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The Minimum Spanning Tree Problem on a Planar Graph
 Discrete Appl. Math
, 1994
"... cle. A spanning forest of G is called a spanning tree when it is connected. In this note, we present a spanning forest as its edge set. Given a graph G and its edge e; Gne denotes the graph obtained by deleting the edge e and G=e denotes the graph obtained by contracting e: For each edge e 2 E; w( ..."
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cle. A spanning forest of G is called a spanning tree when it is connected. In this note, we present a spanning forest as its edge set. Given a graph G and its edge e; Gne denotes the graph obtained by deleting the edge e and G=e denotes the graph obtained by contracting e: For each edge e 2 E; w(e) denotes the weight of the edge e: The weight of an edge subset F; denoted be w(F ); is the sum of the weights of edges in F: A maximal spanning forest F is called a minimum (maximum) weight spanning forest, when F minimizes (maximizes) the weight w(F ): A graph is called planar if it can be drawn in th
Sorting helps for Voronoi diagrams
 In 13th Symp. on Mathematical Programming
, 1988
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A New Evolutionary Approach to the Degree Constrained Minimum Spanning Tree Problem
 IEEE Transactions on Evolutionary Computation
, 2000
"... Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a well studied NPhard problem which is important in network design. We introduce a new method which improves on the best technique previously published for solving the dMST, either using heuristic or evolutionary app ..."
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Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a well studied NPhard problem which is important in network design. We introduce a new method which improves on the best technique previously published for solving the dMST, either using heuristic or evolutionary approaches. The basis of this encoding is a spanningtree construction algorithm which we call the Randomised Primal Method (RPM), based on the wellknown Prim's algorithm [6], and an extension [4] which we call `dPrim's'. We describe a novel encoding for spanning trees, which involves using the RPM to interpret lists of potential edges to include in the growing tree. We also describe a random graph generator which produces particularly challenging dMST problems. On these and other problems, we find that an evolutionary algorithm (EA) using the RPM encoding outperforms the previous best published technique from the operations research literature, and also outperforms simulated...
A lineartime approximation scheme for TSP for planar weighted graphs
 In Proceedings, 46th IEEE Symposium on Foundations of Computer Science
, 2005
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Symbolic Analysis of Large Analog Integrated Circuits By Approximation During Expression Generation
, 1994
"... A novel algorithm is presented that generates approximate symbolic expressions for smallsignal characteristics of large analog integrated circuits. The method is based upon the approximation of an expression while it is being computed. The CPU time and memory requirements are reduced drastically wi ..."
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A novel algorithm is presented that generates approximate symbolic expressions for smallsignal characteristics of large analog integrated circuits. The method is based upon the approximation of an expression while it is being computed. The CPU time and memory requirements are reduced drastically with regard to previous approaches, as only those terms are calculated which will remain in the final expression. As a consequence, the maximum circuit size amenable to symbolic analysis has largely increased. The simplification procedure explicitly takes into account variation ranges of the symbolic parameters to avoid inaccuracies of conventional approaches which use a single value. The new approach is also able to take into account mismatches between the symbolic parameters. INTRODUCTION Symbolic circuit analysis refers to the calculation of network functions H(s,x) in the form: (1) where x T ={x 1 , x 2 , . . . x Q } is the vector of circuit parameters which remain as symbols, and the...
PROXIMITY PROBLEMS FOR POINTS ON A RECTILINEAR PLANE WITH RECTANGULAR OBSTACLES
, 1993
"... We consider the following four problems for a set S of k points on a plane, equipped with the rectilinear metric and containing a set R of n disjoint rectangular obstacles (so that distance is measured by a shortest rectilinear path avoiding obstacles in R): (a) nd a closest pair of points in S, (b) ..."
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We consider the following four problems for a set S of k points on a plane, equipped with the rectilinear metric and containing a set R of n disjoint rectangular obstacles (so that distance is measured by a shortest rectilinear path avoiding obstacles in R): (a) nd a closest pair of points in S, (b) nd a nearest neighbor for each point inS, (c) compute the rectilinear Voronoi diagram of S, and (d) compute a rectilinear minimal spanning tree of S. Wedescribe O((n + k) log(n + k)) time sequential algorithms for (a) and (b) based on planesweep, and the consideration of geometrically special types of shortest paths, socalled z rst paths. For (c) we present an O((n + k) log(n + k)logn) time sequential algorithm that implements a sophisticated divideandconquer scheme with an added extension phase. In the extension phase of this scheme we introduce novel geometric structures, in particular socalled zdiagrams, and techniques associated with the Voronoi diagram. Problem (d) can be reduced to (c) and solved in O((n + k) log(n + k)logn) time as well. All our algorithms are nearoptimal, as well as easy to implement.
CPlanarity of cconnected clustered graphs
, 2008
"... We present the first characterization of cplanarity for cconnected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the underlying graph. Based on such a characterization, we ..."
