Geodesic
On the heapability of finite partial orders
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1.

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We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing such a minimal decomposition. On the other hand, in the particular case of sets and sequences of intervals we prove that this minimal decomposition can be computed by a simple greedy-type algorithm. The paper ends with a couple of open problems related to the analog of the Ulam-Hammersley problem for decompositions of sets and sequences of random intervals into heapable sets.
DOI : 10.23638/DMTCS-22-1-17
Classification : 06A07, 68Q25 
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Balogh, János; Bonchiş, Cosmin; Diniş, Diana; Istrate, Gabriel; Todinca, Ioan. On the heapability of finite partial orders. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1. doi : 10.23638/DMTCS-22-1-17. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-17/

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