Partially ordered sets appear as a basic tool in computer science and are particularly accurate for modeling dynamic behavior of complex systems. Motivated by considerations on the diagnosis of distributed computations a new kind of algorithm on posets has been developed and is now widely considered. In this paper we present this "on-line" algorithmics on posets and we survey the main results obtained under this approach.
Bouchitté, V., & Rampon, J. X. (1997). On-line algorithms for orders. Theoretical Computer Science, 175(2), 225–238. https://doi.org/10.1016/S0304-3975(97)00200-4