We introduce a new color decomposition for multi-parton amplitudes in QCD,
free of fundamental-representation matrices and structure constants. This
decomposition has a physical interpretation in terms of the flow of color,
which makes it ideal for merging with shower Monte-Carlo programs. The
color-flow decomposition allows for very efficient evaluation of amplitudes
with many quarks and gluons, many times faster than the standard color
decomposition based on fundamental-representation matrices. This will increase
the speed of event generators for multi-jet processes, which are the principal
backgrounds to signals of new physics at colliders.Comment: 23 pages, 11 figures, version to appear on Phys. Rev.