Complexity of the Directed Robust b‐Matching Problem and Its Variants on Different Graph Classes

ABSTRACT The b$$ b $$‐matching problem is a well‐known generalization of the classical matching problem with various applications in operations research and computer science. Given an undirected graph, each vertex v$$ v $$ has a capacity bv$$ {b}_v $$, indicating the maximum number of times it can b...

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Bibliographic Details
Published in:Networks Vol. 86; no. 2; pp. 220 - 237
Main Authors: Segschneider, Jenny, Koster, Arie M. C. A.
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.09.2025
Wiley Subscription Services, Inc
Subjects:
Complexity
computational complexity
directed matching
graph and network algorithms
Matching
Polynomials
robust optimization
Robustness
Uncertainty
ISSN:0028-3045, 1097-0037
Online Access:Get full text
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Summary:ABSTRACT The b$$ b $$‐matching problem is a well‐known generalization of the classical matching problem with various applications in operations research and computer science. Given an undirected graph, each vertex v$$ v $$ has a capacity bv$$ {b}_v $$, indicating the maximum number of times it can be matched, while edges can also be used multiple times. The problem is solvable in polynomial time and has many real‐world applications. In some of them, a feasible matching must exactly satisfy the capacities bv$$ {b}_v $$, leading to the so‐called perfect b$$ b $$‐matching problem. Typically, the capacities bv$$ {b}_v $$ are assumed to be fixed and known. However, in practice, these capacities often face uncertainties, such as worker availability or customer demand fluctuations. This article analyses a robust variant of both the b$$ b $$‐matching and perfect b$$ b $$‐matching problems, accounting for such capacity uncertainties, termed the Directed Robust b$$ b $$‐Matching Problem (DRUbM$$ b\mathrm{M} $$). We study the computational complexity of this problem across different classes of graphs, providing insights into its tractability for potential applications.
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ISSN:0028-3045
1097-0037
DOI:10.1002/net.22286