2 research outputs found
On the heapability of finite partial orders
Full text linkWe 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
On the heapability of finite partial orders
No full textWe 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
