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### A PTAS for a Disc Covering Problem Using Width-Bounded Separators [chapter]

Zhixiang Chen, Bin Fu, Yong Tang, Binhai Zhu
2005 Lecture Notes in Computer Science
In this paper, we study the following disc covering problem: Given a set of discs of various radii on the plane and centers on the grid points, find a subset of discs to maximize the area covered by exactly  ...  Our techniques are based on the width-bounded geometric separator recently developed in Fu and Wang (2004),Fu (2006).  ...  Acknowledgement: We would like to thank the anonymous referees from COCOON'05 for their helpful comments. We are also grateful to Lusheng Wang for his great help.  ...

### A PTAS for a disc covering problem using width-bounded separators

Zhixiang Chen, Bin Fu, Yong Tang, Binhai Zhu
2006 Journal of combinatorial optimization
In this paper, we study the following disc covering problem: Given a set of discs of various radii on the plane and centers on the grid points, find a subset of discs to maximize the area covered by exactly  ...  Our techniques are based on the width-bounded geometric separator recently developed in Fu and Wang (2004),Fu (2006).  ...  Acknowledgement: We would like to thank the anonymous referees from COCOON'05 for their helpful comments. We are also grateful to Lusheng Wang for his great help.  ...

### On Minimum Sum of Radii and Diameters Clustering

2014 Algorithmica
For the MSD problem on the plane with Euclidean distances, we present a polynomial time approximation scheme.  ...  Given a metric (V, d) and an integer k, we consider the problem of covering the points of V with at most k clusters so as to minimize the sum of radii or the sum of diameters of these clusters.  ...  A PTAS for Euclidean MSD In this section, we present a PTAS for the MSD problem in R 2 . Let P be the set of all convex polygons having all corners from V .  ...

### On Minimum Sum of Radii and Diameters Clustering [chapter]

2012 Lecture Notes in Computer Science
For the MSD problem on the plane with Euclidean distances, we present a polynomial time approximation scheme.  ...  Given a metric (V, d) and an integer k, we consider the problem of covering the points of V with at most k clusters so as to minimize the sum of radii or the sum of diameters of these clusters.  ...  A PTAS for Euclidean MSD In this section, we present a PTAS for the MSD problem in R 2 . Let P be the set of all convex polygons having all corners from V .  ...

### Minimum Covering with Travel Cost [article]

Sandor P. Fekete, Joseph S. B. Mitchell, Christiane Schmidt
2011 arXiv   pre-print
Given a polygon and a visibility range, the Myopic Watchman Problem with Discrete Vision (MWPDV) asks for a closed path P and a set of scan points S, such that (i) every point of the polygon is within  ...  , these problems are NP-hard.  ...  Acknowledgements We thank Justin Iwerks for several suggestions that improved the presentation.  ...

### Discriminating Codes in Geometric Setups [article]

Sanjana Dey, Florent Foucaud, Subhas C Nandy, Arunabha Sen
2020 arXiv   pre-print
We also design a PTAS for both discrete and continuous cases when the intervals are all required to have the same length.  ...  The objective is to choose a subset S^* ⊆ S of minimum cardinality such that the subsets S_i^* ⊆ S^* covering p_i, satisfy S_i^*≠∅ for each i=1,2,..., n, and S_i^* ≠ S_j^* for each pair (i,j), i ≠ j.  ...  We solve this problem using a technique followed in Acharyya et al. (2019) for covering a set of segments using unit squares.  ...

### Multimessenger astronomy with pulsar timing and X-ray observations of massive black hole binaries

A. Sesana, C. Roedig, M. T. Reynolds, M. Dotti
2011 Monthly notices of the Royal Astronomical Society
By employing a standard model for the evolution of MBHBs in circumbinary discs, with the aid of dedicated numerical simulations, we characterize the gas-binary interplay, identifying possible electromagnetic  ...  signatures of the PTA sources.  ...  discs for longer time and at smaller separation.  ...

### Approximation Algorithms for Rectangle Packing Problems (PhD Thesis) [article]

Salvatore Ingala
2017 arXiv   pre-print
We study a generalization of MWISR and use it to improve the approximation for a resource allocation problem called bagUFP.  ...  By finding a (1 + ϵ)-approximation for this problem and exploiting the combinatorial structure of 2DGK, we obtain the first algorithms that break the barrier of 2 for the approximation factor of this problem  ...  If a problem is APX-hard, then the existence of a PTAS for it would imply the existence of a PTAS for every problem in APX.  ...

### A novel local search approximation algorithm for relay node placement in Wireless Sensor Networks

Chaofan Ma, Wei Liang, Meng Zheng, Hamid Sharif
2015 2015 IEEE Wireless Communications and Networking Conference (WCNC)
In this paper, we formulate the relay node placement problem as a Geometric Disc Covering (GDC) problem, and propose a novel local search approximation algorithm (LSAA) to solve the GDC problem.  ...  The set of the SC for each group constitutes a SC of the GDC problem.  ...  of Chinese Academy of Sciences (Network and System Technologies for Safety Monitoring and Information Interacting in Smart Grid).  ...

### Bidimensionality and Geometric Graphs [chapter]

Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which  ...  [JACM 2005 ] as a framework to obtain algorithmic results for hard problems on minor closed graph classes.  ...  Similarly, a PTAS for FEEDBACK VERTEX SET on unit ball graphs in R 3 could be combined with Lemma 14 to yield a PTAS for VERTEX COVER on graphs of maximum degree 3.  ...

### The ultrastructure of a reptilian myoneural junction

J D ROBERTSON
1956 The Journal of Biophysical and Biochemical Cytology
A compound membrane 500 to 700 A thick separates axoplasm from sarcoplasm at the endings. This consists of five distinct layers and is described in detail.  ...  A thin layer of cytoplasm (probably Schwann) separates terminal axoplasm from extracellular space at the surfaces of the junctional troughs.  ...  They are usually separated by a distance about equal to twice their width.  ...

### A systematic search for close supermassive black hole binaries in the Catalina Real-time Transient Survey

Matthew J. Graham, S. G. Djorgovski, Daniel Stern, Andrew J. Drake, Ashish A. Mahabal, Ciro Donalek, Eilat Glikman, Steve Larson, Eric Christensen
2015 Monthly notices of the Royal Astronomical Society
quasars using data from the Catalina Real-time Transient Survey (CRTS) to look for close (< 0.1 pc) SMBH systems.  ...  Looking for a strong Keplerian periodic signal with at least 1.5 cycles over a baseline of nine years, we find a sample of 111 candidate objects.  ...  AC K N OW L E D G E M E N T S We thank the anonymous referee for their comments. We thank Zoltan Haiman, Chiara Mingarelli and Justin Ellis for useful discussions.  ...

### THE ULTRASTRUCTURE OF A REPTILIAN MYONEURAL JUNCTION

J. D. Robertson
1956 Journal of Cell Biology
Holt (24) using a different technique for cholinesterase has obtained similar results.  ...  The clear zone sometimes appeared to be separated from sarcoplasm by a very thin (about 1 micron) cross-striated border.  ...  They are usually separated by a distance about equal to twice their width.  ...

### Detection of eccentric close-binary supermassive black holes with incomplete interferometric data [article]

Andjelka Kovacevic, Yu-Yang Songsheng, Jian-Min Wang, Luka C. Popovic
2022 arXiv   pre-print
We show that using observational time baselines that cover 10 increases the possibility of determining the period, eccentricity, and total mass of an eCBSMBH.  ...  We therefore applied the Bayesian method to fit orbital elements of the eCBSMBH to combined radial velocity and astrometric data covering a small fraction of the orbital period.  ...  The width of pericentre passage is ∼ (1−e) 2 P (Cumming 2004) , which means that for binaries with P = 1yr, e = 0.5, observations should cover a small window of 3 months of periastron passage.  ...

### Bidimensionality and Geometric Graphs [article]

Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh
2011 arXiv   pre-print
In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which  ...  To the best of our knowledge, these results are previously unknown, with the exception of the EPTAS and a subexponential time parameterized algorithm on unit disk graphs for Vertex Cover, which were obtained  ...   used similar approaches to obtain a PTAS for MAXIMUM INDEPENDENT SET and MINIMUM r-DOMINATING SET on map graphs.  ...
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