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Volumn 27, Issue 2, 2004, Pages 151-178

Inner and outer approximations of polytopes using boxes

Author keywords

Approximation; Boxes; Containment; Polytopes; Reachability analysis

Indexed keywords


EID: 84867965619     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(03)00048-8     Document Type: Article
Times cited : (61)

References (17)
  • 3
    • 4243170669 scopus 로고    scopus 로고
    • Exact volume computation for convex polytopes: A practical study
    • G. Kalai, G. Ziegler, DMV-Seminar Birkhauser Verlag
    • B. Büeler, A. Enge, and K. Fukuda Exact volume computation for convex polytopes: A practical study G. Kalai, G. Ziegler, Polytopes, Combinatorics and Computation DMV-Seminar vol. 29 2000 Birkhauser Verlag
    • (2000) Polytopes, Combinatorics and Computation , vol.29
    • Büeler, B.1    Enge, A.2    Fukuda, K.3
  • 4
    • 0018491818 scopus 로고
    • Two algorithms for determining volumes of convex polyhedra
    • J. Cohen, and T. Hickey Two algorithms for determining volumes of convex polyhedra J. ACM 26 3 1979 401 414
    • (1979) J. ACM , vol.26 , Issue.3 , pp. 401-414
    • Cohen, J.1    Hickey, T.2
  • 5
    • 0020145730 scopus 로고
    • Optimal scaling of balls and polyhedra
    • B.C. Eaves, and R.M. Freund Optimal scaling of balls and polyhedra Math. Programming 23 1982 138 147
    • (1982) Math. Programming , vol.23 , pp. 138-147
    • Eaves, B.C.1    Freund, R.M.2
  • 6
    • 0022161165 scopus 로고
    • On the complexity of four polyhedral set containment problems
    • R.M. Freund, and J.B. Orlin On the complexity of four polyhedral set containment problems Math. Programming 33 1985 139 145
    • (1985) Math. Programming , vol.33 , pp. 139-145
    • Freund, R.M.1    Orlin, J.B.2
  • 7
    • 84867983907 scopus 로고    scopus 로고
    • Polyhedral computation FAQ, Both html and ps versions available from
    • K. Fukuda Polyhedral computation FAQ, Both html and ps versions available from http://www.ifor.math.ethz.ch/~fukuda/fukuda.html
    • Fukuda, K.1
  • 8
    • 84867983906 scopus 로고    scopus 로고
    • cdd/cdd+ Reference Manual, Institute for Operations Research ETH-Zentrum 0.61 (cdd) 0.76 (cdd+) edition, December 1997
    • K. Fukuda cdd/cdd+ Reference Manual, Institute for Operations Research ETH-Zentrum http://www.ifor.math.ethz.ch/~fukuda/cdd-home/cdd.html 0.61 (cdd) 0.76 (cdd+) edition, December 1997
    • Fukuda, K.1
  • 10
    • 34250075248 scopus 로고
    • Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces
    • P. Gritzmann, and V. Klee Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces Math. Programming 59 1993 163 213
    • (1993) Math. Programming , vol.59 , pp. 163-213
    • Gritzmann, P.1    Klee, V.2
  • 11
    • 0001535602 scopus 로고
    • On the complexity of some basic problems in computational convexity: I. Containment problems
    • P. Gritzmann, and V. Klee On the complexity of some basic problems in computational convexity: I. Containment problems Discrete Math. 136 1994 129 174
    • (1994) Discrete Math. , vol.136 , pp. 129-174
    • Gritzmann, P.1    Klee, V.2
  • 12
    • 84868000483 scopus 로고    scopus 로고
    • NAG Numerical Algorithms Group Ltd., The MathWorks Inc. NAG Foundation Toolbox - For Use with MATLAB, 1995
    • NAG Numerical Algorithms Group Ltd., The MathWorks Inc. http://www.nag.com NAG Foundation Toolbox - For Use with MATLAB, 1995
  • 16
    • 0031517064 scopus 로고    scopus 로고
    • Approximating convex polyhedra with axis-parallel boxes
    • B. Zhu Approximating convex polyhedra with axis-parallel boxes Internat. J. Comput. Geom. Appl. 7 3 1997 253 267
    • (1997) Internat. J. Comput. Geom. Appl. , vol.7 , Issue.3 , pp. 253-267
    • Zhu, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.