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An Efficient Algorithm for the Partitioning Min-Max Weighted Matching Problem
- Publication Year :
- 2022
- Publisher :
- arXiv, 2022.
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Abstract
- The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted Matching (MMWM) problem. Kress et al. proposed this problem in 2015 and they also provided several algorithms, among which MP$_{\text{LS}}$ is the state-of-the-art. In this work, we observe there is a time bottleneck in the matching phase of MP$_{\text{LS}}$. Hence, we optimize the redundant operations during the matching iterations, and propose an efficient algorithm called the MP$_{\text{KM-M}}$ that greatly speeds up MP$_{\text{LS}}$. The bottleneck time complexity is optimized from $O(n^3)$ to $O(n^2)$. We also prove the correctness of MP$_{\text{KM-M}}$ by the primal-dual method. To test the performance on diverse instances, we generate various types and sizes of benchmarks, and carried out an extensive computational study on the performance of MP$_{\text{KM-M}}$ and MP$_{\text{LS}}$. The evaluation results show that our MP$_{\text{KM-M}}$ greatly shortens the runtime as compared with MP$_{\text{LS}}$ while yielding the same solution quality.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....cf10b8e4cc1a4c4feec438cad7a660de
- Full Text :
- https://doi.org/10.48550/arxiv.2201.10049