This paper considers an emergency communication system controlling multiple unmanned aerial vehicles (UAVs) in the sky over a large-scale disaster-affected area. This system is based on delay-tolerant networking, and information from ground users is relayed by the UAVs through wireless transmission and the movement of UAVs in a store-and-forward manner. Each UAV moves autonomously according to a predetermined flight method, which uses the positions of other UAVs through communication. In this paper, we propose a new method for UAV flight considering the non-uniformity of user distributions. The method is based on the Voronoi cell using the predicted locations of other UAVs. We evaluate the performance of the proposed method through computer simulations with a non-uniform user distribution generated by a general cluster point process. The simulation results demonstrate the effectiveness of the proposed method.

This paper describes graph-based Wave Function Collapse algorithm for procedural content generation. The goal of this system is to enable a game designer to procedurally create key content elements in the game level through simple association rule input. To do this, we propose a graph-based data structure that can be easily integrated with a navigation mesh data structure in a three-dimensional world. With our system, if the user inputs the minimum association rule, it is possible to effectively perform procedural content generation in the three-dimensional world. The experimental results show that the Wave Function Collapse algorithm, which is a texture synthesis algorithm, can be extended to non-grid shape content with high controllability and scalability.

To solve the problem of the self-deployment of heterogeneous directional wireless sensor networks in 3D space, this paper proposes a weighted Voronoi diagram-based self-deployment algorithm (3DV-HDDA) in 3D space. To improve the network coverage ratio of the monitoring area, the 3DV-HDDA algorithm uses the weighted Voronoi diagram to move the sensor nodes and introduces virtual boundary torque to rotate the sensor nodes, so that the sensor nodes can reach the optimal position. This work also includes an improvement algorithm (3DV-HDDA-I) based on the positions of the centralized sensor nodes. The difference between the 3DV-HDDA and the 3DV-HDDA-I algorithms is that in the latter the movement of the node is determined by both the weighted Voronoi graph and virtual force. Simulations show that compared to the virtual force algorithm and the unweighted Voronoi graph-based algorithm, the 3DV-HDDA and 3DV-HDDA-I algorithms effectively improve the network coverage ratio of the monitoring area. Compared to the virtual force algorithm, the 3DV-HDDA algorithm increases the coverage from 75.93% to 91.46% while the 3DV-HDDA-I algorithm increases coverage from 76.27% to 91.31%. When compared to the unweighted Voronoi graph-based algorithm, the 3DV-HDDA algorithm improves the coverage from 80.19% to 91.46% while the 3DV-HDDA-I algorithm improves the coverage from 72.25% to 91.31%. Further, the energy consumption of the proposed algorithms after 60 iterations is smaller than the energy consumption using a virtual force algorithm. Experimental results demonstrate the accuracy and effectiveness of the 3DV-HDDA and the 3DV-HDDA-I algorithms.

Due to the structure complexity, it is difficult to display structure of large-scale network fully. To solve the problem, this paper research on network simplification and accelerating drawing. Specific research content includes accelerated network layout based on quadtree and community geometric constrain, aiming to provide overall situation perception of network topology. Experiment results show that this method can quickly visualize complex structure of large-scale network, and present overall situation and structural characteristics of the network by clear and understandable visual expression, and contribute to mining and awareness of network connection mode and structural characteristics.

In this paper, the Voronoi region of the transmitted codeword is employed to improve the sphere bound on the maximum-likelihood decoding (MLD) performance of binary linear block codes over additive white Gaussian noise (AWGN) channels. We obtain the improved sphere bounds both on the frame-error probability and the bit-error probability. With the framework of the sphere bound proposed by Kasami et al., we derive the conditional decoding error probability on the spheres by defining a subset of the Voronoi region of the transmitted codeword, since the Voronoi regions of a binary linear block code govern the decoding error probability analysis over AWGN channels. The proposed bound improves the sphere bound by Kasami et al. and the sphere bound by Herzberg and Poltyrev. The computational complexity of the proposed bound is similar to that of the sphere bound by Kasami et al.

This paper presents a method to segment single- and multiple-touching characters in offline handwritten Japanese text recognition with practical speed. Distortions due to handwriting and a mix of complex Chinese characters with simple phonetic and alphanumeric characters leave optical handwritten text recognition (OHTR) for Japanese still far from perfection. Segmentation of characters, which touch neighbors on multiple points, is a serious unsolved problem. Therefore, we propose a method to segment them which is made in two steps: coarse segmentation and fine segmentation. The coarse segmentation employs vertical projection, stroke-width estimation while the fine segmentation takes a graph-based approach for thinned text images, which employs a new bridge finding process and Voronoi diagrams with two improvements. Unlike previous methods, it locates character centers and seeks segmentation candidates between them. It draws vertical lines explicitly at estimated character centers in order to prevent vertically unconnected components from being left behind in the bridge finding. Multiple candidates of separation are produced by removing touching points combinatorially. SVM is applied to discard improbable segmentation boundaries. Then, ambiguities are finally solved by the text recognition employing linguistic context and geometric context to recognize segmented characters. The results of our experiments show that the proposed method can segment not only single-touching characters but also multiple-touching characters, and each component in our proposed method contributes to the improvement of segmentation and recognition rates.

