Abstract: We propose new schemes for integrating the stochastic differential equations of dissipative particle dynamics (DPD) in simulations of dilute polymer solutions. The hybrid DPD models consist of hard potentials that describe the microscopic dynamics of polymers and soft potentials that describe the mesoscopic dynamics of the solvent. In particular, we develop extensions to the velocity-Verlet and Lowe's approaches - two representative DPD time-integrators -- following a subcycling procedure whereby the solvent is advanced with a timestep much larger than the one employed in the polymer time-integration. The introduction of relaxation parameters allows optimization studies for accuracy while maintaining the low computational complexity of standard DPD algorithms. We demonstrate through equilibrium simulations that a ten-fold gain in efficiency can be obtained with the time-staggered algorithms without loss of accuracy compared to the non-staggered schemes. We then apply the new approach to investigate the scaling response of polymers in equilibrium as well as the dynamics of lambda-phage DNA molecules subjected to shear.