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129
Succinct Dynamic Data Structures
"... We develop succinct data structures to represent (i) a sequence of values to support partial sum and select queries and update (changing values) and (ii) a dynamic array consisting of a sequence of elements which supports insertion, deletion and access of an element at any given index. For the parti ..."
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Cited by 25 (2 self)
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We develop succinct data structures to represent (i) a sequence of values to support partial sum and select queries and update (changing values) and (ii) a dynamic array consisting of a sequence of elements which supports insertion, deletion and access of an element at any given index. For the partial sums problem...
Dominators in Linear Time
, 1997
"... A linear time algorithm is presented for finding dominators in control flow graphs. ..."
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Cited by 25 (0 self)
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A linear time algorithm is presented for finding dominators in control flow graphs.
Improved shortest paths on the word RAM
 in: 27th Colloquium on Automata, Languages and Programming (ICALP), in: Lecture Notes in Comput. Sci
"... Abstract. Thorup recently showed that singlesource shortestpaths problems in undirected networks with n vertices, m edges, and edge weights drawn from {0,...,2 w − 1} can be solved in O(n + m) time and space on a unitcost randomaccess machine with a word length of w bits. His algorithm works by ..."
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Cited by 24 (0 self)
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Abstract. Thorup recently showed that singlesource shortestpaths problems in undirected networks with n vertices, m edges, and edge weights drawn from {0,...,2 w − 1} can be solved in O(n + m) time and space on a unitcost randomaccess machine with a word length of w bits. His algorithm works by traversing a socalled component tree. Two new related results are provided here. First, and most importantly, Thorup’s approach is generalized from undirected to directed networks. The resulting time bound, O(n + m log w), is the best deterministic linearspace bound known for sparse networks unless w is superpolynomial in log n. As an application, allpairs shortestpaths problems in directed networks with n vertices, m edges, and edge weights in {−2 w,...,2 w} can be solved in O(nm + n 2 log log n) time and O(n + m) space (not counting the output space). Second, it is shown that the component tree for an undirected network can be constructed in deterministic linear time and space with a simple algorithm, to be contrasted with a complicated and impractical solution suggested by Thorup. Another contribution of the present paper is a greatly simplified view of the principles underlying algorithms based on component trees. 1
Rectilinear Paths among Rectilinear Obstacles
 Discrete Applied Mathematics
, 1996
"... Given a set of obstacles and two distinguished points in the plane the problem of finding a collision free path subject to a certain optimization function is a fundamental problem that arises in many fields, such as motion planning in robotics, wire routing in VLSI and logistics in operations resear ..."
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Cited by 23 (3 self)
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Given a set of obstacles and two distinguished points in the plane the problem of finding a collision free path subject to a certain optimization function is a fundamental problem that arises in many fields, such as motion planning in robotics, wire routing in VLSI and logistics in operations research. In this survey we emphasize its applications to VLSI design and limit ourselves to the rectilinear domain in which the goal path to be computed and the underlying obstacles are all rectilinearly oriented, i.e., the segments are either horizontal or vertical. We consider different routing environments, and various optimization criteria pertaining to VLSI design, and provide a survey of results that have been developed in the past, present current results and give open problems for future research. 1 Introduction Given a set of obstacles and two distinguished points in the plane, the problem of finding a collision free path subject to a certain optimization function is a fundamental probl...
An Empirical Analysis of Algorithms for Constructing a Minimum Spanning Tree
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1991
"... We compare algorithms for the construction of a minimum spanning tree through largescale experimentation on randomly generated graphs of different structures and different densities. In order to extrapolate with confidence, we use graphs with up to 130,000 nodes (sparse) or 750,000 edges (dense). A ..."
