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

2005
*
Lecture Notes in Computer Science
*

In this paper, we study the following

doi:10.1007/11533719_50
fatcat:gz3oswazrraj5ozutbqatsnfzm
*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

2006
*
Journal of combinatorial optimization
*

In this paper, we study the following

doi:10.1007/s10878-006-7132-y
fatcat:7ssnokrdtvem5lcskdkui6cdjm
*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 . ...

##
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Minimum Covering with Travel Cost
[article]

2011
*
arXiv
*
pre-print

Given

arXiv:1101.2360v1
fatcat:i7jzzhh2hraxxdq53cpyjqqyyu
*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]

2020
*
arXiv
*
pre-print

We also design

arXiv:2009.10353v1
fatcat:zev5g5b63vbuvh3vozai7p5h3m
*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

2011
*
Monthly notices of the Royal Astronomical Society
*

By employing

doi:10.1111/j.1365-2966.2011.20097.x
fatcat:bzxqz5fxg5dhvnsy7zvypnf5n4
*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]

2017
*
arXiv
*
pre-print

We study

arXiv:1711.07851v1
fatcat:awwgt5x74fbfzim5mmsmndrlhu
*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

2015
*
2015 IEEE Wireless Communications and Networking Conference (WCNC)
*

In this paper, we formulate the relay node placement

doi:10.1109/wcnc.2015.7127693
dblp:conf/wcnc/MaLZS15
fatcat:3jzc7ni3qjcnzblnzi6jxxty4y
*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]

2012
*
Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
*

In this paper we

doi:10.1137/1.9781611973099.124
dblp:conf/soda/FominLS12
fatcat:s7q42vkczjbp7drdztgo77ool4
*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

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*. ...

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

2015
*
Monthly notices of the Royal Astronomical Society
*

quasars

doi:10.1093/mnras/stv1726
fatcat:hufk4avpjrcz5m5asbejx4pviq
*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

1956
*
Journal of Cell Biology
*

Holt (24)

doi:10.1083/jcb.2.4.381
fatcat:3gf3p7hkffhqnarxvvqpp5ctzm
*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]

2022
*
arXiv
*
pre-print

We show that

arXiv:2205.12783v1
fatcat:3zuo4xobwjdhdduomg3xjp3ltm
*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]

2011
*
arXiv
*
pre-print

In this paper we

arXiv:1107.2221v2
fatcat:hc5q65lts5bl3jh5edwlx5l7w4
*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 ... [16]*used*similar approaches to obtain*a**PTAS**for*MAXIMUM INDEPENDENT SET and MINIMUM r-DOMINATING SET on map graphs. ...
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