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A Combinatorial Bound for Beacon-based Routing in Orthogonal Polygons 正交多边形信标路由的组合界
International Journal of Computational Geometry & Applications Pub Date : 2015-07-13 DOI: 10.20382/jocg.v13i1a2
T. Shermer
{"title":"A Combinatorial Bound for Beacon-based Routing in Orthogonal Polygons","authors":"T. Shermer","doi":"10.20382/jocg.v13i1a2","DOIUrl":"https://doi.org/10.20382/jocg.v13i1a2","url":null,"abstract":"Beacon attraction is a movement system whereby a robot (modeled as a point in 2D) moves in a free space so as to always locally minimize its Euclidean distance to an activated beacon (which is also a point). This results in the robot moving directly towards the beacon when it can, and otherwise sliding along the edge of an obstacle. When a robot can reach the activated beacon by this method, we say that the beacon attracts the robot. A beacon routing from $p$ to $q$ is a sequence $b_1, b_2,$ ..., $b_{k}$ of beacons such that activating the beacons in order will attract a robot from $p$ to $b_1$ to $b_2$ ... to $b_{k}$ to $q$, where $q$ is considered to be a beacon. A routing set of beacons is a set $B$ of beacons such that any two points $p, q$ in the free space have a beacon routing with the intermediate beacons $b_1, b_2,$ ..., $b_{k}$ all chosen from $B$. Here we address the question of \"how large must such a $B$ be?\" in orthogonal polygons, and show that the answer is \"sometimes as large as $[(n-4)/3]$, but never larger.\"","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"21 1","pages":"13-51"},"PeriodicalIF":0.0,"publicationDate":"2015-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84395278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
On Interference Among Moving Sensors and Related Problems 运动传感器间的干扰及相关问题研究
International Journal of Computational Geometry & Applications Pub Date : 2015-07-08 DOI: 10.4230/LIPIcs.ESA.2016.34
J. Carufel, M. J. Katz, Matias Korman, André van Renssen, Marcel Roeloffzen, Shakhar Smorodinsky
{"title":"On Interference Among Moving Sensors and Related Problems","authors":"J. Carufel, M. J. Katz, Matias Korman, André van Renssen, Marcel Roeloffzen, Shakhar Smorodinsky","doi":"10.4230/LIPIcs.ESA.2016.34","DOIUrl":"https://doi.org/10.4230/LIPIcs.ESA.2016.34","url":null,"abstract":"We show that for any set of $n$ points moving along \"simple\" trajectories (i.e., each coordinate is described with a polynomial of bounded degree) in $Re^d$ and any parameter $2 le k le n$, one can select a fixed non-empty subset of the points of size $O(k log k)$, such that the Voronoi diagram of this subset is \"balanced\" at any given time (i.e., it contains $O(n/k)$ points per cell). We also show that the bound $O(k log k)$ is near optimal even for the one dimensional case in which points move linearly in time. As applications, we show that one can assign communication radii to the sensors of a network of $n$ moving sensors so that at any given time their interference is $O(sqrt{nlog n})$. We also show some results in kinetic approximate range counting and kinetic discrepancy. In order to obtain these results, we extend well-known results from $varepsilon$-net theory to kinetic environments.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"25 1","pages":"32-46"},"PeriodicalIF":0.0,"publicationDate":"2015-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75451807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Rigid origami vertices: conditions and forcing sets 刚性折纸顶点:条件和强制集
International Journal of Computational Geometry & Applications Pub Date : 2015-07-06 DOI: 10.20382/jocg.v7i1a9
Zachary Abel, Jason H. Cantarella, E. Demaine, D. Eppstein, Thomas C. Hull, Jason S. Ku, R. Lang, Tomohiro Tachi
{"title":"Rigid origami vertices: conditions and forcing sets","authors":"Zachary Abel, Jason H. Cantarella, E. Demaine, D. Eppstein, Thomas C. Hull, Jason S. Ku, R. Lang, Tomohiro Tachi","doi":"10.20382/jocg.v7i1a9","DOIUrl":"https://doi.org/10.20382/jocg.v7i1a9","url":null,"abstract":"We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"56 1","pages":"171-184"},"PeriodicalIF":0.0,"publicationDate":"2015-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86935248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 53
Approximate Greedy Clustering and Distance Selection for Graph Metrics 图度量的近似贪婪聚类和距离选择
International Journal of Computational Geometry & Applications Pub Date : 2015-07-06 DOI: 10.20382/jocg.v11i1a25
D. Eppstein, Sariel Har-Peled, Anastasios Sidiropoulos
{"title":"Approximate Greedy Clustering and Distance Selection for Graph Metrics","authors":"D. Eppstein, Sariel Har-Peled, Anastasios Sidiropoulos","doi":"10.20382/jocg.v11i1a25","DOIUrl":"https://doi.org/10.20382/jocg.v11i1a25","url":null,"abstract":"$newcommand{eps}{varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path metrics or high-dimensional Euclidean metrics. The first of these problems is the greedy permutation (or farthest-first traversal) of a finite metric space: a permutation of the points of the space in which each point is as far as possible from all previous points. We describe randomized algorithms to find $(1+eps)$-approximate greedy permutations of any graph with $n$ vertices and $m$ edges in expected time $O(eps^{-1}(m+n)log nlog(n/eps))$, and to find $(1+eps)$-approximate greedy permutations of points in high-dimensional Euclidean spaces in expected time $O(eps^{-2} n^{1+1/(1+eps)^2 + o(1)})$. Additionally we describe a deterministic algorithm to find exact greedy permutations of any graph with $n$ vertices and treewidth $O(1)$ in worst-case time $O(n^{3/2}log^{O(1)} n)$. The second of the two problems we consider is distance selection: given $k in [ binom{n}{2} ]$, we are interested in computing the $k$th smallest distance in the given metric space. We show that for planar graph metrics one can approximate this distance, up to a constant factor, in near linear time.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"228 1","pages":"629-652"},"PeriodicalIF":0.0,"publicationDate":"2015-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76179120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
On characterizing terrain visibility graphs 地形可视性图的表征
International Journal of Computational Geometry & Applications Pub Date : 2015-06-02 DOI: 10.20382/jocg.v6i1a5
W. Evans, Noushin Saeedi
{"title":"On characterizing terrain visibility graphs","authors":"W. Evans, Noushin Saeedi","doi":"10.20382/jocg.v6i1a5","DOIUrl":"https://doi.org/10.20382/jocg.v6i1a5","url":null,"abstract":"A terrain  is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph . We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs. Abello et al. [Discrete and Computational Geometry, 14(3):331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo) lines in a generalized configuration of points whose visibility graph is $M$. We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"26 1","pages":"108-141"},"PeriodicalIF":0.0,"publicationDate":"2015-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85279236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
Algorithms for ball hulls and ball intersections in normed planes 规范平面上球壳和球交的算法
International Journal of Computational Geometry & Applications Pub Date : 2015-05-21 DOI: 10.20382/jocg.v6i1a4
Pedro Martín, H. Martini
{"title":"Algorithms for ball hulls and ball intersections in normed planes","authors":"Pedro Martín, H. Martini","doi":"10.20382/jocg.v6i1a4","DOIUrl":"https://doi.org/10.20382/jocg.v6i1a4","url":null,"abstract":"Extending results of Hershberger and Suri for the Euclidean plane, we show that ball hulls and ball intersections of sets of $n$ points in normed planes can be constructed in $O(n log n)$ time. In addition, we confirm that the 2-center problem with constrained circles for arbitrary normed planes can be solved in $O(n^2)$ time. Some ideas about the geometric structure of the ball hull in a normed plane are also presented.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"1999 1","pages":"99-107"},"PeriodicalIF":0.0,"publicationDate":"2015-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88262657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The Lebesgue universal covering problem 勒贝格普遍覆盖问题
International Journal of Computational Geometry & Applications Pub Date : 2015-02-04 DOI: 10.20382/jocg.v6i1a12
J. Baez, Karine Bagdasaryan, P. Gibbs
{"title":"The Lebesgue universal covering problem","authors":"J. Baez, Karine Bagdasaryan, P. Gibbs","doi":"10.20382/jocg.v6i1a12","DOIUrl":"https://doi.org/10.20382/jocg.v6i1a12","url":null,"abstract":"In 1914 Lebesgue defined a 'universal covering' to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pal, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before.  However, Hansen's last reduction was microsopic: he claimed to remove an area of $6 cdot 10^{-18}$, but we show that he actually removed an area of just $8 cdot 10^{-21}$.  In the following, with the help of Greg Egan, we find a new, smaller universal covering with area less than $0.8441153$. This reduces the area of the previous best universal covering by $2.2 cdot 10^{-5}$.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"35 1","pages":"288-299"},"PeriodicalIF":0.0,"publicationDate":"2015-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88304900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
SEGMENTATION OF CYSTS IN KIDNEY AND 3-D VOLUME CALCULATION FROM CT IMAGES 肾囊肿的ct分割及三维体积计算
International Journal of Computational Geometry & Applications Pub Date : 2015-01-31 DOI: 10.5121/IJCGA.2015.5101
Nanzhou Piao, Jong-Gun Kim, Rae-Hong Park
