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Page 2085 of Mathematical Reviews Vol. , Issue 87d
[page]

1987
*
Mathematical Reviews
*

D. (1-RTG-C); Kalantari, B. (1-RTG-C)

*A**lower**bound**to**the**complexity**of**Euclidean**and**rectilinear**matching**algorithms*. Inform. Process. Lett. 22 (1986), no. 2, 73-76. ... *, is shown*to*be*bounded*below by*the*infimum*of**the*worst-case time*complexities**of*all*algorithms*which sort n real numbers. ...##
###
Page 4507 of Mathematical Reviews Vol. , Issue 97G
[page]

1997
*
Mathematical Reviews
*

*The*

*algorithm*works for both

*Euclidean*

*and*

*rectilinear*metrics. ... For

*a*fixed number k,

*the*performance ratio

*of*our

*algorithm*is | + (35c/V3k) for

*the*

*Euclidean*metric

*and*| + (9c/k) for

*the*

*rectilinear*metric. ...

##
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Semi-bipartite Graph Visualization for Gene Ontology Networks
[chapter]

2010
*
Lecture Notes in Computer Science
*

We also present

doi:10.1007/978-3-642-11805-0_24
fatcat:724qxxufdzgthfzrovmnj4nzky
*a**lower**bound*on*the*area*of**rectilinear*drawings,*and**a*upper*bound*on*the*number*of*edges. ... Our drawing*algorithms*minimize*the*number*of*orientations used*to*draw*the*edges*of**the**matching*. Specifically, when embedding*a**matching**and**a*tree, we can draw all*matching*edges horizontally. ...##
###
Page 1315 of Mathematical Reviews Vol. , Issue 2002B
[page]

2002
*
Mathematical Reviews
*

“If

*a**lower**bound*on*the*distance*to**the*target is known, then there is*a*simple strategy which achieves*a*competitive ratio*of*9—independent*of*m. ... “If*the*minimum distance*to**the*target is now known in ad- vance, we show*a**lower**bound*on*the*competitive ratio*of*1+ 2(k + 1)**! ...##
###
Page 5114 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

Existing related results already attain time

*complexity**matching**a*natural*lower**bound*, i.e., O(mm). ... Our parallel*algorithm*requires O(logn) time using*a*total*of*O(n) operations.*The**complexity**of*our*algorithm**matches*that*of**the**algorithm**of*K. M. McDonald*and*J. G. Peters [IEEE Trans. Comput. ...##
###
Efficient Deployment of Base Stations in Wireless Communication Networks

2016
*
Journal of Communications
*

In this paper, we improve

doi:10.12720/jcm.11.6.609-615
fatcat:gmqayuhzdfalhjyly4ht6kumta
*the*time*complexity**of**the*approximation*algorithms**and*conduct simulations*to*demonstrate*the*validness*of*our improvements. ...*The*problem has been proved*to*be NP-hard*and*cannot be approximated in*the*performance ratio 2 in polynomial time in both*Euclidean**and**rectilinear*plane*and*approximation*algorithms*in*the*best possible ... For*the**Euclidean*plane, however,*the*gap between*the**lower**bound**and*upper*bound*2 is still big. ...##
###
Topological Stability of Kinetic k-Centers
[article]

2021
*
arXiv
*
pre-print

We prove upper

arXiv:1810.00794v2
fatcat:unje3yxxwjhopgowka6qcnpwkq
*and**lower**bounds*on*the*ratio between*the*radii*of*an optimal but unstable solution*and**the*radii*of**a*topologically stable solution –*the*topological stability ratio – considering various ... For k = 2 we provide tight*bounds*,*and*for small k > 2 we can obtain nontrivial*lower**and*upper*bounds*. ... Since*the**lower**bound*construction is essentially one dimensional,*the*disks can be interchanged by squares,*and*thus works for both*the**Euclidean**and**the**rectilinear*case. ...##
###
Page 2815 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
*
Mathematical Reviews
*

Edge-packing is an efficient strategy

*to*compute*a**lower**bound*on*the*probability. ... Then*a*turn in perspective is made*and**a*nonoptimal process is analyzed:*the*greedy*matching**algorithm*. ...##
###
Page 1278 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

We provide some explanation for this lack

*of*success by presenting quadratic*lower**bounds*on*the*certificate*complexity**of**the*seemingly difficult problems, in contrast*to**the*known linear certificate ...*The*time*complexity**of**the**algorithm*is O(k log* n). ...##
###
Page 6946 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