With the advances in wireless Internet and mobile positioning technology, location-based services (LBSs) have become popular. In LBSs, users must send their exact locations in order to use the services, but they may be subject to several privacy threats. To solve this problem, query processing algorithms based on a cloaking method have been proposed. The algorithms use spatial cloaking methods to blur the user's exact location in a region satisfying the required privacy threshold (k). With the cloaked region, an LBS server can execute a spatial query processing algorithm preserving their privacy. However, the existing algorithms cannot provide good query processing performance. To resolve this problem, we, in this paper, propose a k-NN query processing algorithm based on network Voronoi diagram for spatial networks. Therefore, our algorithm can reduce network expansion overhead and share the information of the expanded road network. In order to demonstrate the efficiency of our algorithms, we have conducted extensive performance evaluations. The results show that our algorithm achieves better performance on retrieval time than the existing algorithms, such as PSNN and kRNN. This is because our k-NN query processing algorithm can greatly reduce a network expansion cost for retrieving k POIs.

It is known that the optimal sensor coverage of a mission space is performed by a Voronoi partition, which is called a Voronoi coverage problem. We consider the case that the mission space has several obstacles where mobile sensors cannot be deployed and search an optimal deployment to maximize the sensing performance. Inspired by the potential field method, we introduce a repulsive potential for obstacle avoidance and define the objective function by a combination of two functions: one for evaluation of the sensing performance and the other for obstacle avoidance. We introduce a space where a sensor can move, called its moving space. In general, a moving space may not coincide with the mission space. We assume that the respective moving spaces of each sensor may differ from each other. By introducing a barycentric coordinate over the moving space, we show that the Voronoi coverage problem to maximize the objective function is transformed into a potential game. In potential games, local maximizers of a potential function are stable equilibrium points of the corresponding replicator dynamics. We propose a distributed sensor coverage control method based on the replicator dynamics to search a local maximizer of the objective function and a path to it. Using simulations, we also compare the proposed method with the Lloyd and TangentBug algorithm proposed by Breitenmoser et al.

We propose a method for halftoning grayscale images by drawing weighted centroidal Voronoi tessellations (WCVTs) with black lines on white image planes. Based on the fact that CVT approaches a uniform hexagonal lattice asymptotically, we derive a relationship of darkness between input grayscale images and the corresponding halftone images. Then the derived relationship is used for adjusting the contrast of the halftone images. Experimental results show that the generated halftone images can reproduce the original tone in the input images faithfully.

Given a collection of k sets consisting of a total of n points in the plane, the distance from any point in the plane to each of the sets is defined to be the minimum among distances to each point in the set. The farthest-color Voronoi diagram is defined as a generalized Voronoi diagram of the k sets with respect to the distance functions for each of the k sets. The combinatorial complexity of the diagram is known to be Θ(kn) in the worst case. This paper initiates a study on farthest-color Voronoi diagrams having O(n) complexity. We introduce a realistic model, which defines a certain class of the diagrams with desirable geometric properties observed. We finally show that the farthest-color Voronoi diagrams under the model have linear complexity.

With exponentially increasing power densities due to technology scaling and ever increasing demand for performance, chip temperature has become an important issue that limits the performance of computer systems. Typically, it is essential to use a set of on-chip thermal sensors to monitor temperatures during the runtime. The runtime thermal measurements are then employed by dynamic thermal management techniques to manage chip performance appropriately. In this paper, we propose an inverse distance weighting method based on a dynamic Voronoi diagram for the reconstruction of full thermal characterization of integrated circuits with non-uniform thermal sensor placements. Firstly we utilize the proposed method to transform the non-uniformly spaced samples to virtual uniformly spaced data. Then we apply three classical interpolation algorithms to reconstruct the full thermal signals in the uniformly spaced samples mode. To evaluate the effectiveness of our method, we develop an experiment for reconstructing full thermal status of a 16-core processor. Experimental results show that the proposed method significantly outperforms spectral analysis techniques, and can obtain full thermal characterization with an average absolute error of 1.72% using 9 thermal sensors per core.

The Voronoi game is a two-person perfect information game modeling a competitive facility location. The original version of the game is played on a continuous domain. Only two special cases (1-dimensional case and 1-round case) have been extensively investigated. Recently, the discrete Voronoi game of which the game arena is given as a graph was introduced. In this note, we give a complete analysis of the discrete Voronoi game on a path. There are drawing strategies for both the first and the second players, except for some trivial cases.

