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The complexity of the covering radius problem

Venkatesan Guruswami, Daniele Micciancio, Oded Regev
2005 Computational Complexity  
We initiate the study of the computational complexity of the covering radius problem for lattices, and approximation versions of the problem for both lattices and linear codes.  ...  We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.1007/s00037-005-0193-y fatcat:ue4k4gru4zhctob5miisdmtu7y

The complexity of the covering radius problem on lattices and codes

V. Guruswami, D. Micciancio, O. Regev
Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.  
We initiate the study of the computational complexity of the covering radius problem for point lattices, and approximation versions of the problem for both lattices and linear codes.  ...  We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices.  ...  In this paper, we initiate the study of the complexity of the covering radius problem for point lattices, and the complexity of approximating the covering radius in both lattices and linear codes.  ... 
doi:10.1109/ccc.2004.1313831 dblp:conf/coco/GuruswamiMR04 fatcat:3wllbv6fofhk5bvcd5qgawmfh4

Hardness of the Covering Radius Problem on Lattices

I. Haviv, O. Regev
21st Annual IEEE Conference on Computational Complexity (CCC'06)  
We provide the first hardness result for the Covering Radius Problem on lattices (CRP).  ...  This gets close to the factor 2 beyond which the problem is not believed to be Π 2 -hard (Guruswami et al., Computational Complexity, 2005).  ...  Acknowledgement We thank Marcus Schaefer and Chris Umans for maintaining their excellent compendium of problems in the polynomial-time hierarchy [21] which taught us about group coloring problems, and  ... 
doi:10.1109/ccc.2006.23 dblp:conf/coco/HavivR06 fatcat:yhnu35aj7vdx5o5dfsbefsnwg4

Approximation algorithms design for disk partial covering problem

Bin Xiao, Jiannong Cao, Qingfeng Zhuge, Yi He, E.H.-M. Sha
2004 7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.  
In this paper, we study the issue of the partial covering problem such that part of mobile nodes to be covered. Several approximation algorithms are proposed to cover the maximum number of elements.  ...  The experimental results show that the performance of our algorithms is much better than other existing 3-approximation algorithm for the robust k-center problem.  ...  The problem defined in [12] is named by the robust k-center (RKC) problem, which is to cover at least p points (p ≤ n) by k disks with radius r.  ... 
doi:10.1109/ispan.2004.1300466 dblp:conf/ispan/XiaoCZHS04 fatcat:2tuwtccrengvhgn7iikbxggfv4

The slab dividing approach to solve the EuclideanP-Center problem

R. Z. Hwang, R. C. T. Lee, R. C. Chang
1993 Algorithmica  
Given n demand points on the plane, find the smallest radius r and a set S of P points, such that the circles centered at the points in S with radius r can cover all demand points.  ...  DEFINITION (The P-Circle Covering (PCC) Problem).  ...  Therefore the total time complexity of the corresponding algorithm for the EPC problem (also the PCC problem) is O(T(P)).O(log n) = O(n~ 8. Conclusions.  ... 
doi:10.1007/bf01185335 fatcat:alpxiz6fkjeqxbn23e3eirepjq

Proactive Coverage Area Decisions Based on Data Field for Drone Base Station Deployment

Bo Hu, Chuan'an Wang, Shanzhi Chen, Lei Wang, Hanzhang Yang
2018 Sensors  
Meanwhile, when the number of required DBSs is determined, the energy consumption is related to the coverage radius and the altitude of DBSs.  ...  Found in DBS-assisted cellular mobile networks, the deployment of DBSs to cope with the dynamic load requirements is an important problem.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/s18113917 fatcat:75zfga2snjapvhgkcotkcawkmm

New Set of Codes for the Maximum-Likelihood Decoding Problem [article]

Morgan Barbier
2010 arXiv   pre-print
In this paper, we introduce the notion of A-covered codes, that is, codes that can be decoded through a polynomial time algorithm A whose decoding bound is beyond the covering radius.  ...  Focusing on bi- nary BCH codes, we were able to find several examples of A-covered codes, including two codes for which the maximum-likelihood decoding problem can be solved in quasi-quadratic time.  ...  The main difficulty in finding such codes lies in the computation of covering radii.  ... 
arXiv:1011.2834v1 fatcat:opy5a4ipsbagrgdwbiluidfdkm

Page 2729 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
and open problems.” 98d:94048 94B75 Hou, Xiang-dong (1-WRTS; Dayton, OH) On the norm and covering radius of the first-order Reed-Muller codes.  ...  Summary: “We survey important developments in the theory of covering radius during the period 1985-1994.  ... 

