Covering the Optimal Time Window Over Temporal Data

Abstract

In this paper, we propose a new problem: covering the optimal time window over temporal data. Given a duration constraint d and a set of users where each user has multiple time intervals, the goal is to find all time windows which (1) are greater than or equal to the duration d, and (2) can be covered by the intervals from as many as possible users. This problem can be applied to real scenarios where people need to determine the best time for maximizing the number of people to be involved in an activity, e.g., the meeting organization and the online live video broadcasting. As far as we know, there is no existing algorithm that can solve the problem directly. In this paper, we propose two algorithms to solve the problem, the first one is considered as a baseline algorithm called sliding time window (STW), where we utilize the start and end points of all users - intervals to construct time windows satisfying duration d. And then we calculate the number of users whose intervals can cover the current time window. The second method, named TLI, is designed based on the the data structures from the Timeline Index in SAP HANA. In TLI algorithm, we conduct three consecutive phases to achieve the purpose of efficiency improvement, namely construction of Timeline Index, calculation of valid user set and calculation of time windows. Within the third phase, we prune the number of time windows by keeping track of the number of users in current optimal time window, which can help shrink the search space. Through extensive experimental evaluations, we find TLI algorithm outperforms STW two orders of magnitude in terms of querying time.