Minimum flow decomposition in graphs with cycles using integer linear programming Article Swipe
Fernando H.C. Dias
,
Lucia Williams
,
Brendan Mumey
,
Alexandru I. Tomescu
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1007/s10898-025-01556-8
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1007/s10898-025-01556-8
Minimum flow decomposition (MFD) — the problem of finding a minimum set of weighted source-to-sink paths that perfectly decomposes a flow — is a classical problem in Computer Science, and variants of it are powerful models in a different fields such as Bioinformatics and Transportation. Even on acyclic graphs, the problem is NP-hard, and most practical solutions have been via heuristics or approximations. While there is an extensive body of research on acyclic graphs, currently there is no exact solution on graphs with cycles. In this paper we present the first ILP formulation for three natural variants of the MFD problem in graphs with cycles, asking for a decomposition consisting only of weighted source-to-sink paths or cycles, trails, and walks, respectively. On three datasets of increasing levels of complexity from both Bioinformatics and Transportation, our approaches solve any instance in under 12 minutes. Our implementations are freely available at https://github.com/algbio/MFD-ILP .
Related Topics
Concepts
Mathematics
Heuristics
Integer programming
Decomposition
Directed acyclic graph
Set (abstract data type)
Flow (mathematics)
Mathematical optimization
Minimum cut
Linear programming
Decomposition method (queueing theory)
Integer (computer science)
Discrete mathematics
Combinatorics
Implementation
Algorithm
Computational complexity theory
Multi-commodity flow problem
Modular decomposition
Heuristic
Time complexity
Flow network
Tree decomposition
Approximation algorithm
Parameterized complexity
Minimum-cost flow problem
Directed graph
Data flow diagram
Maximum flow problem
Optimization problem
Benders' decomposition
Theoretical computer science
Dynamic programming
Efficient algorithm
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s10898-025-01556-8
- https://link.springer.com/content/pdf/10.1007/s10898-025-01556-8.pdf
- OA Status
- hybrid
- References
- 29
- OpenAlex ID
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All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7106503860Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1007/s10898-025-01556-8Digital Object Identifier
- Title
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Minimum flow decomposition in graphs with cycles using integer linear programmingWork 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
-
2025-11-24Full publication date if available
- Authors
-
Fernando H.C. Dias, Lucia Williams, Brendan Mumey, Alexandru I. TomescuList of authors in order
- Landing page
-
https://doi.org/10.1007/s10898-025-01556-8Publisher landing page
- PDF URL
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https://link.springer.com/content/pdf/10.1007/s10898-025-01556-8.pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://link.springer.com/content/pdf/10.1007/s10898-025-01556-8.pdfDirect OA link when available
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Mathematics, Heuristics, Integer programming, Decomposition, Directed acyclic graph, Set (abstract data type), Flow (mathematics), Mathematical optimization, Minimum cut, Linear programming, Decomposition method (queueing theory), Integer (computer science), Discrete mathematics, Combinatorics, Implementation, Algorithm, Computational complexity theory, Multi-commodity flow problem, Modular decomposition, Heuristic, Time complexity, Flow network, Tree decomposition, Approximation algorithm, Parameterized complexity, Minimum-cost flow problem, Directed graph, Data flow diagram, Maximum flow problem, Optimization problem, Benders' decomposition, Theoretical computer science, Dynamic programming, Efficient algorithmTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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29Number of works referenced by this work