We also prove

*a**lower**bound*n/2 for*the*majority function*and**a**lower**bound*,/n for*the*MidBit function.” ... Both*bounds*improve from n@) in [D.*A*. M. Barrington, R. Beigel*and*S. Rudich, Comput.*Complexity*4 (1994), no. 4, 367-382]*to*Q(n). ...##
###
A Fast Traversal Heuristic and Optimal Algorithm for Effective Environmental Coverage

2010
*
Robotics: Science and Systems VI
*

This approach produces

doi:10.15607/rss.2010.vi.021
dblp:conf/rss/XuS10
fatcat:abiin4polzbu3inoa4ierxhhwe
*a*tractable solution through*the*use*of*low*complexity**algorithms*in*a*branch-*and*-*bound*framework. ... With*a*prior map, an optimal path can be computed using*a*graph*to*represent*the*environment*and*generating*the*solution using known graph*algorithms*. ...*The*views*and*conclusions contained in this document are those*of**the*authors*and*should not be interpreted as representing*the*official policies, either expressed or implied,*of**the*Army Research Laboratory ...##
###
A Fast Traversal Heuristic and Optimal Algorithm for Effective Environmental Coverage
[chapter]

2011
*
Robotics
*

This approach produces

doi:10.7551/mitpress/9123.003.0025
fatcat:r2z43of7ojf3rn4s45ca55i6we
*a*tractable solution through*the*use*of*low*complexity**algorithms*in*a*branch-*and*-*bound*framework. ... With*a*prior map, an optimal path can be computed using*a*graph*to*represent*the*environment*and*generating*the*solution using known graph*algorithms*. ...*The*views*and*conclusions contained in this document are those*of**the*authors*and*should not be interpreted as representing*the*official policies, either expressed or implied,*of**the*Army Research Laboratory ...##
###
Lower and Upper Bounds for Tracking Mobile Users
[chapter]

2002
*
Foundations of Information Technology in the Era of Network and Mobile Computing
*

This paper continues

doi:10.1007/978-0-387-35608-2_5
dblp:conf/ifipTCS/BespamyatnikhBKS02
fatcat:4emhq2vpafftjavwrt6duidjau
*the*research started in our joint paper where we present*lower**bounds**and*efficient*algorithms*for exact*and*approximate maintenance*of**the*1center for*a*set*of*moving points in*the*... In this paper we prove improved*lower**and*upper*bounds*for*the*location*of*mobile facilities (in Loo*and*L2 metrics) under*the*motion*of*clients when facility moves faster than clients. ... We present improved*lower**and*upper*bounds*for mobile*rectilinear**and**Euclidean*1-center when facility is allowed*to*move faster than*the*clients. ...##
###
Chapter 7 A survey of computational geometry
[chapter]

1995
*
Handbooks in Operations Research and Management Science
*

Both elds seem

doi:10.1016/s0927-0507(05)80124-0
fatcat:nogmdqmv6bflni3waox5dxrsiy
*to*have bene ted from each other: combinatorial*bounds*for certain structures have been obtained by analyzing an*algorithm*that enumerates them*and*, conversely,*the*analysis*of**algorithms*...*The*topic*of*path planning is*a*vast one, with problems ranging from nding shortest paths in*a*discrete graph*to*deciding*the*feasible motion*of**a**complex*robot in an environment full*of**complex*obstacles ... Arkin et al. also give*lower**bounds*on*the*number*of*possible*matches**and*generalize*the*problem*to*allow arbitrary piecewise-linear cost functions for*the**matching*. ...##
###
The Geometric Maximum Traveling Salesman Problem
[article]

2003
*
arXiv
*
pre-print

For

arXiv:cs/0204024v2
fatcat:dthzcvkqz5ajtpoeehzhdkpobm
*the*special case*of*two-dimensional metrics with f=4 (which includes*the**Rectilinear**and*Sup norms), we present*a*simple*algorithm*with O(n) running time. ... Thus for example we have O(n^2 log n)*algorithms*for*the*cases*of*points in*the*plane under*the**Rectilinear**and*Sup norms. ... Thanks*to*Henk Meijer, Estie Arkin, Volker Kaibel, Joe Mitchell, Bill Pulleyblank, Mauricio Resende, Peter Shor,*and*Peter Winkler for helpful discussions,*and**to*an anonymous referee for useful comments ...
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