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57
Fibonacci Heaps and Their Uses in Improved Network optimization algorithms
, 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized tim ..."
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Cited by 739 (18 self)
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in the problem graph: ( 1) O(n log n + m) for the singlesource shortest path problem with nonnegative edge lengths, improved from O(m logfmh+2)n); (2) O(n*log n + nm) for the allpairs shortest path problem, improved from O(nm lo&,,,+2,n); (3) O(n*logn + nm) for the assignment problem (weighted bipartite
Faster regular expression matching
 Automata, Languages and Programming
, 2009
"... Abstract. Regular expression matching is a key task (and often the computational bottleneck) in a variety of widely used software tools and applications, for instance, the unix grep and sed commands, scripting languages such as awk and perl, programs for analyzing massive data streams, etc. We show ..."
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Cited by 9 (2 self)
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how to solve this ubiquitous task in linear space and O(nm(log log n)/(logn)3/2+n+m) time where m is the length of the expression and n the length of the string. This is the first improvement for the dominant O(nm / logn) term in Myers ’ O(nm / logn+ (n+m) logn) bound [JACM 1992]. We also get improved
Almost all kcolorable graphs are easy to color
 In: J. Algorithms
, 1988
"... We describe a simple and e cient heuristic algorithm for the graph coloring problem and show that for all k it nds an optimal coloring for almost all kcolorable graphs We also show that an algorithm proposed by Brelaz and justi ed on experimental grounds optimally colors almost all kcolorable gr ..."
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Cited by 72 (0 self)
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graphs E cient implementations of both algorithms are given The rst one runs in O
nm log k time where n is the number of vertices and m the number of edges The new implementation of Brelazs algorithm runs in O
m logn time We observe that the popular greedy heuristic works poorly on kcolorable graphs
Small distortion and volume preserving embeddings for Planar and Euclidean metrics
, 1999
"... A finite metric space, (S,d) , contains a finite set of points and a distance function on pairs of points. A contraction is an embedding, h, of a finite metric space (S, d) into Rd where for any u, v E S, the Euclidean (&) distance between h(u) and h(v) is no more than d(u, v). The distortion of ..."
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Cited by 68 (1 self)
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of the embedding is the maximum over pairs of the ratio of d(u, w) and the Euclidean distance between h(u) and h(v). Bourgain showed that any graphical metric could be embedded with distortion O(logn). Linial, London and Rabinovich and Aumman and Rabani used such embeddings to prove an O(log k) approximate max
A Fast and Simple Algorithm for the Maximum Flow Problem
 OPERATIONS RESEARCH
, 1989
"... We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U. Under the practical assumption that U is polynomially bounded in n, our algorithm runs in time O(nm + n 2 log n). This result improves the previous best b ..."
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Cited by 43 (8 self)
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bound of O(nm log(n 2 /m)), obtained by Goldberg and Taran, by a factor of log n for networks that are both nonsparse and nondense without using any complex data structures. We also describe a parallel implementation of the algorithm that runs in O(n'log U log p) time in the PRAM model with EREW
A Faster Algorithm for Finding the Minimum Cut in a Directed Graph
 JOURNAL OF ALGORITHMS
, 1994
"... We consider the problem of finding the minimum capacity cut in a directed network G with n nodes. This problem has applications to network reliability and survivability and is useful in subroutines for other network optimization problems. One can use a maximum flow problem to find a minimum cut sepa ..."
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Cited by 45 (0 self)
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maximum flow problem. The resulting running time is O(nm log(n 2 /m)) for finding the minimum cut in either a directed or an undirected network. © 1994 Academic Press, Inc. 1.
Computing the Maximum Overlap of Two Convex Polygons Under Translations
 THEORY OF COMPUTING SYSTEMS
, 1996
"... Let P be a convex polygon in the plane with n vertices and let Q be a convex polygon with m vertices. We prove that the maximum number of combinatorially distinct place ments of Q with respect to P under translations is O(n 2 + m + rain(rim + nm)), and we give an example showing that this bound ..."
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Cited by 29 (7 self)
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Let P be a convex polygon in the plane with n vertices and let Q be a convex polygon with m vertices. We prove that the maximum number of combinatorially distinct place ments of Q with respect to P under translations is O(n 2 + m + rain(rim + nm)), and we give an example showing that this bound
Robust and Efficient Detection of Convex Groups
, 1995
"... This paper describes an algorithm that robustly locates convex collections of line segments in an image. The algorithm is guaranteed to find all convex sets of line segments in which the length of the line segments accounts for at least some fixed proportion of the length of their convex hull. This ..."
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Cited by 43 (1 self)
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. This enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise. We perform an expected case analysis of the algorithm's performance that shows that its run time is O(n 2 log(n) + nm), when we wish to find the m most salient groups in an image with n line
Global price updates help
, 1997
"... Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of pushrelabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global upd ..."
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Cited by 14 (3 self)
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updates yield a theoretical improvement as well. For bipartite matching, a pushrelabel algorithm that uses global updates runs in O ( √ log(n nm 2) /m) time (matching the best bound log n known) and performs worse by a factor of √ n without the updates. A similar result holds for the assignment problem
A Heuristic Homotopic Path Simplification Algorithm
"... Abstract. We study the wellknown problem of approximating a polygonal path P by a coarse one, whose vertices are a subset of the vertices of P. In this problem, for a given error, the goal is to find a path with the minimum number of vertices while preserving the homotopy in presence of a given set ..."
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set of extra points in the plane. We present a heuristic method for homotopypreserving simplification under any desired measure for general paths. Our algorithm for finding homotopic shortcuts runs in O(m log(n + m) +n log n log(nm)+k) time, where k is the number of homotopic shortcuts. Using
Results 1  10
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