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| referenced_works | https://openalex.org/W4239519089, https://openalex.org/W2164946254, https://openalex.org/W2291157727, https://openalex.org/W2068289888, https://openalex.org/W2009254979, https://openalex.org/W2102090846, https://openalex.org/W2027064478, https://openalex.org/W3082378466, https://openalex.org/W2967499761, https://openalex.org/W1606362855, https://openalex.org/W4226237737, https://openalex.org/W2995527562, https://openalex.org/W2963833316, https://openalex.org/W3197833388, https://openalex.org/W3129752877, https://openalex.org/W2126419817, https://openalex.org/W2156841387, https://openalex.org/W1981313577, https://openalex.org/W2773298966, https://openalex.org/W3017765916, https://openalex.org/W162544871, https://openalex.org/W3164606144, https://openalex.org/W1968882081, https://openalex.org/W2233296499, https://openalex.org/W2049287714, https://openalex.org/W3004548325, https://openalex.org/W1975489634, https://openalex.org/W2118382442, https://openalex.org/W2768985026 |
| referenced_works_count | 29 |
| abstract_inverted_index.. | 151 |
| abstract_inverted_index.a | 10, 20, 24, 38, 108 |
| abstract_inverted_index.12 | 142 |
| abstract_inverted_index.In | 85 |
| abstract_inverted_index.On | 122 |
| abstract_inverted_index.an | 67 |
| abstract_inverted_index.as | 42 |
| abstract_inverted_index.at | 149 |
| abstract_inverted_index.in | 27, 37, 102, 140 |
| abstract_inverted_index.is | 23, 52, 66, 77 |
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| abstract_inverted_index.no | 78 |
| abstract_inverted_index.of | 8, 13, 32, 70, 98, 112, 125, 128 |
| abstract_inverted_index.on | 47, 72, 81 |
| abstract_inverted_index.or | 62, 116 |
| abstract_inverted_index.we | 88 |
| abstract_inverted_index.ILP | 92 |
| abstract_inverted_index.MFD | 100 |
| abstract_inverted_index.Our | 144 |
| abstract_inverted_index.and | 30, 44, 54, 119, 133 |
| abstract_inverted_index.any | 138 |
| abstract_inverted_index.are | 34, 146 |
| abstract_inverted_index.for | 94, 107 |
| abstract_inverted_index.our | 135 |
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| abstract_inverted_index.via | 60 |
| abstract_inverted_index.— | 5, 22 |
| abstract_inverted_index.Even | 46 |
| abstract_inverted_index.been | 59 |
| abstract_inverted_index.body | 69 |
| abstract_inverted_index.both | 131 |
| abstract_inverted_index.flow | 2, 21 |
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| abstract_inverted_index.most | 55 |
| abstract_inverted_index.only | 111 |
| abstract_inverted_index.such | 41 |
| abstract_inverted_index.that | 17 |
| abstract_inverted_index.this | 86 |
| abstract_inverted_index.with | 83, 104 |
| abstract_inverted_index.(MFD) | 4 |
| abstract_inverted_index.While | 64 |
| abstract_inverted_index.exact | 79 |
| abstract_inverted_index.first | 91 |
| abstract_inverted_index.paper | 87 |
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| abstract_inverted_index.asking | 106 |
| abstract_inverted_index.fields | 40 |
| abstract_inverted_index.freely | 147 |
| abstract_inverted_index.graphs | 82, 103 |
| abstract_inverted_index.levels | 127 |
| abstract_inverted_index.models | 36 |
| abstract_inverted_index.walks, | 120 |
| abstract_inverted_index.Minimum | 1 |
| abstract_inverted_index.acyclic | 48, 73 |
| abstract_inverted_index.cycles, | 105, 117 |
| abstract_inverted_index.cycles. | 84 |
| abstract_inverted_index.finding | 9 |
| abstract_inverted_index.graphs, | 49, 74 |
| abstract_inverted_index.minimum | 11 |
| abstract_inverted_index.natural | 96 |
| abstract_inverted_index.present | 89 |
| abstract_inverted_index.problem | 7, 26, 51, 101 |
| abstract_inverted_index.trails, | 118 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.Computer | 28 |
| abstract_inverted_index.NP-hard, | 53 |
| abstract_inverted_index.Science, | 29 |
| abstract_inverted_index.datasets | 124 |
| abstract_inverted_index.instance | 139 |
| abstract_inverted_index.minutes. | 143 |
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| abstract_inverted_index.research | 71 |
| abstract_inverted_index.solution | 80 |
| abstract_inverted_index.variants | 31, 97 |
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| abstract_inverted_index.solutions | 57 |
| abstract_inverted_index.approaches | 136 |
| abstract_inverted_index.complexity | 129 |
| abstract_inverted_index.consisting | 110 |
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| abstract_inverted_index.heuristics | 61 |
| abstract_inverted_index.increasing | 126 |
| abstract_inverted_index.formulation | 93 |
| abstract_inverted_index.decomposition | 3, 109 |
| abstract_inverted_index.respectively. | 121 |
| abstract_inverted_index.Bioinformatics | 43, 132 |
| abstract_inverted_index.source-to-sink | 15, 114 |
| abstract_inverted_index.Transportation, | 134 |
| abstract_inverted_index.Transportation. | 45 |
| abstract_inverted_index.approximations. | 63 |
| abstract_inverted_index.implementations | 145 |
| abstract_inverted_index.https://github.com/algbio/MFD-ILP | 150 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |