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Resolving SINR Queries in a Dynamic Setting
SIAM Journal on Computing ( IF 1.6 ) Pub Date : 2020-12-14 , DOI: 10.1137/19m128733x Boris Aronov , Gali Bar-On , Matthew J. Katz
SIAM Journal on Computing ( IF 1.6 ) Pub Date : 2020-12-14 , DOI: 10.1137/19m128733x Boris Aronov , Gali Bar-On , Matthew J. Katz
SIAM Journal on Computing, Volume 49, Issue 6, Page 1271-1290, January 2020.
We consider a set of transmitters broadcasting simultaneously on the same frequency under the signal to interference plus noise ratio (SINR) model. Transmission power may vary from one transmitter to another, and a transmitter's signal strength at a given point is modeled by the transmitter's power divided by some constant power $\alpha$ of the distance it traveled. Roughly, a receiver at a given location can hear a specific transmitter only if the transmitter's signal is stronger by a specified ratio than the signals of all other transmitters combined. An SINR query is to determine whether a receiver at a given location can hear any transmitter, and if yes, which one. An approximate answer to an SINR query is such that one gets a definite yes or definite no, when the ratio between the strongest signal and all other signals combined is well above or well below the reception threshold, while the answer in the intermediate range is allowed to be either yes or no. We describe compact data structures that support approximate SINR queries in the plane in a dynamic context, i.e., where transmitters may be inserted and deleted over time. We distinguish between two main variants---uniform power and nonuniform power. In both variants the preprocessing time is $O(n\,{polylog} n)$ and the amortized update time is $O({\rm polylog} n)$, while the query time is $O({polylog} n)$ for uniform power, and randomized time $O(\sqrt{n}\,{polylog} n)$ with high probability for nonuniform power. Finally, we observe that in the static context the latter data structure can be implemented differently, so that the query time is also $O({polylog} n)$, thus significantly improving all previous results for this problem.
中文翻译：
解决动态设置中的SINR查询
SIAM计算杂志，第49卷，第6期，第1271-1290页，2020年1月。
我们考虑在信噪比（SINR）模型下以相同频率同时广播的一组发射机。发射功率可能因一个发射器而异，并且在给定点处的发射器信号强度由发射器功率除以其行进距离的某个恒定功率来模拟。大致而言，给定位置的接收器只有在其信号比所有其他发射器的信号总和强特定比例的情况下，才能听到特定的发射器。SINR查询用于确定给定位置的接收器是否可以听到任何发射器，如果可以，则确定是哪个。对SINR查询的近似答案是：确定为是或否，当最强信号与所有其他合并信号之间的比率远高于或远低于接收阈值时，中间范围的答案允许为是或否。我们描述了紧凑的数据结构，这些结构在动态上下文中支持平面中的近似SINR查询，即随时间推移可能会插入和删除发射机。我们区分两个主要变体-均匀功率和非均匀功率。在这两种变体中，预处理时间为$ O（n \，{polylog} n）$，摊销更新时间为$ O（{\ rm polylog} n）$，而查询时间为$ O（{polylog} n）。 $表示均匀功率，而随机时间$ O（\ sqrt {n} \，{polylog} n）$表示不均匀功率的可能性很高。最后，我们观察到在静态上下文中，后者的数据结构可以以不同的方式实现，
更新日期：2021-01-13
We consider a set of transmitters broadcasting simultaneously on the same frequency under the signal to interference plus noise ratio (SINR) model. Transmission power may vary from one transmitter to another, and a transmitter's signal strength at a given point is modeled by the transmitter's power divided by some constant power $\alpha$ of the distance it traveled. Roughly, a receiver at a given location can hear a specific transmitter only if the transmitter's signal is stronger by a specified ratio than the signals of all other transmitters combined. An SINR query is to determine whether a receiver at a given location can hear any transmitter, and if yes, which one. An approximate answer to an SINR query is such that one gets a definite yes or definite no, when the ratio between the strongest signal and all other signals combined is well above or well below the reception threshold, while the answer in the intermediate range is allowed to be either yes or no. We describe compact data structures that support approximate SINR queries in the plane in a dynamic context, i.e., where transmitters may be inserted and deleted over time. We distinguish between two main variants---uniform power and nonuniform power. In both variants the preprocessing time is $O(n\,{polylog} n)$ and the amortized update time is $O({\rm polylog} n)$, while the query time is $O({polylog} n)$ for uniform power, and randomized time $O(\sqrt{n}\,{polylog} n)$ with high probability for nonuniform power. Finally, we observe that in the static context the latter data structure can be implemented differently, so that the query time is also $O({polylog} n)$, thus significantly improving all previous results for this problem.
中文翻译：
解决动态设置中的SINR查询
SIAM计算杂志，第49卷，第6期，第1271-1290页，2020年1月。
我们考虑在信噪比（SINR）模型下以相同频率同时广播的一组发射机。发射功率可能因一个发射器而异，并且在给定点处的发射器信号强度由发射器功率除以其行进距离的某个恒定功率来模拟。大致而言，给定位置的接收器只有在其信号比所有其他发射器的信号总和强特定比例的情况下，才能听到特定的发射器。SINR查询用于确定给定位置的接收器是否可以听到任何发射器，如果可以，则确定是哪个。对SINR查询的近似答案是：确定为是或否，当最强信号与所有其他合并信号之间的比率远高于或远低于接收阈值时，中间范围的答案允许为是或否。我们描述了紧凑的数据结构，这些结构在动态上下文中支持平面中的近似SINR查询，即随时间推移可能会插入和删除发射机。我们区分两个主要变体-均匀功率和非均匀功率。在这两种变体中，预处理时间为$ O（n \，{polylog} n）$，摊销更新时间为$ O（{\ rm polylog} n）$，而查询时间为$ O（{polylog} n）。 $表示均匀功率，而随机时间$ O（\ sqrt {n} \，{polylog} n）$表示不均匀功率的可能性很高。最后，我们观察到在静态上下文中，后者的数据结构可以以不同的方式实现，
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