An efficient algorithm for the limited-capacity many-to-many point matching in one dimension

Matching elements from two sets (bipartite matching), a fundamental subject in computer science, is used in applications such as bipartite data matching (e.g. graph edit distance computation and semantic data matching) and allocating resources in a wireless network. Given two sets S and T , a limite...

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Veröffentlicht in:The Journal of supercomputing Jg. 81; H. 8; S. 920
Hauptverfasser: Rajabi-Alni, Fatemeh, Minaei-Bidgoli, Behrouz, Bagheri, Alireza
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 29.05.2025
Springer Nature B.V
Schlagworte:
Algorithms
Compilers
Computer Science
Dynamic programming
Energy consumption
Euclidean geometry
Interpreters
Matching
Processor Architectures
Programming Languages
Resource allocation
Sensors
Wireless networks
Dynamic programming
One-dimensional points
Limited capacity
Many-to-many matching
ISSN:1573-0484, 0920-8542, 1573-0484
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Zusammenfassung:Matching elements from two sets (bipartite matching), a fundamental subject in computer science, is used in applications such as bipartite data matching (e.g. graph edit distance computation and semantic data matching) and allocating resources in a wireless network. Given two sets S and T , a limited-capacity many-to-many matching (LCMM) between S and T matches each element p in S (resp. T ) to at least 1 and at most Cap ( p ) elements in T (resp. S ), where the function C a p : S ∪ T → Z > 0 denotes the capacity of p . In this paper, we present the first linear time algorithm for finding a minimum-cost one-dimensional LCMM (OLCMM) between S and T when S and T are points lying on a line; the cost of matching each point p ∈ S to q ∈ T equals the Euclidean distance between p ,  q . Our dynamic programming algorithm improves the previous best-known quadratic time algorithm, and moreover, can be used with online arriving input points (which are not known in advance and arrive sequentially one by one).
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ISSN:1573-0484
0920-8542
1573-0484
DOI:10.1007/s11227-025-07408-2