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We present the first characterization of cplanarity for cconnected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the underlying graph. Based on such a characterization, we provide a lineartime cplanarity testing and embedding algorithm for cconnected clustered graphs. The algorithm is reasonably easy to implement, since it exploits as building blocks simple algorithmic tools like the computation of lowest common ancestors, minimum and maximum spanning trees, and counting sorts. It also makes use of wellknown data structures as SPQRtrees and BCtrees. If the test fails, the algorithm identifies a structural element responsible for the noncplanarity of the input clustered graph.
An Efficient Recursive Shortest Spanning Tree Algorithm Using Linking Properties
 IEEE Transactions, Circuit and Systems for Video Technology
"... Abstract—Speed is a great concern in the recursive shortest spanning tree (RSST) algorithm as its applications are focused on image segmentation and video coding, in which a large amount of data is processed. Several efficient RSST algorithms have been proposed in the literature, but the linking pro ..."
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Abstract—Speed is a great concern in the recursive shortest spanning tree (RSST) algorithm as its applications are focused on image segmentation and video coding, in which a large amount of data is processed. Several efficient RSST algorithms have been proposed in the literature, but the linking properties are not properly addressed and used in these algorithms and they are intended to produce a truncated RSST. This paper categorizes the linking process into three classes based on link weights. These linking processes are defined as the linking process for link weight equal to zero (LPLWZ), the linking process for link weight equal to one (LPLWO), and the linking process for link weight equal to real number (LPLWR). We study these linking properties and apply them to an efficient RSST algorithm. The proposed efficient RSST algorithm is novel, as it makes use of linking properties, and its resulting shortest spanning tree is truly identical to that produced by the conventional algorithm. Our experimental results show that the percentages of links for the three classes are 17%, 27%, and 58%, respectively. This paper proposes a prediction method for LPLWO, as a result of which the vertex weight of the next region can be determined by comparing sizes of the merging regions. It is also demonstrated that the proposed LPLWO with prediction approach is applicable to the multiplestage merging. Our experimental results show that the proposed algorithm has a substantial improvement over the conventional RSST algorithm. Index Terms—Edge detection, graph theory, image segmentation, linking property, recursive shortest spanning tree (RSST). I.
Question Answering on Interlinked Data
"... The Data Web contains a wealth of knowledge on a large number of domains. Question answering over interlinked data sources is challenging due to two inherent characteristics. First, different datasets employ heterogeneous schemas and each one may only contain a part of the answer for a certain quest ..."
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The Data Web contains a wealth of knowledge on a large number of domains. Question answering over interlinked data sources is challenging due to two inherent characteristics. First, different datasets employ heterogeneous schemas and each one may only contain a part of the answer for a certain question. Second, constructing a federated formal query across different datasets requires exploiting links between the different datasets on both the schema and instance levels. We present a question answering system, which transforms user supplied queries (i.e. natural language sentences or keywords) into conjunctive SPARQL queries over a set of interlinked data sources. The contribution of this paper is twofold: Firstly, we introduce a novel approach for determining the most suitable resources for a usersupplied query from different datasets (disambiguation). We employ a hidden Markov model, whose parameters were bootstrapped with different distribution functions. Secondly, we present a novel method for constructing a federated formal queries using the disambiguated resources and leveraging the linking structure of the underlying datasets. This approach essentially relies on a combination of domain and range inference as well as a link traversal method for constructing a connected graph which ultimately renders a corresponding SPARQL query. The results of our evaluation with three lifescience datasets and 25 benchmark queries demonstrate the effectiveness of our approach.
Minimum Spanning Tree Pose Estimation
"... The extrinsic camera parameters from video stream images can be accurately estimated by tracking features through the image sequence and using these features to compute parameter estimates. The poses for long video sequences have been estimated in this manner. However, the poses of large sets of sti ..."
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The extrinsic camera parameters from video stream images can be accurately estimated by tracking features through the image sequence and using these features to compute parameter estimates. The poses for long video sequences have been estimated in this manner. However, the poses of large sets of still images cannot be estimated using the same strategy because widebaseline correspondences are not as robust as narrowbaseline feature tracks. Moreover, video pose estimation requires a linear or hierarchicallylinear ordering on the images to be calibrated, reducing the image matches to the neighboring video frames. We propose a novel generalization to the linear ordering requirement of video pose estimation by computing the Minimum Spanning Tree of the camera adjacency graph and using the tree hierarchy to determine the calibration order for a set of input images. We validate the pose accuracy using an error metric that is functionally independent of the estimation process. Because we do not rely on feature tracking for generating feature correspondences, our method can use internally calibrated wide or narrowbaseline images as input, and can estimate the camera poses from multiple video streams without special preprocessing to concatenate the streams. 1