range reporting problem in R 3, we achieve query time O(log n + k) using space O(n log1+ " n), where n denotes the number of storedpoints and k the number of points to be reported. For the range reporting problem onan n * n grid, we achieve query time O(log log n + k) using space O(n log " n). For thetwodimensional semigroup range sum problem we achieve query time O(log n) usingspace O ( n log n).
Improved Labeling Scheme for Ancestor Queries
, 2001
"... We present a labeling scheme for rooted trees that supports ancestor queries. Given a tree, the scheme assigns to each node a label which is a binary string. Given the labels of any two nodes u and v, it can in constant time be determined whether u is ancestor to v alone from these labels. For tr ..."
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Cited by 52 (7 self)
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We present a labeling scheme for rooted trees that supports ancestor queries. Given a tree, the scheme assigns to each node a label which is a binary string. Given the labels of any two nodes u and v, it can in constant time be determined whether u is ancestor to v alone from these labels. For trees of size n our scheme assigns labels of size bounded by log n + O( p log n) bits to each node. This improves a recent result of Abiteboul, Kaplan and Milo at SODA'01, where a labeling scheme with labels of size 3=2 log n+ O(log log n) was presented. The problem is among other things motivated in connection with ecient representation of information for XMLbased search engines for the internet.
Generalized Dominators for Structured Programs
, 1996
"... . Recently it has been discovered that control flow graphs of structured programs have bounded treewidth. In this paper we show that this knowledge can be used to design fast algorithms for control flow analysis. We give a linear time algorithm for the problem of finding the immediate multipleverte ..."
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Cited by 4 (1 self)
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nodes and jEj edges and is due to Alstrup, Clausen and Jørgensen (An O(jV j jEj) Algorithm for Finding Immediate MultipleVertex Dominators, accepted to Information Processing Letters). 1 Introduction Constructing dominator trees for control flow graphs G(V; E; s) has been investigated in many papers
Dominators in Linear Time
, 1997
"... A linear time algorithm is presented for finding dominators in control flow graphs. ..."
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Cited by 37 (0 self)
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A linear time algorithm is presented for finding dominators in control flow graphs.
Labeling Schemes for Small Distances in Trees
, 2003
"... We consider labeling schemes for trees, supporting various relationships between nodes at small distance. For instance, we show that given a tree T and an integer k we can assign labels to each node of T such that given the label of two nodes we can decide, from these two labels alone, if the distan ..."
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Cited by 33 (3 self)
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We consider labeling schemes for trees, supporting various relationships between nodes at small distance. For instance, we show that given a tree T and an integer k we can assign labels to each node of T such that given the label of two nodes we can decide, from these two labels alone, if the distance between v and w is at most k and if so compute it. For trees with n nodes and k> 2, we give a lower bound on the maximum label length of log n + ~(loglogn) bits, and for constant k, we give an upper bound of log n + O(log log n). Bounds for ancestor, sibling, connectivity and bi and triconnectivity labeling schemes are also presented.
Minimizing Diameters of Dynamic Trees
 In Proc. 24th International Colloquium on Automata, Languages, and Programming (ICALP
, 1997
"... . In this paper we consider an online problem related to minimizing the diameter of a dynamic tree T . A new edge f is added, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree T [ffgnfeg. Starting with a tree with n nodes, we show how e ..."
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Cited by 31 (11 self)
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. In this paper we consider an online problem related to minimizing the diameter of a dynamic tree T . A new edge f is added, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree T [ffgnfeg. Starting with a tree with n nodes, we show how each such best swap can be found in worstcase O(log 2 n) time. The problem was raised by Italiano and Ramaswami at ICALP'94 together with a related problem for edge deletions. Italiano and Ramaswami solved both problems in O(n) time per operation. 1 Introduction The diameter of a tree is the length of a longest simple path in the tree and such a path is called a diameter path. The unique midpoint on all diameter paths is called the center, hence the center is the point whose maximal distance to any node is as small as possible. In 1973 Handler [4] showed how one in linear time can compute the diameter (and center) of a tree. However, as pointed out by Rauch [8], too little work has been...
Efficient tree layout in a multilevel memory hierarchy, arXiv:cs.DS/0211010
, 2003
"... We consider the problem of laying out a tree with fixed parent/child structure in hierarchical memory. The goal is to minimize the expected number of block transfers performed during a search along a roottoleaf path, subject to a given probability distribution on the leaves. This problem was previ ..."
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Cited by 27 (7 self)
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We consider the problem of laying out a tree with fixed parent/child structure in hierarchical memory. The goal is to minimize the expected number of block transfers performed during a search along a roottoleaf path, subject to a given probability distribution on the leaves. This problem was previously considered by Gil and Itai, who developed optimal but slow algorithms when the blocktransfer size B is known. We present faster but approximate algorithms for the same problem; the fastest such algorithm runs in linear time and produces a solution that is within an additive constant of optimal. In addition, we show how to extend any approximately optimal algorithm to the cacheoblivious setting in which the blocktransfer size is unknown to the algorithm. The query performance of the cacheoblivious layout is within a constant factor of the query performance of the optimal knownblocksize layout. Computing the cacheoblivious layout requires only logarithmically many calls to the layout algorithm for known block size; in particular, the cacheoblivious layout can be computed in O(N lg N) time, where N is the number of nodes. Finally, we analyze two greedy strategies, and show that they have a performance ratio between Ω(lg B / lg lg B) and O(lg B) when compared to the optimal layout.
Optimal static range reporting in one dimension
 IN PROC. 33RD ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC'01)
, 2001
"... ..."
Optimal Online Decremental Connectivity in Trees
 IPL
, 1997
"... Let T be a tree with n nodes from which edges are deleted interspersed with m online connectivity queries. Even and Shiloach gave an O(n log n + m) algorithm to process edge deletion and m queries (An OnLine EdgeDeletion problem, J. ACM, Vol. 28, Nr. 1, 1981). In this paper we present an O(n + ..."
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Cited by 12 (3 self)
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Let T be a tree with n nodes from which edges are deleted interspersed with m online connectivity queries. Even and Shiloach gave an O(n log n + m) algorithm to process edge deletion and m queries (An OnLine EdgeDeletion problem, J. ACM, Vol. 28, Nr. 1, 1981). In this paper we present an O(n +m) algorithm for the same problem.
A Simple and Optimal Algorithm for Finding Immediate Dominators in Reducible Graphs
, 1996
"... We present two simple algorithm for finding immediate dominator in reducible graphs with n nodes and m edges: A O(n + m) RAM algorithm and a O(n +m log log n) pointer machine algorithm. 1 Introduction Algorithms for finding dominator trees for control flow graphs are described in [5, 7, 8]. Dominat ..."
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Cited by 4 (0 self)
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We present two simple algorithm for finding immediate dominator in reducible graphs with n nodes and m edges: A O(n + m) RAM algorithm and a O(n +m log log n) pointer machine algorithm. 1 Introduction Algorithms for finding dominator trees for control flow graphs are described in [5, 7, 8]. Dominator trees are used in control flow analysis [1, 4]. In [5] a linear time algorithm is given. This algorithm is complicated and to our knowledge no experimental results using this algorithm have been published. This is the motivation for presenting two simpler algorithms, one of which runs on a pointer machine [10]. The algorithms presented in this paper have previously been described by the authors of this paper and also independently and simultaneously in [9]. But at that time the important results from [2, 3], were not applied, so the contribution of this paper is only a compilation. 2 Notation A control flow graph CFG(V;E; s) is a directed graph with a start node s, from which all nodes i...
Results 1  10
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113