在移动实体间维持低拥塞势的频率竞争查询策略
Frequency-Competitive Query Strategies to Maintain Low Congestion Potential Among Moving Entities
AI总结：
本文研究移动实体拥塞监测的对偶问题，即在保证拥塞势固定界的前提下最小化查询频率，提出适配算法并得到查询频率的紧竞争界，结果与此前最小化拥塞势的研究相呼应且存在意外差异。
摘要：
我们研究了在d维欧氏空间中，利用位置查询监测一组以有界速度移动但运动方式不可预测的实体间拥塞势的问题。由于两次查询之间实体可能发生移动，其位置存在不确定性，导致每个时刻都存在一个可能的实体构型空间，这些构型的拥塞特性可能差异极大。我们基于与实体关联的不确定区域的（动态）相交图，定义了此类空间的多种拥塞势度量，用以描述实际可能发生的拥塞情况。\n 在相同的不确定性模型下，此前的研究[SoCG'13, EuroCG'14, SICOMP'16, SODA'19]解决了在查询频率有界的条件下最小化拥塞势的问题。研究表明，在相同的查询频率约束下，可以设计一种在最坏情况拥塞势方面达到O(1)竞争比的查询方案，其性能可与甚至能预知所有实体运动轨迹的全知查询方案相比。\n 本文研究其对偶问题：如何在保证拥塞势不超过固定阈值的前提下，在任意固定时间区间内最小化查询频率，频率以查询总次数或查询间的最小间隔（粒度）衡量。这一互补的目标需要采用截然不同的算法与分析方法。尽管如此，我们的结果与此前论文的结论相呼应，具体而言，我们得到了所需查询频率的紧竞争界，同时也存在一些出人意料的差异。
英文摘要：
We consider the problem of using location queries to monitor the congestion potential among a collection of entities moving, with bounded speed but otherwise unpredictably, in $d$-dimensional Euclidean space. Uncertainty in entity locations due to potential motion between queries gives rise to a space of possible entity configurations at each moment in time, with possibly very different congestion properties. We define different measures of what we call the congestion potential of such spaces, in terms of the (dynamic) intersection graph of the uncertainty regions associated with entities, to describe the congestion that might actually occur. Previous work [SoCG'13, EuroCG'14, SICOMP'16, SODA'19], in the same uncertainty model, addressed the problem of minimizing congestion potential using location queries of some bounded frequency. It was shown that it is possible to design a query scheme that is $O(1)$-competitive, in terms of worst-case congestion potential, with other, even clairvoyant query schemes (that know the trajectories of all entities), subject to the same bound on query frequency. In this paper we address the dual problem: how to guarantee a fixed bound on congestion potential while minimizing the query frequency, measured in terms of total number of queries or the minimum spacing between queries (granularity), over any fixed time interval. This complementary objective necessitates quite different algorithms and analyses. Nevertheless, our results parallel those of the earlier papers, specifically tight competitive bounds on required query frequency, with a few surprising differences.
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。
