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Separating Geometric Data with Minimum Cost: Two Disjoint Convex Hulls
[article]

2021
*
arXiv
*
pre-print

Furthermore, it has been illustrated that the new problem known as "

arXiv:2106.09974v1
fatcat:3l7kr32bgjgi3lnel5adzgzcyu
*Two**Disjoint**Convex**Hulls*" can be solved in polynomial time due to some combinatorial aspects and*geometric*properties. ... In this study, a*geometric*version of an NP-hard problem ("Almost 2-SAT" problem) is introduced which has potential applications in clustering,*separation*axis, binary sensor networks, shape*separation*... It chooses the pair*with*the*minimum**cost*and returns the points that should make the*separating*axis. ...##
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A general soft method for learning SVM classifiers with -norm penalty

2008
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Pattern Recognition
*

Intrinsically, the resulting soft algorithms are to find -optimal nearest points between

doi:10.1016/j.patcog.2007.08.004
fatcat:bhqybd42snac3glaoct72v4xpe
*two*soft*convex**hulls*. ... Based on the*geometric*interpretation of support vector machines (SVMs), this paper presents a general technique that allows almost all the existing L 2 -norm penalty based*geometric*algorithms, including ... Hence, in this paper, it is natural to assume that the*two*soft*convex**hulls*are*separable**with*a choice of . ...##
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Shooting Permanent Rays among Disjoint Polygons in the Plane

2012
*
SIAM journal on computing (Print)
*

obstacles

doi:10.1137/100804310
fatcat:m2qdeqgnnnbudes7wcykr7u5jm
*with*a total of n vertices in the plane, a permutation of the reflex vertices, and a half-line at each reflex vertex that partitions the reflex angle into*two**convex*angles, then the*convex*partitioning ... We present a*data*structure for ray shooting and insertion in the free space between*disjoint*polygonal obstacles*with*a total of n vertices in the plane, where each ray starts at the boundary of some ... For a set S of points in the plane, the*convex**hull*is the*minimum*set that contains S and is*convex*(i.e., contains the line segment between any*two*of its points). ...##
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Shooting permanent rays among disjoint polygons in the plane

2009
*
Proceedings of the 25th annual symposium on Computational geometry - SCG '09
*

obstacles

doi:10.1145/1542362.1542372
dblp:conf/compgeom/IshaqueST09
fatcat:rfpvi5zswjhs7bceufibsedcgi
*with*a total of n vertices in the plane, a permutation of the reflex vertices, and a half-line at each reflex vertex that partitions the reflex angle into*two**convex*angles, then the*convex*partitioning ... We present a*data*structure for ray shooting and insertion in the free space between*disjoint*polygonal obstacles*with*a total of n vertices in the plane, where each ray starts at the boundary of some ... For a set S of points in the plane, the*convex**hull*is the*minimum*set that contains S and is*convex*(i.e., contains the line segment between any*two*of its points). ...##
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Linear Separability in Spatial Databases
[article]

2016
*
arXiv
*
pre-print

Given

arXiv:1602.04399v1
fatcat:t6c34xkchfhp5llm62dfi3e5vu
*two*point sets R and B in the plane,*with*cardinalities m and n, respectively, and each set stored in a*separate*R-tree, we present an algorithm to decide whether R and B are linearly*separable*. ... We also present an algorithm to compute the*convex**hull*of n planar points given in an R-tree, running in O(n n) time in the worst case. ... Among the*geometric*problems in spatial databases, this later work is well related to the results of this paper since linear the*separability*of*two*point sets can be decided by computing the*convex**hull*...##
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Cluster Hull: A Technique for Summarizing Spatial Data Streams

2006
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22nd International Conference on Data Engineering (ICDE'06)
*

The

doi:10.1109/icde.2006.38
dblp:conf/icde/HershbergerSS06
fatcat:6yoym6w5vvchjlyva7n55kom2q
*convex**hulls*need not be*disjoint*, but together these*hulls*are limited to m vertices, which is our memory budget. ... The algorithm attempts to maintain a partition of the point stream*with**minimum*total*cost*, using its fixed O(k) memory budget. ...##
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Efficient geometric algorithms for parsing in two dimensions

2005
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Eighth International Conference on Document Analysis and Recognition (ICDAR'05)
*

Each

doi:10.1109/icdar.2005.98
dblp:conf/icdar/LiangNSV05
fatcat:kzy2kmfsebhehlobzc6z37zko4
*data*structure embodies a different*geometrical*constraint on the set of possible valid parses. ... Assuming a clean design for the parsing software, the same parsing framework can be tested*with*various*geometric*constraints to determine the most effective combination. ... Essentially the recurrence states that the score for A is computed by finding a low*cost*decomposition of the terminals into*two**disjoint*sets. ...##
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Data Gathering by Mobile Mules in a Spatially Separated Wireless Sensor Network

2009
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2009 Tenth International Conference on Mobile Data Management: Systems, Services and Middleware
*

