Results 1  10
of
2,316
Fibonacci Heaps and Their Uses in Improved Network . . .
, 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 t ..."
Abstract

Cited by 746 (18 self)
 Add to MetaCart
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 time and all other standard heap operations in o ( 1) amortized time. Using Fheaps we are able to obtain improved running times for several network optimization algorithms. In particular, we obtain the following worstcase bounds, where n is the number of vertices and m the number of edges 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 matching), improved from O(nm log0dn+2)n); (4) O(mj3(m, n)) for the minimum spanning tree problem, improved from O(mloglo&,,.+2,n), where j3(m, n) = min {i 1 log % 5 m/n). Note that B(m, n) 5 log*n if m 2 n. Of these results, the improved bound for minimum spanning trees is the most striking, although all the
Cortical surfacebased analysis II: Inflation, flattening, and a surfacebased coordinate system
 NEUROIMAGE
, 1999
"... The surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds. As such, it is a difficult domain for computational as well as visualization purposes. We have therefore designed a set of procedures for modifying the representation of the c ..."
Abstract

Cited by 697 (42 self)
 Add to MetaCart
The surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds. As such, it is a difficult domain for computational as well as visualization purposes. We have therefore designed a set of procedures for modifying the representation of the cortical surface to (i) inflate it so that activity buried inside sulci may be visualized, (ii) cut and flatten an entire hemisphere, and (iii) transform a hemisphere into a simple parameterizable surface such as a sphere for the purpose of establishing a surfacebased coordinate system.
Pregel: A system for largescale graph processing
 IN SIGMOD
, 2010
"... Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model ..."
Abstract

Cited by 472 (0 self)
 Add to MetaCart
(Show Context)
Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertexcentric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and faulttolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distributionrelated details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.
The Spatial Semantic Hierarchy
 Artificial Intelligence
, 2000
"... The Spatial Semantic Hierarchy is a model of knowledge of largescale space consisting of multiple interacting representations, both qualitative and quantitative. The SSH is inspired by the properties of the human cognitive map, and is intended to serve both as a model of the human cognitive map and ..."
Abstract

Cited by 333 (34 self)
 Add to MetaCart
(Show Context)
The Spatial Semantic Hierarchy is a model of knowledge of largescale space consisting of multiple interacting representations, both qualitative and quantitative. The SSH is inspired by the properties of the human cognitive map, and is intended to serve both as a model of the human cognitive map and as a method for robot exploration and mapbuilding. The multiple levels of the SSH express states of partial knowledge, and thus enable the human or robotic agent to deal robustly with uncertainty during both learning and problemsolving. The control level represents useful patterns of sensorimotor interaction with the world in the form of trajectoryfollowing and hillclimbing control laws leading to locally distinctive states. Local geometric maps in local frames of reference can be constructed at the control level to serve as observers for control laws in particular neighborhoods. The causal level abstracts continuous behavior among distinctive states into a discrete model ...
Intelligent Scissors for Image Composition
 In Computer Graphics, SIGGRAPH Proceedings
, 1995
"... We present a new, interactive tool called Intelligent Scissors which we use for image segmentation and composition. Fully automated segmentation is an unsolved problem, while manual tracing is inaccurate and laboriously unacceptable. However, Intelligent Scissors allow objects within digital images ..."
Abstract

Cited by 290 (8 self)
 Add to MetaCart
(Show Context)
We present a new, interactive tool called Intelligent Scissors which we use for image segmentation and composition. Fully automated segmentation is an unsolved problem, while manual tracing is inaccurate and laboriously unacceptable. However, Intelligent Scissors allow objects within digital images to be extracted quickly and accurately using simple gesture motions with a mouse. When the gestured mouse position comes in proximity to an object edge, a livewire boundary “snaps ” to, and wraps around the object of interest. Livewire boundary detection formulates discrete dynamic programming (DP) as a twodimensional graph searching problem. DP provides mathematically optimal boundaries while greatly reducing sensitivity to local noise or other intervening structures. Robustness is further enhanced with onthefly training which causes the boundary to adhere to the specific type of edge currently being followed, rather than simply the strongest edge in the neighborhood. Boundary cooling automatically freezes unchanging segments and automates input of additional seed points. Cooling also allows the user to be much more free with the gesture path, thereby increasing the efficiency and finesse with which boundaries can be extracted. Extracted objects can be scaled, rotated, and composited using livewire masks and spatial frequency equivalencing. Frequency equivalencing is performed by applying a Butterworth filter which matches the lowest frequency spectra to all other image components. Intelligent Scissors allow creation of convincing compositions from existing images while dramatically increasing the speed and precision with which objects can be extracted. 1.
Approximate distance oracles
 J. ACM
"... Let G = (V, E) be an undirected weighted graph with V  = n and E  = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately, in ..."
Abstract

Cited by 279 (10 self)
 Add to MetaCart
Let G = (V, E) be an undirected weighted graph with V  = n and E  = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately, in O(k) time. The approximate distance returned is of stretch at most 2k − 1, i.e., the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k−1. A 1963 girth conjecture of Erdős, implies that Ω(n 1+1/k) space is needed in the worst case for any real stretch strictly smaller than 2k + 1. The space requirement of our algorithm is, therefore, essentially optimal. The most impressive feature of our data structure is its constant query time, hence the name “oracle”. Previously, data structures that used only O(n 1+1/k) space had a query time of Ω(n 1/k). Our algorithms are extremely simple and easy to implement efficiently. They also provide faster constructions of sparse spanners of weighted graphs, and improved tree covers and distance labelings of weighted or unweighted graphs. 1
The Watershed Transform: Definitions, Algorithms and Parallelization Strategies
, 2001
"... The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the li ..."
Abstract

Cited by 227 (3 self)
 Add to MetaCart
The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the literature. The need to distinguish between definition, algorithm specification and algorithm implementation is pointed out. Various examples are given which illustrate differences between watershed transforms based on different definitions and/or implementations. The second part of the paper surveys approaches for parallel implementation of sequential watershed algorithms.
An Overview of QualityofService Routing for the Next Generation HighSpeed Networks: Problems and Solutions
"... The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. On ..."
Abstract

Cited by 223 (22 self)
 Add to MetaCart
(Show Context)
The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. One of the key issues is the QualityofService (QoS) routing. It selects network routes with sufficient resources for the requested QoS parameters. The goal of routing solutions is twofold: (1) satisfying the QoS requirements for every admitted connection and (2) achieving the global efficiency in resource utilization. Many unicast/multicast QoS routing algorithms were published recently, and they work with a variety of QoS requirements and resource constraints. Overall, they can be partitioned into three broad classes: (1) source routing, (2) distributed routing and (3) hierarchical routing algorithms. In this paper we give an overview of the QoS routing problem as well as the existing solutions. We present the strengths and the weaknesses of different routing strategies and outline the challenges. We also discuss the basic algorithms in each class, classify and compare them, and point out possible future directions in the QoS routing area.
Multicast Routing for Multimedia Communication
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1993
"... We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend delay along the paths from source to each destination, and ii) minimum cost of the multicast tree, where edge cost and edge delay can be independent metrics. This problem of computing such ..."
Abstract

Cited by 216 (9 self)
 Add to MetaCart
We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend delay along the paths from source to each destination, and ii) minimum cost of the multicast tree, where edge cost and edge delay can be independent metrics. This problem of computing such a constrained multicast tree is NPcomplete. We show that the heuristics demonstrate good average case behavior in terms of cost, as determined through simulations on a large number of graphs.