The rational approach to pharmaceutical drug design begins with an investig
ation of the relationship between chemical structure and biological activit
y. Information gained from this analysis is used to aid the design of new,
or improved, drugs. Primary considerations during this investigation are th
e geometric and chemical characteristics of the molecules. Computational ch
emists who are involved in rational drug design routinely use an array of p
rograms to compute, among other things, molecular surfaces and molecular vo
lume, models of receptor sites, dockings of ligands inside protein cavities
, and geometric invariants among different molecules that exhibit similar a
ctivity. There is a pressing need for efficient and accurate solutions to t
he above problems. Often, limiting assumptions need to be made, in order to
make the calculations tractable. Also, the amount of data processed when s
earching for a potential drug is currently very large and is only expected
to grow larger in the future. This paper describes some areas of computer-a
ided drug design that are important to computational chemists but are also
rich in algorithmic problems. It surveys recent work in these areas both fr
om the computational chemistry and the computer science literature.