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.

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.

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.

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.

This paper presents a new proof to a polynomial-time algorithm for determining whether a given embedded graph is a Delaunay graph, i. e. , whether it is topologically equivalent to a Delaunay triangulation. The problem of recognizing the Delaunay graph had long been open. Recently Hodgson et al. gave a combinatorial characterization of the Delaunay graph, and thus constructed the polynomial-time algorithm for recognizing the Delaunay graphs. Their proof is based on sophisticated discussions on hyperbolic geometry. On the other hand, this paper gives another and simpler proof based on primitive arguments on Euclidean geometry. Moreover, the algorithm is applied to study the distribution of non-Delaunay graphs.

This paper surveys recent progress in the investigation of the underlying discrete proximity structures of geometric clustering with respect to the divergence in information geometry. Geometric clustering with respect to the divergence provides powerful unsupervised learning algorithms, and can be applied to classifying and obtaining generalizations of complex objects represented in the feature space. The proximity relation, defined by the Voronoi diagram by the divergence, plays an important role in the design and analysis of such algorithms.

This paper presents a simple method for avoiding both numerical errors and degeneracy in an incremental-type algorithm for constructing the Voronoi diagram with respect to points on a plane. It is assumed that the coordinates of the given points are represented with a certain fixed number of bits. All the computations in the algorithm are carried out in four times higher precision, so that degeneracy can be discerned precisely. Every time degeneracy is found, the points are perturbed symbolically according to a very simple rule and thus are reduced to a nondegenerate case. The present technique makes a computer program simple in the sense that it avoids all numerical errors and requires no exceptional branches of processing for degenerate cases.