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Simple heuristics for unit disk graphs
 NETWORKS
, 1995
"... Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NPhard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring ..."
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Cited by 151 (6 self)
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Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NPhard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum
Unit Disk Graph Approximation
 In Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIALM
, 2004
"... Finding a good embedding of a unit disk graph given by its connectivity information is a problem of practical importance in a variety of fields. In wireless ad hoc and sensor networks, such an embedding can be used to obtain virtual coordinates. In this paper, we prove a nonapproximability result f ..."
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Cited by 62 (10 self)
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Finding a good embedding of a unit disk graph given by its connectivity information is a problem of practical importance in a variety of fields. In wireless ad hoc and sensor networks, such an embedding can be used to obtain virtual coordinates. In this paper, we prove a nonapproximability result
On Coloring Unit Disk Graphs
 ALGORITHMICA
, 1994
"... In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark, Colbourn and Johnson (1 ..."
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Cited by 41 (0 self)
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In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark, Colbourn and Johnson
Dispersion in unit disks
, 2009
"... We present two new approximation algorithms with (improved) constant ratios for selecting n points in n unit disks such that the minimum pairwise distance among the points is maximized. (I) A very simple O(n log n)time algorithm with ratio 0.5110 for disjoint unit disks. In combination with an algo ..."
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Cited by 2 (1 self)
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We present two new approximation algorithms with (improved) constant ratios for selecting n points in n unit disks such that the minimum pairwise distance among the points is maximized. (I) A very simple O(n log n)time algorithm with ratio 0.5110 for disjoint unit disks. In combination
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 140 (11 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges
Kinetic Connectivity for Unit Disks
 In Proc. 16th Annu. ACM Sympos. Comput. Geom
, 2000
"... We describe a kinetic data structure (KDS) that maintains the connected components of the union of a set of unitradius disks moving in the plane. We assume that the motion of each disk can be specified by a lowdegree algebraic trajectory; this trajectory, however, can be modified in an online ..."
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Cited by 22 (5 self)
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We describe a kinetic data structure (KDS) that maintains the connected components of the union of a set of unitradius disks moving in the plane. We assume that the motion of each disk can be specified by a lowdegree algebraic trajectory; this trajectory, however, can be modified in an on
MOTION IN THE UNIT DISK *. BY
"... Abstract. We study the heat diffusion in a domain with an obstacle inside. More precisely, we are interested in the quantity of heat in so far as a function of the position of the heat source at time 0. This quantity is also equal to the expectation of the sojourn time of the Brownian motion, refle ..."
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, reflected on the boundary of a small disk contained in the unit disk, and killcd on the unit circle. We g v e the explicit expression of this expectation. This allows us to make some numerical estimates and thus to illustrate the behaviour of this expectation as a function of starting point of the Brownian
AND HARMONIC FUNCTIONS IN THE UNIT DISK
, 1995
"... Abstract. Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal I in L 1 (G//K) , the space of radial integrable functions on G = SU(1, 1) , so that I = L 1 (G//K) or I = L 1 0 (G//K)—the ideal of L1 (G//K) functions whose integral is zero. ..."
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. This is then used to prove a generalization of Furstenberg’s theorem which characterizes harmonic functions on the unit disk by a mean value property and a “two circles ” Morera type theorem (earlier announced by Agranovskiĭ). 1.
On random points in the unit disk
, 2006
"... Let n be a positive integer and λ> 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(λ,n) to be the graph with vertex set Vn, in which two vertices are adjacent if and only if their Euclidean distance is at most λ. We call this ..."
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Cited by 2 (0 self)
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Let n be a positive integer and λ> 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(λ,n) to be the graph with vertex set Vn, in which two vertices are adjacent if and only if their Euclidean distance is at most λ. We call
Unit Disk or Symplectic Geometry of Siegel Unit Disk will be
"... Abstract: This paper deals with geometry of covariance matrices to define new advanced Radar Doppler Processing based on Metric Space tools. Information Geometry has been introduced by C.R.Rao, and axiomatized by N. Chentsov, to define a distance between statistical distributions that is invariant t ..."
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Abstract: This paper deals with geometry of covariance matrices to define new advanced Radar Doppler Processing based on Metric Space tools. Information Geometry has been introduced by C.R.Rao, and axiomatized by N. Chentsov, to define a distance between statistical distributions that is invariant to nonsingular parameterization transformations. For Doppler/Array/STAP Radar Processing, Information Geometry Approach will give key role to Homogenous Symmetric bounded domains geometry. For Radar, we will observe that Information Geometry metric could be related to Kähler metric, given by Hessian of Kähler potential (Entropy of Radar Signal given by – log[det(R)]). To take into account Toeplitz structure of Time/Space Covariance Matrix or ToeplitzBlockToeplitz structure of SpaceTime Covariance matrix, Parameterization known as Partial Iwasawa Decomposition could be applied
Results 1  10
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151,836