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44
Building Irregular Pyramids by Dual Graph Contraction
 IEEPROC. VISION, IMAGE AND SIGNAL PROCESSING
, 1994
"... Many image analysis tasks lead to or make use of graph structures that are related through the analysis process with the planar layout of a digital image. This paper presents a theory that allows to build different types of hierarchies on top of such image graphs. The theory is based on the properti ..."
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Cited by 56 (24 self)
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Many image analysis tasks lead to or make use of graph structures that are related through the analysis process with the planar layout of a digital image. This paper presents a theory that allows to build different types of hierarchies on top of such image graphs. The theory is based on the properties of a pair of dual image graphs that the reduction process should preserve, e.g. the structure of a particular input graph. The reduction process is controlled by decimation parameters, i.e. a selected subset of vertices, called survivors, and a selected subset of the graph's edges, the parentchild connections. It is formally shown that two phases of contractions transform a dual image graph to a dual image graph built by the surviving vertices. Phase one operates on the original (neighborhood) graph and eliminates all nonsurviving vertices. Phase two operates on the dual (face) graph and eliminates all degenerated faces that have been created in phase one. The resulting graph preserves the structure of the survivors, it is minimal and unique with respect to the selected decimation parameters. The result is compared with two modified specifications, the one already in use for building stochastic and adaptive irregular pyramids.
An Algorithm for Exact Bounds on the Time Separation of Events in Concurrent Systems
 IEEE Transactions on Computers
, 1993
"... Determining the time separation of events is a fundamental problem in the analysis, synthesis, and optimization of concurrent systems. Applications range from logic optimization of asynchronous digital circuits to evaluation of execution times of programs for realtime systems. We present an efficie ..."
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Cited by 47 (7 self)
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Determining the time separation of events is a fundamental problem in the analysis, synthesis, and optimization of concurrent systems. Applications range from logic optimization of asynchronous digital circuits to evaluation of execution times of programs for realtime systems. We present an efficient algorithm to find exact (tight) bounds on the separation time of events in an arbitrary process graph without conditional behavior. This result is more general than the methods presented in several previously published papers as it handles cyclic graphs and yields the tightest possible bounds on event separations. The algorithm is based on a functional decomposition technique that permits the implicit evaluation of an infinitely unfolded process graph. Examples are presented that demonstrate the utility and efficiency of the solution. The algorithm will form a basis for exploration of timingconstrained synthesis techniques. Index terms: Abstract algebra, asynchronous systems, concurrent ...
Finding the k shortest hyperpaths
"... The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. Ho ..."
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Cited by 17 (4 self)
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The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated. In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.
Qualityofservice and qualityofprotection issues in preplanned recovery schemes using redundant trees
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATION
, 2003
"... In this paper, we study qualityofservice (QoS) and qualityofprotection (QoP) issues in redundant tree based preplanned recovery schemes for a singlelink failure in twoedge connected graphs and for a singlenode failure in twoconnected graphs. We present schemes (to be called GMFBG schemes) ..."
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Cited by 13 (0 self)
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In this paper, we study qualityofservice (QoS) and qualityofprotection (QoP) issues in redundant tree based preplanned recovery schemes for a singlelink failure in twoedge connected graphs and for a singlenode failure in twoconnected graphs. We present schemes (to be called GMFBG schemes) that generalize the schemes (to be called MFBG schemes) developed by Médard et al. to construct a pair of redundant trees, called red and blue trees, which guarantees fast recovery from any singlelink/node failure, as long as the failed node is not the root node. Using the GMFBG schemes, we study QoS issues relating to red/blue trees. We present effective heuristics for computing a pair of redundant trees with low average delay or small total cost. We develop an optimal algorithm for computing a pair of red/blue trees with maximum bandwidth. Furthermore, a pair of red/blue trees guarantees fast recovery from simultaneous multiple failures if it satisfies certain properties. This leads us to define the concept of QoP of a pair of red/blue trees. We present an effective heuristic to construct a pair of red/blue trees with high QoP. The paper concludes with a discussion of computational results that demonstrate the effectiveness of the different algorithms presented.
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 definition ..."
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Cited by 12 (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.
