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About 8,940 papers for “Unit disk”

Disk Dosing Unit

National Cancer Institute · Definitions · 2020

Ope n Pe e r Re v ie w on Qe ios

Cited by 0Open access

Unit disk graphs

Brent N. Clark, Charles J. Colbourn, David Johnson · Discrete Mathematics · 1990

Cited by 1,427

Unit Disk or Symplectic Geometry of Siegel Unit Disk will be

2015

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 non-singular 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 Toeplitz-Block-Toeplitz structure of Space-Time Covariance matrix, Parameterization known as Partial Iwasawa Decomposition could be applied

Cited by 0

Embedding Unit Disk Graphs

Prof Roger Wattenhofer, Jan-maarten Verbree · 2008

the ETH Zürich. During this time I was mainly supervised by Regina O’Dell at the ETH, but my initial contact

Cited by 0

Optical disk drive unit

OTA SHUICHI, KITAMURA YUJI · Institutional Repository of Xi'an Institute of Optics and Fine Mechanics, Chinese Academy of Sciences (Xian Institute of Optics and Precision Mechanics) · 1992

PURPOSE:To prevent camber from occurring due to temperature difference on two planes of an optical disk even when an ordinary optical disk to which no specific working is applied is used. CONSTITUTION:A pair of thermistor supporting tubes 5a, 5b and copper plates 6a, 6b connected to the thermal terminal of a Peltier element 8 in a Peltier element driving control circuit substrate 4 are arranged by neighboring to the upper and lower planes of the case 7 of an optical disk cartridge loaded on an optical disk drive unit, and the magnitude and direction of a current permitted to flow on the Peltier element from a circuit in the substrate 4 are controlled so as to set temperature detected by each thermistor in the thermistor supporting tubes 5a, 5b equal.

Cited by 0

Bisectored unit disk graphs

John P. Nolan · Networks · 2004

Abstract Unit disk graphs form a natural model for cellular radio channel assignment problems under the assumption of equally powerful, omnidirectional transmitters located on a uniform, flat plane. Here, we introduce and give motivation for an extension of this model, namely, sectorization at transmitter sites. We define and analyze properties of one case of sectorization, bisectored unit disk graphs, in particular, investigating properties concerning their chromatic number. Finally, we provide some experimental evidence to draw comparisons between graphs of this model and other classes of graphs. © 2004 Wiley Periodicals, Inc.

Cited by 4

Dynamic Unit-Disk Range Reporting

Wang, Haitao, Zhao, Yiming · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2025

For a set P of n points in the plane and a value r > 0, the unit-disk range reporting problem is to construct a data structure so that given any query disk of radius r, all points of P in the disk can be reported efficiently. We consider the dynamic version of the problem where point insertions and deletions of P are allowed. The previous best method provides a data structure of O(n log n) space that supports O(log^{3+ε} n) amortized insertion time, O(log^{5+ε} n) amortized deletion time, and O(log² n/log log n+k) query time, where ε is an arbitrarily small positive constant and k is the output size. In this paper, we improve the query time to O(log n+k) while keeping other complexities the same as before. A key ingredient of our approach is a shallow cutting algorithm for circular arcs, which may be interesting in its own right. A related problem that can also be solved by our techniques is the dynamic unit-disk range emptiness queries: Given a query unit disk, we wish to determine whether the disk contains a point of P. The best previous work can maintain P in a data structure of O(n) space that supports O(log² n) amortized insertion time, O(log⁴n) amortized deletion time, and O(log² n) query time. Our new data structure also uses O(n) space but can support each update in O(log^{1+ε} n) amortized time and support each query in O(log n) time.

