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.

Kuhn-Munkres (KM) 算法是一种经典的组合优化算法，广泛用于许多实际应用中的最小成本二分匹配，例如交通运输。例如，叫车服务可以使用它来找到司机与乘客的最佳分配，以最大限度地减少整体等待时间。通常，给定两个二分集，此过程涉及计算所有二分对之间的边缘成本并找到最佳匹配。然而，现有的工作忽略了边缘成本计算对整体运行时间的影响。在现实中，边计算通常大大超过优化分配本身的计算，例如将司机分配给乘客，这涉及计算昂贵的图最短路径。继此之后，我们还观察到常见的现实世界设置展示了一个有用的属性，它允许我们使用廉价的下界启发式方法仅根据需要增量计算边缘成本。与原始 KM 算法相比，这种技术显着降低了分配的总体成本，正如我们在多个真实世界数据集和工作负载上进行的实验演示一样。此外，我们的算法不限于此领域，并且可能适用于其他下限启发式可用的设置。