  Incoherent dedispersion is a computationally intensive problem that appears
frequently in pulsar and transient astronomy. For current and future transient
pipelines, dedispersion can dominate the total execution time, meaning its
computational speed acts as a constraint on the quality and quantity of science
results. It is thus critical that the algorithm be able to take advantage of
trends in commodity computing hardware. With this goal in mind, we present
analysis of the 'direct', 'tree' and 'sub-band' dedispersion algorithms with
respect to their potential for efficient execution on modern graphics
processing units (GPUs). We find all three to be excellent candidates, and
proceed to describe implementations in C for CUDA using insight gained from the
analysis. Using recent CPU and GPU hardware, the transition to the GPU provides
a speed-up of 9x for the direct algorithm when compared to an optimised
quad-core CPU code. For realistic recent survey parameters, these speeds are
high enough that further optimisation is unnecessary to achieve real-time
processing. Where further speed-ups are desirable, we find that the tree and
sub-band algorithms are able to provide 3-7x better performance at the cost of
certain smearing, memory consumption and development time trade-offs. We finish
with a discussion of the implications of these results for future transient
surveys. Our GPU dedispersion code is publicly available as a C library at:
http://dedisp.googlecode.com/
