This invention relates to methods and devices for synchronization using linear programming, especially over packet networks using, for example, the IEEE 1588 Precision Time Protocol (PTP). Timing protocol messages are exposed to artifacts in the network such as packet delay variations (PDV) or packet losses. Embodiments of the invention provide a two-dimensional linear programming technique for estimating clock offset and skew, particularly from two-way exchange of timing messages between a master and a slave device. Some embodiments include a skew and offset adjustable free-running counter for regenerating the master time and frequency at the slave device.