We contribute to a body of research asserting that the fractional and integ
ral optima of column-sparse integer programs are "nearby". This yields impr
oved approximation algorithms for some generalizations of the knapsack prob
lem, with applications to low-congestion routing in networks, file replicat
ion in distributed databases, and other packing problems. (C) 2000 Elsevier
Science B.V. All rights reserved.