Cited by 0Open access

CDS in Unit Disk Graph

Ding‐Zhu Du, Peng‐Jun Wan · Springer optimization and its applications · 2012

Cited by 0

Dynamic unit-disk range reporting

Wang, Haitao, Zhao, Yiming · Journal of Computational Geometry (Carleton University) · 2025

For a set $P$ of $n$ points in the plane and a value $r > 0$, the unit-disk range reporting problem is to construct a data structure so that given any query disk of radius $r$, all points of $P$ in the disk can be reported efficiently. We consider the dynamic version of the problem where point insertions and deletions of $P$ are allowed. The previous best method provides a data structure of $O(n \log n)$ space that supports $O(\log^{3 + \epsilon} n)$ amortized insertion time, $O(\log^{5 + \epsilon} n)$ amortized deletion time, and $O(\log^2 n / \log\log n + k)$ query time, where $\epsilon$ is an arbitrarily small positive constant and $k$ is the output size. In this paper, we improve the query time to $O(\log n + k)$ while keeping other complexities the same as before. A key ingredient of our approach is a shallow cutting algorithm for circular arcs, which may be interesting in its own right. A related problem that can also be solved by our techniques is the dynamic unit-disk range emptiness queries: Given a query unit disk, we wish to determine whether the disk contains a point of $P$. The best previous work can maintain $P$ in a data structure of $O(n)$ space that supports $O(\log^2 n)$ amortized insertion time, $O(\log^4 n)$ amortized deletion time, and $O(\log^2 n)$ query time. Our new data structure also uses $O(n)$ space but can support each update in $O(\log^{1 + \epsilon} n)$ amortized time and support each query in $O(\log n)$ time.

Cited by 0Open access

Intelligent multi-unit disk controller

Poirot, Lucien, CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France) · OpenGrey (Institut de l'Information Scientifique et Technique) · 1982

Cited by 0

Subcoloring of (Unit) Disk Graphs

Marin, Malory, Watrigant, Rémi · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2025

A subcoloring of a graph is a partition of its vertex set into subsets (called colors), each inducing a disjoint union of cliques. It is a natural generalization of the classical proper coloring, in which each color must instead induce an independent set. Similarly to proper coloring, we define the subchromatic number of a graph as the minimum integer k such that it admits a subcoloring with k colors, and the corresponding problem k-Subcoloring which asks whether a graph has subchromatic number at most k. In this paper, we initiate the study of the subcoloring of (unit) disk graphs. One motivation stems from the fact that disk graphs can be seen as a dense generalization of planar graphs where, intuitively, each vertex can be blown into a large clique-much like subcoloring generalizes proper coloring. Interestingly, it can be observed that every unit disk graph admits a subcoloring with at most 7 colors. We first prove that the subchromatic number can be 3-approximated in polynomial-time in unit disk graphs. We then present several hardness results for special cases of unit disk graphs which somehow prevents the use of classical approaches for improving this result. We show in particular that 2-Subcoloring remains NP-hard in triangle-free unit disk graphs, as well as in unit disk graphs representable within a strip of bounded height. We also solve an open question of Broersma, Fomin, Nešetřil, and Woeginger (2002) by proving that 3-Subcoloring remains NP-hard in co-comparability graphs (which contain unit disk graphs representable within a strip of height √3/2). Finally, we prove that every n-vertex disk graph admits a subcoloring with at most O(log³(n)) colors and present a O(log²(n))-approximation algorithm for computing the subchromatic number of such graphs. This is achieved by defining a decomposition and a special type of co-comparability disk graph, called Δ-disk graphs, which might be of independent interest.

Cited by 0Open access

Improper coloring of unit disk graphs

Frédéric Havet, Ross J. Kang, Jean‐Sébastien Sereni · Networks · 2009

Abstract Motivated by a satellite communications problem, we consider a generalized coloring problem on unit disk graphs. A coloring is k ‐improper if no more than k neighbors of every vertex have the same colour as that assigned to the vertex. The k ‐improper chromatic number χ k ( G ) is the least number of colors needed in a k ‐improper coloring of a graph G . The main subject of this work is analyzing the complexity of computing χ k for the class of unit disk graphs and some related classes, e.g., hexagonal graphs and interval graphs. We show NP‐completeness in many restricted cases and also provide both positive and negative approximability results. Because of the challenging nature of this topic, many seemingly simple questions remain: for example, it remains open to determine the complexity of computing χ k for unit interval graphs. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

Cited by 23