In this paper, we consider the possibility that a WSN may be spatially

doi:10.1109/mdm.2009.43
dblp:conf/mdm/WuHT09
fatcat:22fhrfdp4fd5tkp5y3woky3yr4
*separated*into multiple subnetworks. ...*Data*gathering, which is a fundamental mission of WSN, thus may rely on a mobile mule ("mule" for short) to conduct*data*gathering by visiting each subnetwork. ... In addition, the*convex**hull*never intersects*with*itself. These observations motivate us to conduct path construction and path improvement based on*convex**hulls*. ...##
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Adaptive sampling for geometric problems over data streams

2004
*
Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '04
*

One can also pose queries over multiple streams: track the

doi:10.1145/1055558.1055595
dblp:conf/pods/HershbergerS04
fatcat:rxvbcljspbconibxzp636cvpay
*minimum*distance between the*convex**hulls*of*two**data*streams; or report when datasets A and B are no longer linearly*separable*. ...*With*our sample*convex**hull*, all the queries mentioned above can be answered in either O(log r) or O(r) time. ... Linear*Separation*: Given approximate*convex**hulls*for*two*point streams, A and B, we can track the*minimum*distance between them, or determine when they are no longer linearly*separable*. ...##
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Summarizing Spatial Data Streams Using ClusterHulls

2006
*
2006 Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments (ALENEX)
*

We are not aware of other schemes specifically designed for capturing shape information in

doi:10.1137/1.9781611972863.3
dblp:conf/alenex/HershbergerSS06
fatcat:xrih2rf7f5fpxndqegqhuh7bva
*geometric**data*streams, and so we compare Cluster-*Hull**with*some of the best general-purpose clustering schemes ... We propose a novel scheme, called ClusterHull, which represents the shape of the stream as a dynamic collection of*convex**hulls*,*with*a total of at most m vertices, where m is the size of the memory. ... The first 2k points that arrive in a*data*stream are paired up into k*two*-point*convex**hulls*, each*with**cost*zero, and the pairing will be arbitrary. ...##
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Summarizing spatial data streams using ClusterHulls

2009
*
ACM Journal of Experimental Algorithmics
*

We are not aware of other schemes specifically designed for capturing shape information in

doi:10.1145/1412228.1412238
fatcat:3znugdcymvgwbnrfkasel5lkvu
*geometric**data*streams, and so we compare Cluster-*Hull**with*some of the best general-purpose clustering schemes ... We propose a novel scheme, called ClusterHull, which represents the shape of the stream as a dynamic collection of*convex**hulls*,*with*a total of at most m vertices, where m is the size of the memory. ... The first 2k points that arrive in a*data*stream are paired up into k*two*-point*convex**hulls*, each*with**cost*zero, and the pairing will be arbitrary. ...##
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Kinetic Data Structures
[chapter]

2006
*
Geometric Data Structures for Computer Graphics
*

A number of other authors have dealt

doi:10.1201/b10626-9
fatcat:25iax4fy55bavpa5iujdck4f6i
*with**geometric*problems arising from motion, such as collision detection or*minimum**separation*determination [GJS96, ST95, ST96] . ... For*two*moving*convex*polygons in the plane, a kinetic algorithm where the number of events is a function of the relative*separation*of the*two*polygons is given in [EGSZ99] . ...##
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Kinetic Data Structures
[chapter]

2004
*
Handbook of Data Structures and Applications
*

A number of other authors have dealt

doi:10.1201/9781420035179.ch23
fatcat:s6v4u4nlrfhzdm5fg2cp52soca
*with**geometric*problems arising from motion, such as collision detection or*minimum**separation*determination [GJS96, ST95, ST96] . ... For*two*moving*convex*polygons in the plane, a kinetic algorithm where the number of events is a function of the relative*separation*of the*two*polygons is given in [EGSZ99] . ...##
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Convex and concave hulls for classification with support vector machine

2013
*
Neurocomputing
*

The proposed

doi:10.1016/j.neucom.2013.05.040
fatcat:37waggvmzrca3pskdokj2jqzsu
*convex*-concave*hull*SVM classifier has distinctive advantages on dealing*with*large*data*sets*with*higher accuracy. ... The training of a support vector machine (SVM) has the time complexity of O(n 3 )*with**data*number n . Normal SVM algorithms are not suitable for classification of large*data*sets. ...*Convex*and Concave*Hull**Convex**Hull*The*convex**hull*(CH) of a set of points S is the*minimum**convex*set that contains S. ...##
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Adaptive sampling for geometric problems over data streams

2008
*
Computational geometry
*

One can also pose queries over multiple streams: for instance, track the

doi:10.1016/j.comgeo.2006.10.004
fatcat:mgvq22ynifhybbk3pkbt26g7xe
*minimum*distance between the*convex**hulls*of*two**data*streams, report when datasets A and B are no longer linearly*separable*, or ...*Geometric*coordinates are an integral part of many*data*streams. ... the*convex**hulls*of*two**data*streams; report when*data*streams A and B are no longer linearly*separable*; track the overlap between the spatial extents of streams A and B; report when points of*data*stream ...
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