{"title":"SEGMENTATION OF CYSTS IN KIDNEY AND 3-D VOLUME CALCULATION FROM CT IMAGES","authors":"Nanzhou Piao, Jong-Gun Kim, Rae-Hong Park","doi":"10.5121/IJCGA.2015.5101","DOIUrl":"https://doi.org/10.5121/IJCGA.2015.5101","url":null,"abstract":"This paper proposes a segmentation method and a three-dimensional (3-D) volume calculation method of cysts in kidney from a number of computer tomography (CT) slice images. The input CT slice images contain both sides of kidneys. There are two segmentation steps used in the proposed method: kidney segmentation and cyst segmentation. For kidney segmentation, kidney regions are segmented from CT slice images by using a graph-cut method that is applied to the middle slice of input CT slice images. Then, the same method is used for the remaining CT slice images. In cyst segmentation, cyst regions are segmented from the kidney regions by using fuzzy C-means clustering and level-set methods that can reduce noise of non-cyst regions. For 3-D volume calculation, cyst volume calculation and 3-D volume visualization are used. In cyst volume calculation, the area of cyst in each CT slice image equals to the number of pixels in the cyst regions multiplied by spatial density of CT slice images, and then the volume of cysts is calculated by multiplying the cyst area and thickness (interval) of CT slice images. In 3-D volume visualization, a 3-D visualization technique is used to show the distribution of cysts in kidneys by using the result of cyst volume calculation. The total 3-D volume is the sum of the calculated cyst volume in each CT slice image. Experimental results show a good performance of 3-D volume calculation. The proposed cyst segmentation and 3-D volume calculation methods can provide practical supports to surgery options and medical practice to medical students.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"5 1","pages":"1-16"},"PeriodicalIF":0.0,"publicationDate":"2015-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70617804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
TERRA FORMATION CONTROL (O R HOW TO MOVE MOUNTAINS ) 地形控制(或如何移动山脉)
International Journal of Computational Geometry & Applications Pub Date : 2015-01-31 DOI: 10.5121/IJCGA.2015.5103
J. Rankin
{"title":"TERRA FORMATION CONTROL (O R HOW TO MOVE MOUNTAINS )","authors":"J. Rankin","doi":"10.5121/IJCGA.2015.5103","DOIUrl":"https://doi.org/10.5121/IJCGA.2015.5103","url":null,"abstract":"The new Uplift Model of terrain generation is generalized here and provides new possibilities for terra formation control unlike previous fractal terrain generation methods. With the Uplift Model fine-grained editing is possible allowing the designer to move mountains and small hills to more suitable locations creating gaps or valleys or deep bays rather than only being able to accept the positions dictated by the algorithm itself. Coupled with this is a compressed file storage format considerably smaller in size that the traditional height field or height map storage requirements.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"5 1","pages":"39-46"},"PeriodicalIF":0.0,"publicationDate":"2015-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.5121/IJCGA.2015.5103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70617879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MULTIMEDIA MINING RESEARCH - AN OVERVIEW 多媒体挖掘研究综述
International Journal of Computational Geometry & Applications Pub Date : 2015-01-31 DOI: 10.5121/IJCGA.2015.5105
S. Vijayarani, A. Sakila
{"title":"MULTIMEDIA MINING RESEARCH - AN OVERVIEW","authors":"S. Vijayarani, A. Sakila","doi":"10.5121/IJCGA.2015.5105","DOIUrl":"https://doi.org/10.5121/IJCGA.2015.5105","url":null,"abstract":"Multimedia data mining is a popular research domain which helps to extract interesting knowledge from multimedia data sets such as audio, video, images, graphics, speech, text and combination of several types of data sets. Normally, multimedia data are categorized into unstructured and semi-structured data. These data are stored in multimedia databases and multimedia mining is used to find useful information from large multimedia database system by using various multimedia techniques and powerful tools. This paper provides the basic concepts of multimedia mining and its essential characteristics. Multimedia mining architectures for structured and unstructured data, research issues in multimedia mining, data mining models used for multimedia mining and applications are also discussed in this paper. It helps the researchers to get the knowledge about how to do their research in the field of multimedia mining.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"5 1","pages":"69-77"},"PeriodicalIF":0.0,"publicationDate":"2015-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.5121/IJCGA.2015.5105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70618074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 28
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