Discrete & Computational Geometry

, Volume 2, Issue 4, pp 319-326

First online:

Computing the volume is difficult

  • Imre BárányAffiliated withDepartment of Operations Research and Industrial Engineering, Cornell University
  • , Zoltán FürediAffiliated withRUTCOR, Rutgers University

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For every polynomial time algorithm which gives an upper bound\(\overline {vol}\)(K) and a lower boundvol(K) for the volume of a convex setKR d , the ratio\(\overline {vol}\)(K)/vol(K) is at least (cd/logd) d for some convex setKR d .