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The complexity of the covering radius problem

2005
*
Computational Complexity
*

We initiate

doi:10.1007/s00037-005-0193-y
fatcat:ue4k4gru4zhctob5miisdmtu7y
*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. ...##
###
The complexity of the covering radius problem on lattices and codes

*
Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.
*

We initiate

doi:10.1109/ccc.2004.1313831
dblp:conf/coco/GuruswamiMR04
fatcat:3wllbv6fofhk5bvcd5qgawmfh4
*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. ...##
###
Hardness of the Covering Radius Problem on Lattices

*
21st Annual IEEE Conference on Computational Complexity (CCC'06)
*

We provide

doi:10.1109/ccc.2006.23
dblp:conf/coco/HavivR06
fatcat:yhnu35aj7vdx5o5dfsbefsnwg4
*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 ...##
###
Approximation algorithms design for disk partial covering problem

2004
*
7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.
*

In this paper, we study

doi:10.1109/ispan.2004.1300466
dblp:conf/ispan/XiaoCZHS04
fatcat:2tuwtccrengvhgn7iikbxggfv4
*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. ...##
###
The slab dividing approach to solve the EuclideanP-Center problem

1993
*
Algorithmica
*

Given n demand points on

doi:10.1007/bf01185335
fatcat:alpxiz6fkjeqxbn23e3eirepjq
*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. ...##
###
Proactive Coverage Area Decisions Based on Data Field for Drone Base Station Deployment

2018
*
Sensors
*

Meanwhile, when

doi:10.3390/s18113917
fatcat:75zfga2snjapvhgkcotkcawkmm
*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. ...##
###
New Set of Codes for the Maximum-Likelihood Decoding Problem
[article]

2010
*
arXiv
*
pre-print

In this paper, we introduce

arXiv:1011.2834v1
fatcat:opy5a4ipsbagrgdwbiluidfdkm
*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. ...##
###
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]

2012
*
arXiv
*
pre-print

Given a set D

arXiv:1209.2951v1
fatcat:knrkk5vwvjezxny2677ygodth4
*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] . ...##
###
Roadmap-Based Level Clearing of Buildings
[chapter]

2011
*
Lecture Notes in Computer Science
*

This approach utilizes an encoding

doi:10.1007/978-3-642-25090-3_29
fatcat:5vw7z6bbsrdmrohipjn3xjcei4
*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. ...##
###
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

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 ). ...

##
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A PTAS for the disk cover problem of geometric objects

2013
*
Operations Research Letters
*

We present PTASes for

doi:10.1016/j.orl.2013.06.014
fatcat:fa37frm7yjblla6j6xfbmovj4i
*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. ...##
###
Placement Optimization of UAV-Mounted Mobile Base Stations

2017
*
IEEE Communications Letters
*

Numerical results show that

doi:10.1109/lcomm.2016.2633248
fatcat:2yntu6ms3bestjtnkzcz4laofi
*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*...##
###
Stabbing Line Segments with Disks: Complexity and Approximation Algorithms
[chapter]

2017
*
Lecture Notes in Computer Science
*

Computational

doi:10.1007/978-3-319-73013-4_33
fatcat:ie5aadxkwzeuhpc2s4m65ignfy
*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 ...
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