On the Complexity of the Robust Spanning Tree Problem With Interval Data
"... This paper studies the complexity of the robust spanning tree problem with interval data (RSTID). It settles the conjecture of Kouvelis and Yu [9] and shows that the problem remains NPcomplete even when the underlying graph is complete or when the cost intervals are all [0; 1]. These results prove ..."
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Cited by 11 (0 self)
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This paper studies the complexity of the robust spanning tree problem with interval data (RSTID). It settles the conjecture of Kouvelis and Yu [9] and shows that the problem remains NPcomplete even when the underlying graph is complete or when the cost intervals are all [0; 1]. These results prove that the diculty of RSTID stems from two distinct aspects: the topology of the graph and the numerical properties of the cost intervals. As a consequence, they suggest new directions for improving and evaluating existing search algorithms [2,15,20] for this problem, since they have so far focused only on one of these aspects.
Minimal Cycle Bases of Outerplanar Graphs
, 1998
"... 2connected outerplanar graphs have a unique minimal cycle basis with length 2jEj \Gamma jV j. They are the only Hamiltonian graphs with a cycle basis of this length. Keywords: Minimal Cycle Basis, Outerplanar Graphs AMS Subject Classification: Primary 05C38. Secondary 92D20. The electronic journa ..."
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Cited by 11 (0 self)
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2connected outerplanar graphs have a unique minimal cycle basis with length 2jEj \Gamma jV j. They are the only Hamiltonian graphs with a cycle basis of this length. Keywords: Minimal Cycle Basis, Outerplanar Graphs AMS Subject Classification: Primary 05C38. Secondary 92D20. The electronic journal of combinatorics 5 (1998), #R16 2 1. Introduction The description of cyclic structures is an important problem in graph theory (see e.g. [16]). Cycle bases of graphs have a variety of applications in science and engineering, among them in structural analysis [11] and in chemical structure storage and retrieval systems [7]. Naturally, minimal cycles bases are of particular practical interest. In this contribution we prove that outerplanar graphs have a unique minimal cycle basis. This result was motivated by the analysis of the structures of biopolymers. In addition we derive upper and lower bounds on the length of minimal cycle basis in 2connected graphs. Biopolymers, such as RNA, DNA,...
CLICK: Clustering Categorical Data Using Kpartite Maximal Cliques
, 2004
"... Clustering is one of the central data mining problems and numerous approaches have been proposed in this field. However, few of these methods focus on categorical data. The categorical techniques that do exist have significant shortcomings in terms of performance, the clusters they detect, and their ..."
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Cited by 11 (2 self)
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Clustering is one of the central data mining problems and numerous approaches have been proposed in this field. However, few of these methods focus on categorical data. The categorical techniques that do exist have significant shortcomings in terms of performance, the clusters they detect, and their ability to locate clusters in subspaces.
Circuit Bases of Strongly Connected Digraphs
, 2001
"... The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is ..."
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Cited by 7 (0 self)
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The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is outlined.
Scalable Decoding on Factor Trees: A Practical Solution for Wireless Sensor Networks
 IEEE TRANSACTIONS ON COMMUNICATIONS
, 2005
"... We consider the problem of jointly decoding the correlated data picked up and transmitted by the nodes of a largescale sensor network. Assuming that each sensor node uses a very simple encoder (a scalar quantizer and a modulator), we focus on decoding algorithms that exploit the correlation struct ..."
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Cited by 7 (3 self)
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We consider the problem of jointly decoding the correlated data picked up and transmitted by the nodes of a largescale sensor network. Assuming that each sensor node uses a very simple encoder (a scalar quantizer and a modulator), we focus on decoding algorithms that exploit the correlation structure of the sensor data to produce the best possible estimates under the minimum mean square error (MMSE) criterion. Our analysis shows that a standard implementation of the optimal MMSE decoder is unfeasible for large scale sensor networks, because its complexity grows exponentially with the number of nodes in the network. Seeking a scalable alternative, we use factor graphs to obtain a simplified model for the correlation structure of the sensor data. This model allows us to use the sumproduct decoding algorithm, whose complexity can be made to grow linearly with the size of the network. Considering large sensor networks with arbitrary topologies, we focus on factor trees and give an exact characterization of the decoding complexity, as well as mathematical tools for factorizing Gaussian sources and optimization algorithms for finding optimal factor trees under the KullbackLeibler criterion.