This paper presents a novel algorithm for Nearest Neighbor (NN) classifier. NN classification is a well-known method of pattern classification having the following properties: * it performs maximum-margin classification and achieves less than twice the ideal Bayesian error, * it does not require knowledge of pattern distributions, kernel functions or base classifiers, and * it can naturally be applied to multiclass classification problems. Among the drawbacks are A) inefficient memory use and B) ineffective pattern classification speed. This paper deals with the problems A and B. In most cases, NN search algorithms, such as k-d tree, are employed as a pattern search engine of the NN classifier. However, NN classification does not always require the NN search. Based on this idea, we propose a novel algorithm named k-d decision tree (KDDT). Since KDDT uses Voronoi-condensed prototypes, it consumes less memory than naive NN classifiers. We have confirmed that KDDT is much faster than NN search-based classifier through a comparative experiment (from 9 to 369 times faster than NN search based classifier). Furthermore, in order to extend applicability of the KDDT algorithm to high-dimensional NN classification, we modified it by incorporating Gabriel editing or RNG editing instead of Voronoi condensing. Through experiments using simulated and real data, we have confirmed the modified KDDT algorithms are superior to the original one.

This letter proposes a novel mobile sensor deployment scheme for maximizing coverage. The basic idea is to force mobile sensors to move to predetermined target points that are the optimal layout in a distributed manner using Voronoi diagram data structure. A simulation shows that the result of the proposed scheme is quite close to the optimal result and outperforms previous works.

We consider the problem of triangulating an x-monotone polygon with a small number of different edge lengths using Steiner points. Given a parameter α, where 0<α<1, we shall present an algorithm for finding an almost uniform triangular mesh with 3π/8α2+o(1/α2) different edge lengths such that every edge length is between l and (2+α)l. Experiments demonstrate the effectiveness of this algorithm.

This paper describes a dynamic and adaptive scheme for three-dimensional mesh morphing. Using several control maps, the connectivity of intermediate meshes is dynamically changing and the mesh vertices are adaptively modified. The 2D control maps in parametric space that include curvature map, area deformation map and distance map, are used to schedule the inserting and deleting vertices in each frame. Then, the positions of vertices are adaptively moved to better positions using weighted centroidal voronoi diagram (WCVD) and a Delaunay triangulation is finally used to determine the connectivity of mesh. In contrast to most previous work, the intermediate mesh connectivity gradually changes and is much less complicated. We demonstrate several examples of aesthetically pleasing morphs created by the proposed method.

Based on the dimensionality reduction technique and the solution for proximate points problem, we achieve the optimality of the three-dimensional Euclidean distance transform (3D_EDT) computation. For an N N N binary image, our algorithms for both 3D_EDT and its applications can be performed in O (log log N) time using CRCW processors or in O (log N) time using EREW processors. To the best of our knowledge, all results described above are the best known. As for the n-dimensional Euclidean distance transform (nD_EDT) and its applications of a binary image of size Nn, all of them can be computed in O (nlog log N) time using CRCW processors or in O (nlog N) time using EREW processors.

In this paper we deal with Voronoi diagram in simply connected complete manifold with non positive curvature, called Hadamard manifold. We prove that a part of the Voronoi diagram can be characterized by hyperbolic Voronoi diagram. Voronoi diagram in simply connected complete manifold is also characterized for a given set of points satisfying a distance condition.

This paper introduces a new approach based on the geographic nearest neighbors for constructing the Delaunay triangulation (a dual of the Voronoi diagram) of a set of n sites in the plane under the L1 metric. In general, there is no inclusion relationship between the Delaunay triangulation and the octant neighbor graph. We however find that under the L1 metric the octant neighbor graph contains at least one edge of each triangle in the Delaunay triangulation. By using this observation and employing a range tree scheme, we design an algorithm for constructing the Delaunay triangulation (thus the Voronoi diagram) in the L1 metric. This algorithm takes O(n log n) sequential time for constructing the Delaunay triangulation in the L1 metric. This algorithm can easily be parallelized, and takes O(log n) time with O(n) processors on a CREW-PRAM.

In this paper we consider the k-clustering problem for a set S of n points pi=(xi) in the d-dimensional space with variance-based errors as clustering criteria, motivated from the color quantization problem of computing a color lookup table for frame buffer display. As the inter-cluster criterion to minimize, the sum of intra-cluster errors over every cluster is used, and as the intra-cluster criterion of a cluster Sj, |Sj|α-1 Σpi Sj ||xi - - x (Sj)||2 is considered, where |||| is the L2 norm and - x (Sj) is the centroid of points in Sj, i. e. , (1/|Sj|)Σpi Sj xi. The cases of α=1,2 correspond to the sum of squared errors and the all-pairs sum of squared errors, respectively. The k-clustering problem under the criterion with α = 1,2 are treated in a unified manner by characterizing the optimum solution to the k-clustering problem by the ordinary Euclidean Voronoi diagram and the weighted Voronoi diagram with both multiplicative and additive weights. With this framework, the problem is related to the generalized primary shatter function for the Voronoi diagrams. The primary shatter function is shown to be O(nO(kd)), which implies that, for fixed k, this clustering problem can be solved in a polynomial time. For the problem with the most typical intra-cluster criterion of the sum of squared errors, we also present an efficient randomized algorithm which, roughly speaking, finds an ε-approximate 2-clustering in O(n(1/ε)d) time, which is quite practical and may be used to real large-scale problems such as the color quantization problem.