Extracting the set of chains from a partial order
Yes there is, have a look at :

Chen, Yangjun, and Yibin Chen. "On the Decomposition of Posets." Computer Science &amp; Service System (CSSS), 2012 International Conference on. IEEE, 2012.

and also this: 

Daskalakis, C., Karp, R. M., Mossel, E., Riesenfeld, S. J., &amp; Verbin, E. (2011). Sorting and selection in posets. SIAM Journal on Computing, 40(3), 597-622.