Enumeration of irredundant forests

Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees. If the literature proposes solutions to enumerate singletons...

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Veröffentlicht in:Theoretical computer science Jg. 922; S. 312 - 334
Hauptverfasser: Ingels, Florian, Azaïs, Romain
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 24.06.2022
Elsevier
Schlagworte:
Combinatorics
Computer Science
Data Structures and Algorithms
Directed acyclic graph
Discrete Mathematics
Enumeration
Forest
Mathematics
Reverse search
Unordered trees
Directed acyclic graph
Forest
Enumeration
Reverse search
Unordered trees
Unordered Trees
Directed Acyclic Graph
Reverse Search
ISSN:0304-3975, 1879-2294
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Zusammenfassung:Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees. If the literature proposes solutions to enumerate singletons of trees, we study in this article a more general problem, the enumeration of sets of trees – forests. Specifically, we mainly study irredundant forests, i.e., where no tree is a subtree of another. By compressing each such forest into a Directed Acyclic Graph (DAG), we develop a reverse search like method to enumerate DAGs compressing irredundant forests. Remarkably, we prove that these DAGs are in bijection with the row-Fishburn matrices, a well-studied class of combinatorial objects. In a second step, we derive our irredundant forest enumeration to provide algorithms for tackling related problems: (i) enumeration of forests in their classical sense (where redundancy is allowed); (ii) the enumeration of “subforests” of a forest, and (iii) the frequent “subforest” mining problem. All the methods presented in this article enumerate each item uniquely, up to isomorphism.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.04.033