Unit Disk Cover Problem [article]

Rashmisnata Acharyya, Manjanna B., Gautam K. Das
2012 arXiv   pre-print
Given a set D of unit disks in the Euclidean plane, we consider (i) the discrete unit disk cover (DUDC) problem and (ii) the rectangular region cover (RRC) problem.  ...  The solution of DUDC problem is based on a PTAS for the subproblem LSDUDC, where all the points in P are on one side of a line and covered by the disks centered on the other side of that line.  ...  The time complexity of 3-factor approximation algorithm for the WS-DUDC problem is O(m 6 n) [12] .  ... 
arXiv:1209.2951v1 fatcat:knrkk5vwvjezxny2677ygodth4

Roadmap-Based Level Clearing of Buildings [chapter]

Samuel Rodriguez, Nancy M. Amato
2011 Lecture Notes in Computer Science  
This approach utilizes an encoding of the environment in the form of a graph (roadmap) that is used to encode feasible paths through the environment.  ...  The roadmap is partitioned into regions, e.g., one per level, and we design region-based search strategies to cover and clear the environment.  ...  The number of agents needed to cover the roadmap with a view radius of 60 units is similar to when they have a view radius of 300.  ... 
doi:10.1007/978-3-642-25090-3_29 fatcat:5vw7z6bbsrdmrohipjn3xjcei4

Page 6070 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
He gives some implications of this result for the determination of t[n,k], the smallest covering radius among binary [n, k] codes. Harold N.  ...  Summary: “The covering radius of all ternary cyclic codes of length up to 25 is given. Some of the results were obtained by computer and for others mathematical reasonings were applied.  ... 

The choice of key geometric parameters in the numerical optimization of centrifugal compressor impellers

Vladimir Neverov, Yuri Kozhukhov, Sergey Kartashov, Vyacheslav Ivanov, A. Borodinecs, V. Sergeev, N. Vatin
2018 MATEC Web of Conferences  
The article deals with the choice of key geometric parameters and the range of their variation in solving the optimization problem of centrifugal compressor impellers using computational fluid dynamics  ...  Other parameters may not be considered within the optimization problem, and can be assigned to the standard values. In addition, recommendations on optimal ranges of parameter values were given.  ...  The variants of the rounding of the main disk are considered: the radius disk (Figure 5a ) and the complex one (Figure 5c ).  ... 
doi:10.1051/matecconf/201824509008 fatcat:3fppjhwp5fbh7njjo3a7fxdanq

A PTAS for the disk cover problem of geometric objects

Pedro J. de Rezende, Flávio K. Miyazawa, Anderson T. Sasaki
2013 Operations Research Letters  
We present PTASes for the disk cover problem: given geometric objects and a finite set of disk centers, minimize the total cost for covering those objects with disks under a polynomial cost function on  ...  We describe the first FPTAS for covering a line segment when the disk centers form a discrete set, and a PTAS for when a set of geometric objects, described by polynomial algebraic inequalities, must be  ...  radius equal to half of the length of the covered portion.  ... 
doi:10.1016/j.orl.2013.06.014 fatcat:fa37frm7yjblla6j6xfbmovj4i

Placement Optimization of UAV-Mounted Mobile Base Stations

Jiangbin Lyu, Yong Zeng, Rui Zhang, Teng Joon Lim
2017 IEEE Communications Letters  
Numerical results show that the proposed algorithm performs favorably compared to other schemes in terms of the total number of required MBSs and/or time complexity.  ...  Each MBS is placed to cover as many uncovered GTs as possible, with higher priority given to the GTs on the boundary to reduce the occurrence of outlier GTs that each may require one dedicated MBS for  ...  In step 3 of Algorithm 2, to check whether a set P of K points can be covered by a single disk of radius r, we need to solve the 1-center problem, which finds the location u of the center from which the  ... 
doi:10.1109/lcomm.2016.2633248 fatcat:2yntu6ms3bestjtnkzcz4laofi

Stabbing Line Segments with Disks: Complexity and Approximation Algorithms [chapter]

Konstantin Kobylkin
2017 Lecture Notes in Computer Science  
Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii r>0 where the set of  ...  We give strong NP-hardness of the problem for edge sets of Delaunay triangulations, Gabriel graphs and other subgraphs (which are often used in network design) for r∈ [d_,η d_] and some constant η where  ...  Let us consider the following problem: Cover endpoints of segments with disks (CESD): given an arbitrary set S E ⊆ V which covers the set E, find the smallest cardinality set of radius r disks whose union  ... 
doi:10.1007/978-3-319-73013-4_33 fatcat:ie5aadxkwzeuhpc2s4m65ignfy
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