메뉴 건너뛰기




Volumn 18, Issue 4, 2009, Pages 376-392

New algorithms for k-center and extensions

Author keywords

2 SAT; Approximation algorithms; Branch and bound; Computational geometry; Containment; Core sets; Diameter partition; Geometric inequalities; K center; SOCP

Indexed keywords

APPROXIMATION ALGORITHMS; COMPUTATIONAL GEOMETRY;

EID: 84898011546     PISSN: 13826905     EISSN: 15732886     Source Type: Journal    
DOI: 10.1007/s10878-009-9226-9     Document Type: Article
Times cited : (11)

References (40)
  • 2
    • 0032266683 scopus 로고    scopus 로고
    • Efficient algorithms for geometric optimization
    • Agarwal PK, Sharir M (1998) Efficient algorithms for geometric optimization. ACM Comput Surv 30(4):412-458
    • (1998) ACM Comput Surv , vol.30 , Issue.4 , pp. 412-458
    • Agarwal, P.K.1    Sharir, M.2
  • 4
    • 0040979813 scopus 로고
    • Diameter partitioning
    • Avis D (1986) Diameter partitioning. Discrete Comput Geom 1:265-276
    • (1986) Discrete Comput Geom , vol.1 , pp. 265-276
    • Avis, D.1
  • 6
    • 0034251215 scopus 로고    scopus 로고
    • Covering a set of points by two axis-parallel boxes
    • Bespamyatnikh S, Segal M (2000) Covering a set of points by two axis-parallel boxes. Inf Process Lett 75(3):95-100
    • (2000) Inf Process Lett , vol.75 , Issue.3 , pp. 95-100
    • Bespamyatnikh, S.1    Segal, M.2
  • 7
    • 0001316189 scopus 로고
    • Convex regions and projections in Minkowski spaces
    • Bohnenblust HF (1938) Convex regions and projections in Minkowski spaces. Ann Math 39:301-308
    • (1938) Ann Math , vol.39 , pp. 301-308
    • Bohnenblust, H.F.1
  • 10
    • 84897977140 scopus 로고    scopus 로고
    • Optimal containment under homothetics. A simple cutting plane approach
    • (to appear).
    • Brandenberg R, Roth L (2009) Optimal containment under homothetics. A simple cutting plane approach. Comput Optim Appl (to appear).
    • (2009) Comput Optim Appl
    • Brandenberg, R.1    Roth, L.2
  • 13
    • 0000131150 scopus 로고    scopus 로고
    • More planar two-center algorithms
    • Chan TM (1999) More planar two-center algorithms. Comput Geom Theory Appl 13(3):189-198
    • (1999) Comput Geom Theory Appl , vol.13 , Issue.3 , pp. 189-198
    • Chan, T.M.1
  • 15
    • 0021938963 scopus 로고
    • Clustering to minimize the maximum intercluster distance
    • Gonzalez TF (1985) Clustering to minimize the maximum intercluster distance. Theor Comput Sci 38:293-306
    • (1985) Theor Comput Sci , vol.38 , pp. 293-306
    • Gonzalez, T.F.1
  • 16
    • 0000012770 scopus 로고
    • Inner and outer j-radii of convex bodies in finite-dimensional normed spaces
    • Gritzmann P, Klee V (1992) Inner and outer j-radii of convex bodies in finite-dimensional normed spaces. Discrete Comput Geom 7:255-280
    • (1992) Discrete Comput Geom , vol.7 , pp. 255-280
    • Gritzmann, P.1    Klee, V.2
  • 17
    • 0001535602 scopus 로고
    • On the complexity of some basic problems in computational convexity I: Containment problems
    • Gritzmann P, Klee V (1994) On the complexity of some basic problems in computational convexity I: Containment problems. Discrete Math 136:129-174
    • (1994) Discrete Math , vol.136 , pp. 129-174
    • Gritzmann, P.1    Klee, V.2
  • 18
    • 0036462083 scopus 로고    scopus 로고
    • The 2-center problem with obstacles
    • Halperin D, Sharir M, Goldberg K (2002) The 2-center problem with obstacles. J Algebra 42(1):109-134
    • (2002) J Algebra , vol.42 , Issue.1 , pp. 109-134
    • Halperin, D.1    Sharir, M.2    Goldberg, K.3
  • 20
    • 0000998989 scopus 로고
    • Über Mengen konvexer Körper mit gemeinschaftlichen Punkten
    • Helly E (1923) Über Mengen konvexer Körper mit gemeinschaftlichen Punkten. Jahresbericht Deutsch Math Verein 32:175-176
    • (1923) Jahresbericht Deutsch Math Verein , vol.32 , pp. 175-176
    • Helly, E.1
  • 21
    • 0027912875 scopus 로고
    • A faster algorithm for the two-center decision problem
    • Hershberger J (1993) A faster algorithm for the two-center decision problem. Inf Process Lett 47(1):23-29
    • (1993) Inf Process Lett , vol.47 , Issue.1 , pp. 23-29
    • Hershberger, J.1
  • 22
    • 84867966435 scopus 로고    scopus 로고
    • A simple linear algorithm for computing rectilinear 3-centers
    • Hoffmann M (2005) A simple linear algorithm for computing rectilinear 3-centers. Comput Geom Theory Appl 31(3):150-165
    • (2005) Comput Geom Theory Appl , vol.31 , Issue.3 , pp. 150-165
    • Hoffmann, M.1
  • 24
