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arXiv · 1706.01230

On the heapability of finite partial orders

János Balogh·Cosmin Bonchiş·Diana Diniş·Gabriel Istrate·Ioan Todinca
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Abstract

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.

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János Balogh, Cosmin Bonchiş, Diana Diniş, Gabriel Istrate, Ioan Todinca. 2017-06-05. On the heapability of finite partial orders. https://doi.org/10.23638/dmtcs-22-1-17

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