We perform Monte Carlo simulations of ring and linear polymers in linear matrices, and investigate the diffusivity of the probes. As the matrix chain length N-m is increased from 10 to 300 monomers, the diffusivity D-l of a linear probe (N-l=300) decreases monotonically, while that of a ring probe D-r varies non-monotonically, with a peak around N-m approximate to 30-75. We perform additional simulations with a single probe molecule (N-r=N-l=150) in a linear matrix (N-m=10-150). The nonmonotonicity in D-r persists even after ring-ring interactions are eliminated. Topology dependent differences in the short-time dynamics of the probes are observed; unlike linear probes, mean-squared displacements of ring probes depend on N-m. Primitive path analysis suggests that the difference in dynamics originates from differences in entanglement structure. For linear probes, the degree of entanglement is independent of N-m. For ring probes, we observe two regimes: when N-m is small, the number of threadings decreases as N-m increases, eventually transitioning to a plateau. In the small N-m regime, the change in the degree of entanglement offsets the change in the mobility of the matrix chains, leading to a nonmonotonic variation in D-r. (C) 2016 Wiley Periodicals, Inc.