On the heapability of finite partial orders

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 th...

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Vydáno v:Discrete mathematics and theoretical computer science Ročník 22 no. 1; číslo Combinatorics; s. 1 - 23
Hlavní autoři: Balogh, János, Bonchiş, Cosmin, Diniş, Diana, Istrate, Gabriel, Todinca, Ioan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Nancy DMTCS 01.01.2020
Discrete Mathematics & Theoretical Computer Science
Témata:
05a18, 68c05, 60k35
Algorithms
Combinatorics
Computation
Computer Science
computer science - data structures and algorithms
computer science - discrete mathematics
Data Structures and Algorithms
Decomposition
Greedy algorithms
Integers
Intervals
mathematics - combinatorics
Nodes
Permutations
Polynomials
Sequences
Set theory
ISSN:1365-8050, 1462-7264, 1365-8050
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.23638/DMTCS-22-1-17