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Cited by 20 (1 self)
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We compare algorithms for the construction of a minimum spanning tree through largescale experimentation on randomly generated graphs of different structures and different densities. In order to extrapolate with confidence, we use graphs with up to 130,000 nodes (sparse) or 750,000 edges (dense). Algorithms included in our experiments are Prim's algorithm (implemented with a variety of priority queues), Kruskal's algorithm (using presorting or demand sorting), Cheriton and Tarjan's algorithm, and Fredman and Tarjan 's algorithm. We also ran a large variety of tests to investigate lowlevel implementation decisions for the data structures, as well as to enable us to eliminate the effect of compilers and architectures. Within the range of sizes used, Prim's algorithm, using pairing heaps or sometimes binary heaps, is clearly preferable. While versions of Prim's algorithm using efficient implementations of Fibonacci heaps or rankrelaxed heaps often approach and (on the densest graphs) so...
Shortest Path Algorithms: Engineering Aspects
 In Proc. ESAAC ’01, Lecture Notes in Computer Science
, 2001
"... We review shortest path algorithms based on the multilevel bucket data structure [6] and discuss the interplay between theory and engineering choices that leads to e#cient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an ..."
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Cited by 20 (3 self)
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We review shortest path algorithms based on the multilevel bucket data structure [6] and discuss the interplay between theory and engineering choices that leads to e#cient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an e#cient algorithm, both on typical and on hard inputs, for a wide range of arc lengths.
Floats, Integers, and Single Source Shortest Paths
 Journal of Algorithms
, 2000
"... Floats are ugly, but to everyone but theoretical computer scientists, they are the real thing. A linear time algorithm is presented for the undirected single source shortest paths problem with positive floating point weights. 1 Introduction The technical goal of this paper is to present a linear ti ..."
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Cited by 19 (2 self)
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Floats are ugly, but to everyone but theoretical computer scientists, they are the real thing. A linear time algorithm is presented for the undirected single source shortest paths problem with positive floating point weights. 1 Introduction The technical goal of this paper is to present a linear time solution to the undirected single source shortest paths problem (USSSP) where the weights are positive floating points, or just floats. On a more philosophical level, the goal is to draw attention to the problem of making efficient algorithms for floats. Suppose, for example, we have an algorithm for the maxflow problem whose running time includes a factor log C, where C is the maximal capacity. If we allow floating points, such an algorithm is not even polynomial, i.e. log C is the exponent of C, and the exponent is stored with log log C bits. Floating points are at least as used as integers, by everybody but theoretical computer scientists, who seem to prefer integers. To multiply two...
Fast and compact regular expression matching, 2005. Submitted to a journal. Preprint availiable at arxiv.org/cs/0509069
"... We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmicsized words to be manipulated in constant time. We show how to imp ..."
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Cited by 19 (4 self)
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We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmicsized words to be manipulated in constant time. We show how to improve the space and/or remove a dependency on the alphabet size for each problem using either an improved tabulation technique of an existing algorithm or by combining known algorithms in a new way.
Distributed Verification of Minimum Spanning Trees
 Proc. 25th Annual Symposium on Principles of Distributed Computing
, 2006
"... The problem of verifying a Minimum Spanning Tree (MST) was introduced by Tarjan in a sequential setting. Given a graph and a tree that spans it, the algorithm is required to check whether this tree is an MST. This paper investigates the problem in the distributed setting, where the input is given in ..."
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Cited by 19 (17 self)
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The problem of verifying a Minimum Spanning Tree (MST) was introduced by Tarjan in a sequential setting. Given a graph and a tree that spans it, the algorithm is required to check whether this tree is an MST. This paper investigates the problem in the distributed setting, where the input is given in a distributed manner, i.e., every node “knows ” which of its own emanating edges belong to the tree. Informally, the distributed MST verification problem is the following. Label the vertices of the graph in such a way that for every node, given (its own label and) the labels of its neighbors only, the node can detect whether these edges are indeed its MST edges. In this paper we present such a verification scheme with a maximum label size of O(log n log W), where n is the number of nodes and W is the largest weight of an edge. We also give a matching lower bound of Ω(log n log W) (except when W ≤ log n). Both our bounds improve previously known bounds for the problem. Our techniques (both for the lower bound and for the upper bound) may indicate a strong relation between the fields of proof labeling schemes and implicit labeling schemes. For the related problem of tree sensitivity also presented by Tarjan, our method yields rather efficient schemes for both the distributed and the sequential settings.