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22
A Functional Approach to External Graph Algorithms
 Algorithmica
, 1998
"... . We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete w ..."
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Cited by 109 (2 self)
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. We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete with those of previous approaches. Unlike previous approaches, ours is purely functionalwithout side effectsand is thus amenable to standard checkpointing and programming language optimization techniques. This is an important practical consideration for applications that may take hours to run. 1 Introduction We present a divideandconquer approach for designing external graph algorithms, i.e., algorithms on graphs that are too large to fit in main memory. Our approach is simple to describe and implement: it builds a succession of graph transformations that reduce to sorting, selection, and a recursive bucketing technique. No sophisticated data structures are needed. We apply our t...
Protocols and impossibility results for gossipbased communication mechanisms
, 2002
"... In recent years, gossipbased algorithms have gained prominence as a methodology for designing robust and scalable communication schemes in large distributed systems. The premise underlying distributed gossip is very simple: in each time step, each node v in the system selects some other node w as a ..."
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Cited by 70 (3 self)
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In recent years, gossipbased algorithms have gained prominence as a methodology for designing robust and scalable communication schemes in large distributed systems. The premise underlying distributed gossip is very simple: in each time step, each node v in the system selects some other node w as a communication partner — generally by a simple randomized rule — and exchanges information with w; over a period of time, information spreads through the system in an “epidemic fashion”. A fundamental issue which is not well understood is the following: how does the underlying lowlevel gossip mechanism — the means by which communication partners are chosen — affect one’s ability to design efficient highlevel gossipbased protocols? We establish one of the first concrete results addressing this question, by showing a fundamental limitation on the power of the commonly used uniform gossip mechanism for solving nearestresource location problems. In contrast, very efficient protocols for this problem can be designed using a nonuniform spatial gossip mechanism, as established in earlier work with Alan Demers. We go on to consider the design of protocols for more complex problems, providing an efficient distributed gossipbased protocol for a set of nodes in Euclidean space to construct an approximate minimum spanning tree. Here too, we establish a contrasting limitation on the power of uniform gossip for solving this problem. Finally, we investigate gossipbased packet routing as a primitive that underpins the communication patterns in many protocols, and as a way to understand the capabilities of different gossip mechanisms at a general level.
Engineering an External Memory Minimum Spanning Tree Algorithm
 IN PROC. 3RD IFIP INTL. CONF. ON THEORETICAL COMPUTER SCIENCE
, 2004
"... We develop an external memory algorithm for computing minimum spanning trees. The algorithm is considerably simpler than previously known external memory algorithms for this problem and needs a factor of at least four less I/Os for realistic inputs. Our implementation indicates that this algorithm ..."
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Cited by 24 (6 self)
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We develop an external memory algorithm for computing minimum spanning trees. The algorithm is considerably simpler than previously known external memory algorithms for this problem and needs a factor of at least four less I/Os for realistic inputs. Our implementation indicates that this algorithm processes graphs only limited by the disk capacity of most current machines in time no more than a factor 2–5 of a good internal algorithm with sufficient memory space.
Segmentation Graph Hierarchies
 In: Proceedings of Joint Workshops on Structural, Syntactic, and Statistical Pattern Recognition S+SSPR. Volume 3138 of Lecture Notes in Computer Science
, 2004
"... The region's internal properties (color, texture, ...) help to identify them and their external relations (adjacency, inclusion, ...) are used to build groups of regions having a particular consistent meaning in a more abstract context. Lowlevel cue image segmentation in a bottomup way, c ..."
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Cited by 16 (4 self)
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The region's internal properties (color, texture, ...) help to identify them and their external relations (adjacency, inclusion, ...) are used to build groups of regions having a particular consistent meaning in a more abstract context. Lowlevel cue image segmentation in a bottomup way, cannot and should not produce a complete final "good" segmentation. We present a hierarchical partitioning of images using a pairwise similarity function on a graphbased representation of an image.
Hierarchical Image Partitioning with Dual Graph Contraction
 Proc. of 25th DAGM Symposium LNCS
, 2003
"... We present a hierarchical partitioning of images using a pairwise similarity function on a graphbased representation of an image. This function measures the difference along the boundary of two components relative to a measure of differences of the components' internal differences. This defini ..."
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Cited by 14 (4 self)
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We present a hierarchical partitioning of images using a pairwise similarity function on a graphbased representation of an image. This function measures the difference along the boundary of two components relative to a measure of differences of the components' internal differences. This definition tries to encapsulate the intuitive notion of contrast. Two components are merged if there is a lowcost connection between them. Each component's internal difference is represented by the maximum edge weight of its minimum spanning tree. External differences are the smallest weight of edges connecting components. We use this idea for building a minimum spanning tree to find region borders quickly and effortlessly in a bottomup way, based on local differences in a specific feature.
