多商品流的目标选址问题
Target Location Problem for Multi-commodity Flow
摘要：
受地理分布数据分析中调度问题的启发，提出了一种多商品流的目标定位问题（LoMuF）。给定从其资源发送的商品，LoMuF旨在定位其目标，以便在某种意义上优化多商品流。LoMuF是两个基本问题的组合，即设施定位问题和网络流问题。我们研究的硬度和算法的问题，在各种设置。研究结果包括三个方面。首先，一系列NP-硬度和APX-硬度的结果，揭示了解决这个问题的内在困难。其次，我们提出了一般无向网络的近似算法和无向树的精确算法，从而自然地导出了有向网络的有效近似算法。第三，我们观察到有向网络和无向网络之间的分离，这表明在边缘上施加方向会使问题更加困难。这些结果显示了问题的丰富性，并为进一步的研究铺平了道路。
英文摘要：
Motivated by scheduling in Geo-distributed data analysis, we propose a target location problem for multi-commodity flow (LoMuF for short). Given commodities to be sent from their resources, LoMuF aims at locating their targets so that the multi-commodity flow is optimized in some sense. LoMuF is a combination of two fundamental problems, namely, the facility location problem and the network flow problem. We study the hardness and algorithmic issues of the problem in various settings. The findings lie in three aspects. First, a series of NP-hardness and APX-hardness results are obtained, uncovering the inherent difficulty in solving this problem. Second, we propose an approximation algorithm for general undirected networks and an exact algorithm for undirected trees, which naturally induce efficient approximation algorithms on directed networks. Third, we observe separations between directed networks and undirected ones, indicating that imposing direction on edges makes the problem strictly harder. These results show the richness of the problem and pave the way to further studies.
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