利用可重用性：可重用资源贪心算法改进的竞争比
Leveraging Reusability: Improved Competitive Ratio of Greedy for Reusable Resources
AI总结：
研究可重用资源的在线加权二分匹配问题，通过引入量化资源可重用程度的参数p，证明贪心策略的竞争比提升至1/(2-p)，几何分布下达到紧的(1+p)/2，揭示了资源可重用性对在线算法性能的提升作用。
摘要：
我们研究可重用资源的在线加权二分匹配问题，其中资源的对抗性请求序列随时间到达。被匹配的资源会被“使用”一段随机时长，该时长独立地从依赖于资源的分布中抽取，之后资源返回并能够再次被匹配。我们研究了贪心策略的性能，该策略将请求匹配到产生最高奖励的资源。此前已知贪心策略相对于提前知道请求序列的预知基准具有1/2的竞争比。在本工作中，我们通过引入一个量化资源可重用程度的参数改进了这一结果。具体而言，如果p表示在使用分布中，被匹配资源在一个时间步内返回的最小概率，那么贪心策略的竞争比可达到$1/(2-p)$。此外，当使用分布为几何分布时，我们建立了一个更强的竞争比$(1+p)/2$，并证明该竞争比是紧的。这两个结果均与两种极端场景下的已知结果一致：p = 0对应于不可重用资源，已知其竞争比1/2是紧的；而p = 1对应于每个资源立即返回，此时贪心策略是最优策略，因此竞争比为1。最后，我们证明这两个结果对贪心策略的近似同样具有鲁棒性。我们的工作表明，与不可重用设置相比，资源的可重用性可以提升性能，并且当可重用程度较高时，简单的贪心策略就足够了。我们的见解有助于理解资源可重用性如何影响在线算法的性能，并强调了随着可重用程度提高而带来性能提升的潜力。
英文摘要：
We study online weighted bipartite matching of reusable resources where an adversarial sequence of requests for resources arrive over time. A resource that is matched is 'used' for a random duration, drawn independently from a resource-dependent distribution, after which it returns and is able to be matched again. We study the performance of the greedy policy, which matches requests to the resource that yields the highest reward. Previously, it was known that the greedy policy is 1/2 competitive against a clairvoyant benchmark that knows the request sequence in advance. In this work, we improve this result by introducing a parameter that quantifies the degree of reusability of the resources. Specifically, if p represents the smallest probability over the usage distributions that a matched resource returns in one time step, the greedy policy achieves a competitive ratio of $1/(2-p)$. Furthermore, when the usage distributions are geometric, we establish a stronger competitive ratio of $(1+p)/2$, which we demonstrate to be tight. Both of these results align with the known results in the two extreme scenarios: p = 0 corresponds to non-reusable resources, where 1/2 is known to be tight, while p = 1 corresponds to every resource returning immediately, where greedy is the optimal policy and hence the competitive ratio is 1. Finally, we show that both results are robust to approximations of the greedy policy. Our work demonstrates that the reusability of resources can enhance performance compared to the non-reusable setting, and that a simple greedy policy suffices when the degree of reusability is high. Our insights contribute to the understanding of how resource reusability can influence the performance of online algorithms, and highlight the potential for improved performance as the degree of reusability increases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
