Tree Recovery by Dynamic Programming

Tree-like structures are common, naturally occurring objects that are of interest to many fields of study, such as plant science and biomedicine. Analysis of these structures is typically based on skeletons extracted from captured data, which often contain spurious cycles that need to be removed. We...

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Veröffentlicht in:IEEE transactions on pattern analysis and machine intelligence Jg. 45; H. 12; S. 1 - 15
Hauptverfasser: Gratacos, Gustavo, Chakrabarti, Ayan, Ju, Tao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.12.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
beam search
carving decomposition
Costs
Dynamic programming
Heuristic algorithms
Merging
Optimization
Partitioning algorithms
Polytrees
Recovery
Search algorithms
Shape
Skeleton
Tree recovery
Trees (mathematics)
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
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Zusammenfassung:Tree-like structures are common, naturally occurring objects that are of interest to many fields of study, such as plant science and biomedicine. Analysis of these structures is typically based on skeletons extracted from captured data, which often contain spurious cycles that need to be removed. We propose a dynamic programming algorithm for solving the NP-hard tree recovery problem formulated by Estrada et al. [1], which seeks a least-cost partitioning of the graph nodes that yields a directed tree. Our algorithm finds the optimal solution by iteratively contracting the graph via node-merging until the problem can be trivially solved. By carefully designing the merging sequence, our algorithm can efficiently recover optimal trees for many real-world data where [1] only produces sub-optimal solutions. We also propose an approximate variant of dynamic programming using beam search, which can process graphs containing thousands of cycles with significantly improved optimality and efficiency compared with [1].
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2023.3299868