Efficient Timestamps for Capturing Causality

Consider an asynchronous system consisting of processes that communicate via message-passing.The processes communicate over a potentially incomplete communication network consisting of reli-able bidirectional communication channels. Thus, not every pair of processes is necessarily able tocommunicate with each other directly.The goal of the algorithms discussed in this paper is to assign timestamps to the events at all theprocesses such that (a) distinct events are assigned distinct timestamps, and (b) the happened-beforerelationship between the events can be inferred from the timestamps. We consider three types ofalgorithms for assigning timestamps to events: (i) Online algorithms that must (greedily) assign atimestamp to each event when the event occurs. (ii) Offline algorithms that assign timestamps toevent after a finite execution is complete. (iii) Inline algorithms that assign a timestamp to eachevent when it occurs, but may modify some elements of a timestamp again at a later time.For specific classes of graphs, particularly star graphs and graphs with connectivity ≥ 1, the paperpresents bounds on the length of vector timestamps assigned by an online algorithm. The paperthen presents an inline algorithm, which typically assigns substantially smaller timestamps than theoptimal-length online vector timestamps. In particular, the inline algorithm assigns timestamp inthe form of a tuple containing 2c+ 2 integer elements, where c is the size of the vertex cover for theunderlying communication graph. A version of this report, excluding Section 5.1, was submitted for review to a conference on May 11, 2016. 1arXiv:1606.05962v1[cs.DC]20Jun2016