The filterkruskal minimum spanning tree algorithm
, 2009
"... We present FilterKruskal – a simple modification of Kruskal’s algorithm that avoids sorting edges that are “obviously” not in the MST. For arbitrary graphs with random edge weights FilterKruskal runs in time O (m + n lognlog m n, i.e. in linear time for not too sparse graphs. Experiments indicate ..."
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Cited by 10 (1 self)
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We present FilterKruskal – a simple modification of Kruskal’s algorithm that avoids sorting edges that are “obviously” not in the MST. For arbitrary graphs with random edge weights FilterKruskal runs in time O (m + n lognlog m n, i.e. in linear time for not too sparse graphs. Experiments indicate that the algorithm has very good practical performance over the entire range of edge densities. An equally simple parallelization seems to be the currently best practical algorithm on multicore machines.
Pyramid segmentation algorithms revisited
, 2006
"... The main goal of this work is to compare pyramidal structures proposed to solve segmentation tasks. Segmentation algorithms based on regular and irregular pyramids are described, together with the data structures and decimation procedures which encode and manage the information in the pyramid. In or ..."
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Cited by 9 (1 self)
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The main goal of this work is to compare pyramidal structures proposed to solve segmentation tasks. Segmentation algorithms based on regular and irregular pyramids are described, together with the data structures and decimation procedures which encode and manage the information in the pyramid. In order to compare the different segmentation algorithms, we have employed three types of quality measurements: the shift variance measure, the F function and the Q function.
Approximation Algorithms for Network Design: A Survey
"... In a typical instance of a network design problem, we are given a directed or undirected graph G = (V,E), nonnegative edgecosts ce for all e ∈ E, and our goal is to find a minimumcost subgraph H of G that satisfies some design criteria. For example, we may wish to find a minimumcost set of edges ..."
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Cited by 9 (1 self)
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In a typical instance of a network design problem, we are given a directed or undirected graph G = (V,E), nonnegative edgecosts ce for all e ∈ E, and our goal is to find a minimumcost subgraph H of G that satisfies some design criteria. For example, we may wish to find a minimumcost set of edges that induces a connected graph (this is the minimumcost spanning tree problem), or we might want to find a minimumcost set of arcs in a directed graph such that every vertex can reach every other vertex (this is the minimumcost strongly connected subgraph problem). This abstract model for network design problems has a large number of practical applications; the design process of telecommunication and traffic networks, and VLSI chip design are just two examples. Many practically relevant instances of network design problems are NPhard, and thus likely intractable. This survey focuses on approximation algorithms as one possible way of circumventing this impasse. Approximation algorithms are efficient (i.e., they run in polynomialtime), and they compute solutions to a given instance of an optimization problem whose objective values are close to those of the respective optimum solutions. More concretely, most of the problems discussed in this survey are minimization problems. We then say that an algorithm is an αapproximation for a given problem if the ratio of the cost of an approximate solution computed by the algorithm to that of an optimum solution is at most α over all instances. In the
Hierarchy of Partitions with Dual Graph Contraction
 In Proceedings of the DAGM conference
, 2003
"... We present a hierarchical partitioning of images using a pairwise similarity function on a graphbased representation of an image. ..."
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Cited by 7 (4 self)
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We present a hierarchical partitioning of images using a pairwise similarity function on a graphbased representation of an image.
StateoftheArt Algorithms for Minimum Spanning Trees  A Tutorial Discussion
, 1997
"... The classic “easy” optimization problem is to find the minimum spanning tree (MST) of a connected, undirected graph. Good polynomialtime algorithms have been known since 1930. Over the last 10 years, however, the standard O(mlogn) results of Kruskal and Prim have been improved to linear or nearli ..."
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Cited by 7 (0 self)
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The classic “easy” optimization problem is to find the minimum spanning tree (MST) of a connected, undirected graph. Good polynomialtime algorithms have been known since 1930. Over the last 10 years, however, the standard O(mlogn) results of Kruskal and Prim have been improved to linear or nearlinear time. The new methods use several tricks of general interest in order to reduce the number of edge weight comparisons and the amount of other work. This tutorial reviews those methods, building up strategies step by step so as to expose the insights behind the algorithms. Implementation details are clarified, and some generalizations are given. Specifically, the paper attempts to shed light on the classical algorithms of Kruskal, of Prim, and of Bor˙uvka; the improved approach of Gabow, Galil, and Spencer, which takes time only O(mlog(log*n−log * m n)); and the randomized O(m) algorithm of Karger, Klein, and Tarjan,