Time in Privacy Preserving LBSs: An Overlooked Dimension

Table 1

Notation table.

𝑅	A spatial region
𝑆(𝑅)	Set of users having footprints in 𝑅
𝐸(𝑅)	Entropy of region 𝑅
𝑃(𝑅)	Popularity of region 𝑅
𝑝𝑖	𝑖th time period, 0≤𝑖≤𝜌
𝜌	Number of periods from system start-up
𝑇^𝑝𝑖	𝑖th time slice of a period 𝑝
𝑞	𝑙/𝑠, number of slices composing a period
𝑇𝑗	Time frame 𝑇𝑗={𝑇^𝑝0𝑗,𝑇^𝑝1𝑗,…,𝑇^𝑝𝜌𝑗}
𝐸(𝑅,𝑇𝑗)	Entropy of region 𝑅, during time slice 𝑥 of time period 𝑝
𝑃(𝑅,𝑇𝑗)	Popularity of region 𝑅, for time frame 𝑇𝑗
𝑢𝑖	Generic 𝑖th user of a set of users, 1≤𝑖≤𝑚, 𝑚∈ℕ
𝑢𝑖,𝑇𝑗	Generic 𝑖th user who have footprints in 𝑅 in time frame 𝑇𝑗
𝑛𝑖	Number of footprints of user 𝑢𝑖 in 𝑅
𝑛𝑖,𝑇𝑗	Number of footprints of user 𝑢𝑖 in 𝑅 in time frame 𝑇𝑗
𝑁	Total number of footprints in a region 𝑅