Abstract
The Kuhn-Munkres (KM) algorithm is a classical combinatorial optimization algorithm that is widely used for minimum cost bipartite matching in many real-world applications, such as transportation. For example, a ride-hailing service may use it to find the optimal assignment of drivers to passengers to minimize the overall wait time. Typically, given two bipartite sets, this process involves computing the edge costs between all bipartite pairs and finding an optimal matching. However, existing works overlook the impact of edge cost computation on the overall running time. In reality, edge computation often significantly outweighs the computation of the optimal assignment itself, as in the case of assigning drivers to passengers which involves computation of expensive graph shortest paths. Following on from this, we also observe common real-world settings exhibit a useful property that allows us to incrementally compute edge costs only as required using an inexpensive lower-bound heuristic. This technique significantly reduces the overall cost of assignment compared to the original KM algorithm, as we demonstrate experimentally on multiple real-world data sets and workloads. Moreover, our algorithm is not limited to this domain and is potentially applicable in other settings where lower-bounding heuristics are available.
- How does Uber match riders with drivers? https: //www.uber.com/us/en/marketplace/matching/.Google Scholar
- T. Abeywickrama, M. A. Cheema, and A. Khan. K-spin: Efficiently processing spatial keyword queries on road networks. IEEE Trans. Knowl. Data Eng., 32(5):983--997, 2019.Google ScholarCross Ref
- T. Abeywickrama, M. A. Cheema, and S. Storandt. Hierarchical graph traversal for aggregate k nearest neighbors search in road networks. In ICAPS, pages 2--10, 2020.Google Scholar
- T. Abeywickrama, V. Liang, and K.-L. Tan. Optimizing bipartite matching in real-world applications by incremental cost computation. PVLDB, 14(7):1150--1158.Google Scholar
- P. K. Agarwal and R. Sharathkumar. Approximation algorithms for bipartite matching with metric and geometric costs. In STOC, pages 555--564, 2014.Google ScholarDigital Library
- J. Edmonds and R. M. Karp. Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM, 19(2):248--264, 1972.Google ScholarDigital Library
- L. R. Ford and D. R. Fulkerson. Maximal flow through a network. Canadian Journal of Mathematics, 8:399--404, 1956.Google ScholarCross Ref
- G. Gao, M. Xiao, and Z. Zhao. Optimal multi-taxi dispatch for mobile taxi-hailing systems. In 2016 45th International Conference on Parallel Processing (ICPP), pages 294--303, 2016.Google ScholarCross Ref
- R. Geisberger, P. Sanders, D. Schultes, and D. Delling. Contraction hierarchies: Faster and simpler hierarchical routing in road networks. In WEA, pages 319--333, 2008.Google ScholarDigital Library
- A. V. Goldberg and C. Harrelson. Computing the shortest path: A* search meets graph theory. In SODA, pages 156--165, 2005.Google ScholarDigital Library
- Y. Guo, Y. Zhang, J. Yu, and X. Shen. A spatiotemporal thermo guidance based real-time online ride-hailing dispatch framework. IEEE Access, 8:115063--115077, 2020.Google ScholarCross Ref
- R. Jonker and T. Volgenant. Improving the hungarian assignment algorithm. Oper. Res. Lett., 5(4):171--175, 1986.Google ScholarDigital Library
- H. W. Kuhn. The hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2(1--2):83--97, 1955.Google Scholar
- H. U. Leong, K. Mouratidis, M. L. Yiu, and N. Mamoulis. Optimal matching between spatial datasets under capacity constraints. ACM TODS, 35(2), 2010.Google Scholar
- J. Munkres. Algorithms for the assignment and transportation problems. Journal of the Society for Industrial and Applied Mathematics, 5(1):32--38, 1957.Google ScholarCross Ref
- L. Ramshaw and R. E. Tarjan. A weight-scaling algorithm for min-cost imperfect matchings in bipartite graphs. In FOCS, pages 581--590, 2012.Google ScholarDigital Library
- T. Roughgarden. Cs261: A second course in algorithms, lecture #5: Minimum-cost bipartite matching, January 2016.Google Scholar
- Y. Tang, L. H. U, Y. Cai, N. Mamoulis, and R. Cheng. Earth mover's distance based similarity search at scale. PVLDB, 7(4):313--324, 2013.Google ScholarDigital Library
- N. Tomizawa. On some techniques useful for solution of transportation network problems. Networks, 1(2):173--194, 1971.Google ScholarCross Ref
- I. H. Toroslu and G. ´¸coluk. Incremental assignment problem. Inf. Sci., 177(6):1523--1529, 2007.Google ScholarDigital Library
- Z. Xu, Z. Li, Q. Guan, D. Zhang, Q. Li, J. Nan, C. Liu, W. Bian, and J. Ye. Large-scale order dispatch in on-demand ride-hailing platforms: A learning and planning approach. In SIGKDD, pages 905--913, 2018.Google ScholarDigital Library
- L. Zhang, T. Hu, Y. Min, G. Wu, J. Zhang, P. Feng, P. Gong, and J. Ye. A taxi order dispatch model based on combinatorial optimization. In SIGKDD, pages 2151--2159, 2017.Google ScholarDigital Library
- L. Zheng, L. Chen, and J. Ye. Order dispatch in price-aware ridesharing. PVLDB, 11(8):853--865, 2018.Google ScholarDigital Library
- R. Zhong, G. Li, K.-L. Tan, L. Zhou, and Z. Gong. G-tree: An efficient and scalable index for spatial search on road networks. IEEE Trans. Knowl. Data Eng., 27(8):2175--2189, 2015.Google ScholarDigital Library
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