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Top of worlds: estimating time complexity of calculating rank order in multi-dimensional hierarchical sets

The increasing number of mobile devices, such as smartphones, has brought attention to participatory sensing in which real-world data are collected via personal devices. To collect data via participatory sensing, it is important to motivate participants. Thus, we previously proposed Top of Worlds, a method for encouraging user participation by presenting their rank order. In this paper, we estimate its time complexity in order to understand how often we can present a rank order in planning phase of services.