Effectiveness of delaying timestamp computation

Practical algorithms for determining causality by assigning times-tamps to events have focused on online algorithms, where a permanent timestamp is assigned to an event as soon as it is created. We address the problem of reducing size of the timestamp by utilizing the underlying topology (which is often not fully connected since not all processes talk to each other) and deferring the assignment of a timestamp to an event for a suitably chosen period of time after the event occurs. Specifically, we focus on inline timestamps, which are a generalization of offine timestamps that are assigned after the computation terminates. We show that for a graph with vertex cover VC, it is possible to assign inline timestamps which contains only 2/VC/+2 elements. In particular, for a system with n processes and K events per process, the size of a timestamp for any event is at most log₂ n+(2/VC/+1) log₂(K+1) bits. By contrast, if online timestamps are desired, then even for a star network, vector timestamp of length n (for the case of integer elements) or n - 1 (for the case of real-valued elements) is required. Moreover, in addition to being efficient, the inline timestamps developed can be used to solve typical problems such as predicate detection, replay, recovery that are solved with vector clocks.