A General Framework for Finding Diverse Solutions via Network Flow and Its Applications Article Swipe
Iwamasa, Yuni
,
Matsuda Tomoki
,
Morihira, Shunya
,
Sumita Hanna
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.4230/lipics.isaac.2025.41
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.4230/lipics.isaac.2025.41
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find k solutions that maximize a specified diversity measure - the sum of pairwise Hamming distances or the size of the union of the k solutions. Our framework applies to problems satisfying two structural properties: (i) All solutions are of equal size and (ii) the family of all solutions can be represented by a surjection from the family of ideals of some finite poset. Under these conditions, we show that the problem of computing k diverse solutions can be reduced to the minimum cost flow problem and the maximum s-t flow problem. As applications, we demonstrate that both the unweighted minimum s-t cut problem and the stable matching problem satisfy the requirements of our framework. By utilizing the recent advances in network flows algorithms, we improve the previously known time complexities of the diverse problems, which were based on submodular function minimization.
Related Topics
Concepts
Submodular set function
Mathematical optimization
Mathematics
Flow network
Pairwise comparison
Matching (statistics)
Measure (data warehouse)
Function (biology)
Maximum flow problem
Flow (mathematics)
Hamming distance
Optimization problem
Minimum cut
Computer science
Matroid
Combinatorial optimization
Cover (algebra)
Surjective function
Minimum-cost flow problem
Theoretical computer science
Node (physics)
Hamming code
Algorithm
Discrete mathematics
Genetic algorithm
Comparability
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.41
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7110044404
All OpenAlex metadata
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https://openalex.org/W7110044404Canonical identifier for this work in OpenAlex
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https://doi.org/10.4230/lipics.isaac.2025.41Digital Object Identifier
- Title
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A General Framework for Finding Diverse Solutions via Network Flow and Its ApplicationsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-01-01Full publication date if available
- Authors
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Iwamasa, Yuni, Matsuda Tomoki, Morihira, Shunya, Sumita HannaList of authors in order
- Landing page
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https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.41Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.41Direct OA link when available
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Submodular set function, Mathematical optimization, Mathematics, Flow network, Pairwise comparison, Matching (statistics), Measure (data warehouse), Function (biology), Maximum flow problem, Flow (mathematics), Hamming distance, Optimization problem, Minimum cut, Computer science, Matroid, Combinatorial optimization, Cover (algebra), Surjective function, Minimum-cost flow problem, Theoretical computer science, Node (physics), Hamming code, Algorithm, Discrete mathematics, Genetic algorithm, ComparabilityTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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| abstract_inverted_index.computing | 10, 98 |
| abstract_inverted_index.distances | 40 |
| abstract_inverted_index.diversity | 32 |
| abstract_inverted_index.framework | 7, 52 |
| abstract_inverted_index.instance, | 20 |
| abstract_inverted_index.problems, | 159 |
| abstract_inverted_index.problems. | 16 |
| abstract_inverted_index.solutions | 12, 27, 62, 73, 101 |
| abstract_inverted_index.specified | 31 |
| abstract_inverted_index.utilizing | 141 |
| abstract_inverted_index.framework. | 139 |
| abstract_inverted_index.previously | 152 |
| abstract_inverted_index.satisfying | 56 |
| abstract_inverted_index.solutions. | 50 |
| abstract_inverted_index.structural | 58 |
| abstract_inverted_index.submodular | 164 |
| abstract_inverted_index.surjection | 79 |
| abstract_inverted_index.unweighted | 124 |
| abstract_inverted_index.algorithms, | 148 |
| abstract_inverted_index.conditions, | 91 |
| abstract_inverted_index.demonstrate | 120 |
| abstract_inverted_index.efficiently | 9 |
| abstract_inverted_index.properties: | 59 |
| abstract_inverted_index.represented | 76 |
| abstract_inverted_index.complexities | 155 |
| abstract_inverted_index.optimization | 15 |
| abstract_inverted_index.requirements | 136 |
| abstract_inverted_index.applications, | 118 |
| abstract_inverted_index.combinatorial | 14 |
| abstract_inverted_index.minimization. | 166 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile.value | 0.83109452 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |