For every polynomial time algorithm which gives an upper bound
[`(vol)]\overline {vol}
(
K) and a lower bound
vol(
K) for the volume of a convex set
K[`(vol)]\overline {vol}
(
K)/
vol(
K) is at least (
cd/log
d)
d
for some convex set
K
R
d
.
This paper was partly written when both authors were on leave from the Mathematical Institute of the Hungarian Academy of Sciences, 1364 Budapest, P.O. Box 127, Hungary.