The cost of data transfers, and in particular of I/O operations, is a growing problem in parallel computing. A promising approach to alleviating this bottleneck is to schedule parallel I/O operations explicitly. We develop a class of decentralized algorithms for scheduling parallel I/O operations, where the objective is to reduce the time required to complete a given set of transfers. These algorithms, based on edge-coloring and matching of bipartite graphs, rely upon simple heuristics to obtain shorter schedules. We present simulation results indicating that the best of our algorithms can produce schedules whose length is within 2--20% of the optimal schedule, a substantial improvement on previous decentralized algorithms. We discuss theoretical and experimental work in progress and possible extensions.