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194
Mobile Robot Localisation and Mapping in Extensive Outdoor Environments
, 2002
"... This thesis addresses the issues of scale for practical implementations of simultaneous localisation and mapping (SLAM) in extensive outdoor environments. Building an incremental map while also using it for localisation is of prime importance for mobile robot navigation but, until recently, has bee ..."
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Cited by 67 (8 self)
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This thesis addresses the issues of scale for practical implementations of simultaneous localisation and mapping (SLAM) in extensive outdoor environments. Building an incremental map while also using it for localisation is of prime importance for mobile robot navigation but, until recently, has been confined to smallscale, mostly indoor, environments. The critical problems for largescale implementations are as follows. First, data association finding correspondences between map landmarks and robot sensor measurementsbecomes difficult in complex, cluttered environments, especially if the robot location is uncertain. Second, the information required to maintain a consistent map using traditional methods imposes a prohibitive computational burden as the map increases in size. And third, the mathematics for SLAM relies on assumptions of small errors and nearlinearity, and these become invalid for larger maps.
Replicator Equations, Maximal Cliques, and Graph Isomorphism
, 1999
"... We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to fo ..."
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Cited by 64 (12 self)
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We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear onetoone correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the socalled replicator equations—a class of straightforward continuous and discretetime dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate meanfield annealing heuristics.
A New GraphTheoretic Approach to Clustering, with Applications to Computer Vision
, 2004
"... This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given ..."
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Cited by 62 (6 self)
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This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given dataset. Many problems of computer vision have precisely this goal, namely to find which visual entities belong to an inherent structure, e.g. in an image or in a database of images. For example, a meaningful structure in the context of image segmentation is a set of pixels which correspond to the same object in a scene. Clustering algorithms can be used to partition the pixels of an image into meaningful parts, which may correspond to different objects. In this work we focus on the problems of image segmentation and image database organization. The visual entities to consider are pixels and images, respectively. Our first contribution in this work is a novel partitional (flat) clustering algorithm. The algorithm uses pairwise representation, where the visual objects (pixels,
A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences
, 2004
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Bipartite Graphs as Models of Complex Networks
 Aspects of Networking
, 2004
"... It appeared recently that the classical random graph model used to represent realworld complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here the first model which achieves the following challenges: it produces ..."
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Cited by 49 (6 self)
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It appeared recently that the classical random graph model used to represent realworld complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here the first model which achieves the following challenges: it produces graphs which have the three main wanted properties (clustering, degree distribution, average distance), it is based on some realworld observations, and it is sufficiently simple to make it possible to prove its main properties. This model consists in sampling a random bipartite graph with prescribed degree distribution. Indeed, we show that any complex network can be viewed as a bipartite graph with some specific characteristics, and that its main properties can be viewed as consequences of this underlying structure. We also propose a growing model based on this observation. Introduction.
RankTwo Relaxation Heuristics for MaxCut and Other Binary Quadratic Programs
 SIAM Journal on Optimization
, 2000
"... The GoemansWilliamson randomized algorithm guarantees a highquality approximation to the MaxCut problem, but the cost associated with such an approximation can be excessively high for largescale problems due to the need for solving an expensive semidefinite relaxation. In order to achieve better ..."
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Cited by 43 (3 self)
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The GoemansWilliamson randomized algorithm guarantees a highquality approximation to the MaxCut problem, but the cost associated with such an approximation can be excessively high for largescale problems due to the need for solving an expensive semidefinite relaxation. In order to achieve better practical performance, we propose an alternative, ranktwo relaxation and develop a specialized version of the GoemansWilliamson technique. The proposed approach leads to continuous optimization heuristics applicable to MaxCut as well as other binary quadratic programs, for example the MaxBisection problem. A computer code based on the ranktwo relaxation heuristics is compared with two stateoftheart semidefinite programming codes that implement the GoemansWilliamson randomized algorithm, as well as with a purely heuristic code for effectively solving a particular MaxCut problem arising in physics. Computational results show that the proposed approach is fast and scalable and, more importantly, attains a higher approximation quality in practice than that of the GoemansWilliamson randomized algorithm. An extension to MaxBisection is also discussed as well as an important difference between the proposed approach and the GoemansWilliamson algorithm, namely that the new approach does not guarantee an upper bound on the MaxCut optimal value. Key words. Binary quadratic programs, MaxCut and MaxBisection, semidefinite relaxation, ranktwo relaxation, continuous optimization heuristics. AMS subject classifications. 90C06, 90C27, 90C30 1.
Evolutionary algorithm with the guided mutation for the maximum clique problem
 IEEE Transactions on Evolutionary Computation
, 2005
"... Abstract—Estimation of distribution algorithms sample new solutions (offspring) from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The location information of solutions found so far (i.e., the actual positions of these solutio ..."
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Cited by 42 (15 self)
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Abstract—Estimation of distribution algorithms sample new solutions (offspring) from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The location information of solutions found so far (i.e., the actual positions of these solutions in the search space) is not directly used for generating offspring in most existing estimation of distribution algorithms. This paper introduces a new operator, called guided mutation. Guided mutation generates offspring through combination of global statistical information and the location information of solutions found so far. An evolutionary algorithm with guided mutation (EA/G) for the maximum clique problem is proposed in this paper. Besides guided mutation, EA/G adopts a strategy for searching different search areas in different search phases. Marchiori’s heuristic is applied to each new solution to produce a maximal clique in EA/G. Experimental results show that EA/G outperforms the heuristic genetic algorithm of Marchiori (the best evolutionary algorithm reported so far) and a MIMIC algorithm on DIMACS benchmark graphs. Index Terms—Estimation of distribution algorithms, evolutionary algorithm, guided mutation, heuristics, hybrid genetic algorithm, maximum clique problem (MCP). I.
Clique relaxations in social network analysis: The maximum kplex problem
, 2006
"... This paper introduces and studies the maximum kplex problem, which arises in social network analysis, but can also be used in several other important application areas, including wireless networks, telecommunications, and graphbased data mining. We establish NPcompleteness of the decision version ..."
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Cited by 41 (5 self)
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This paper introduces and studies the maximum kplex problem, which arises in social network analysis, but can also be used in several other important application areas, including wireless networks, telecommunications, and graphbased data mining. We establish NPcompleteness of the decision version of the problem on arbitrary graphs. An integer programming formulation is presented and basic polyhedral study of the problem is carried out. A branchandcut implementation is discussed and computational test results on the proposed benchmark instances and reallife scalefree graphs are also provided.
Design and implementation of the HPCS graph analysis benchmark on symmetric multiprocessors
 The 12th International Conference on High Performance Computing (HiPC 2005)
, 2005
"... Graph theoretic problems are representative of fundamental computations in traditional and emerging scientific disciplines like scientific computing and computational biology, as well as applications in national security. We present our design and implementation of a graph theory application that su ..."
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Cited by 36 (1 self)
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Graph theoretic problems are representative of fundamental computations in traditional and emerging scientific disciplines like scientific computing and computational biology, as well as applications in national security. We present our design and implementation of a graph theory application that supports the kernels from the Scalable Synthetic Compact Applications (SSCA) benchmark suite, developed under the DARPA High Productivity Computing Systems (HPCS) program. This synthetic benchmark consists of four kernels that require irregular access to a large, directed, weighted multigraph. We have developed a parallel implementation of this benchmark in C using the POSIX thread library for commodity symmetric multiprocessors (SMPs). In this paper, we primarily discuss the data layout choices and algorithmic design issues for each kernel, and also present execution time and benchmark validation results.