    • 0028015214 scopus 로고
    • An efficient algorithm for the Euclidean two-center problem
    • Jaromczyk JW, Kowaluk M (1994) An efficient algorithm for the Euclidean two-center problem. In: Symp comp geom, pp 303-311
    • (1994) Symp Comp Geom , pp. 303-311
    • Jaromczyk, J.W.1    Kowaluk, M.2
  • 25
    • 0002940114 scopus 로고
    • Extremum problems with inequalities as subsidiary conditions
    • New York
    • John F (1948) Extremum problems with inequalities as subsidiary conditions. In: Courant anniversary volume. Interscience, New York, pp 187-204
    • (1948) Courant Anniversary Volume. Interscience , pp. 187-204
    • John, F.1
  • 26
    • 84942225364 scopus 로고
    • Über die kleinste Kugel, die eine räumliche Figur einschließt
    • Jung HWE (1901) Über die kleinste Kugel, die eine räumliche Figur einschließt. J Reine Angew Math 123:241-257
    • (1901) J Reine Angew Math , vol.123 , pp. 241-257
    • Jung, H.W.E.1
  • 28
    • 72849123507 scopus 로고    scopus 로고
    • Approximate minimum enclosing balls in high dimensions using core-sets
    • Kumar P, Mitchell JSB, Yildirim EA (2003) Approximate minimum enclosing balls in high dimensions using core-sets. J Exp Algorithm 8
    • (2003) J Exp Algorithm , vol.8
    • Kumar, P.1    Jsb, M.2    Yildirim, E.A.3
  • 30
    • 0004534203 scopus 로고
    • Zwei Extremalprobleme der Minkowski-Geometrie
    • Leichtweiß K (1955) Zwei Extremalprobleme der Minkowski-Geometrie. Math Z 62:37-49
    • (1955) Math Z , vol.62 , pp. 37-49
    • Leichtweiß, K.1
  • 31
    • 0003085879 scopus 로고
    • Pattern recognition via linear programming: Theory and application to medical diagnosis
    • Coleman TF, Li Y (eds) SIAM, Philadelphia
    • Mangasarian OL, Setiono R, Wolberg WH (1990) Pattern recognition via linear programming: theory and application to medical diagnosis. In: Coleman TF, Li Y (eds) Large-scale numerical optimization. Computer sciences TR, vol 878. SIAM, Philadelphia, pp 22-31
    • (1990) Large-scale Numerical Optimization. Computer Sciences TR , vol.878 , pp. 22-31
    • Mangasarian, O.L.1    Setiono, R.2    Wolberg, W.H.3
  • 32
    • 0012527124 scopus 로고
    • On the complexity of some geometric problems in unbounded dimension
    • Megiddo N (1990) On the complexity of some geometric problems in unbounded dimension. J Symb Comput 10(3/4):327-334
    • (1990) J Symb Comput , vol.10 , Issue.3-4 , pp. 327-334
    • Megiddo, N.1
  • 35
    • 0029713034 scopus 로고    scopus 로고
    • A near-linear algorithm for the planar 2-center problem
    • Sharir M (1996) A near-linear algorithm for the planar 2-center problem. In: Proc symp comp geom, pp 106-112
    • (1996) Proc Symp Comp Geom , pp. 106-112
    • Sharir, M.1
  • 36
    • 0033296299 scopus 로고    scopus 로고
    • Using SEDUMI 1.02, a MATLAB toolbox for optimization over symmetric cones
    • Sturm JF (1999) Using SEDUMI 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim Methods Softw 11-12:625-653
    • (1999) Optim Methods Softw , vol.11-12 , pp. 625-653
    • Sturm, J.F.1
  • 37
    • 0033295027 scopus 로고    scopus 로고
    • SDPT3 - A Matlab software package for semidefinite programming
    • Toh KC, Todd MJ, Tütüncü RH (1999) SDPT3 - a Matlab software package for semidefinite programming. Optim Methods Softw 11:545-581
    • (1999) Optim Methods Softw , vol.11 , pp. 545-581
    • Toh, K.C.1    Todd, M.J.2    Tütüncü, R.H.3
  • 38
    • 3142743708 scopus 로고    scopus 로고
    • Solving semidefinite-quadratic-linear programs using SDPT3
    • Tütüncü RH, Toh KC, Todd MJ (2003) Solving semidefinite-quadratic-linear programs using SDPT3. Math Program Ser B 95:189-217
    • (2003) Math Program ser B , vol.95 , pp. 189-217
    • Tütüncü, R.H.1    Toh, K.C.2    Todd, M.J.3
  • 39
    • 85158161749 scopus 로고    scopus 로고
    • On 2-SAT and renamable Horn
    • AAAI/MIT Press, Menlo Park/Cambridge
    • del Val A (2000) On 2-SAT and renamable Horn. In: Proc 17th nat conf on artif intel. AAAI/MIT Press, Menlo Park/Cambridge, p 111
    • (2000) Proc 17th Nat Conf on Artif Intel , pp. 111
    • Del Val, A.1
  • 40
    • 33750060445 scopus 로고    scopus 로고
    • Solving the continuous space p-centre problem: Planning application issues
    • Wei H, Murray AT, Xiao N (2006) Solving the continuous space p-centre problem: planning application issues. IMA J Manag Math 17:413-425
    • (2006) IMA J Manag Math , vol.17 , pp. 413-425
    • Wei, H.1    Murray, A.T.2    Xiao, N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.