通过分配智能体以提升基于网络的邻域多样性
Assigning Agents to Increase Network-Based Neighborhood Diversity
AI总结：
本文研究将两类智能体分配到网络顶点以最大化邻域多样性的NP难问题，提出一般图的1/2近似局部改进算法、基于半定规划的改进随机化方法、树宽有界图的高效算法及平面图PTAS，并通过实验验证算法性能。
摘要：
受公共住房分配等实际应用启发，我们研究了将一组智能体分配到网络顶点（例如空间位置）以最大化多样性水平的问题。具体而言，智能体分为两种类型（由特征刻画），我们以至少拥有一个不同类型邻居的智能体数量来衡量多样性。该问题已知是NP难的，我们专注于开发具有可证明性能保证的近似算法。我们首先针对一般图提出一种局部改进算法，其近似比为1/2。对于智能体子群规模相近的特殊情形，我们提出一种基于半定规划的随机化方法，可获得优于1/2的近似比。进一步，我们证明当底层图具有有界树宽时该问题可高效求解，并为平面图上的该问题获得一个多项式时间近似方案（PTAS）。最后，我们进行实验以评估所提算法在合成网络和真实世界网络上的性能。
英文摘要：
Motivated by real-world applications such as the allocation of public housing, we examine the problem of assigning a group of agents to vertices (e.g., spatial locations) of a network so that the diversity level is maximized. Specifically, agents are of two types (characterized by features), and we measure diversity by the number of agents who have at least one neighbor of a different type. This problem is known to be NP-hard, and we focus on developing approximation algorithms with provable performance guarantees. We first present a local-improvement algorithm for general graphs that provides an approximation factor of 1/2. For the special case where the sizes of agent subgroups are similar, we present a randomized approach based on semidefinite programming that yields an approximation factor better than 1/2. Further, we show that the problem can be solved efficiently when the underlying graph is treewidth-bounded and obtain a polynomial time approximation scheme (PTAS) for the problem on planar graphs. Lastly, we conduct experiments to evaluate the per-performance of the proposed algorithms on synthetic and real-world networks.
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