In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees[3], the proposed data structure permits insertion of a segment with interval range beyond the interval range of the existing tree, which is the interval between minimum and maximum values of the end points of all the segments. Moreover, the number of nodes in the proposed tree is lesser as compared to the dynamic version of the standard segment trees, and is able to answer both stabbing and range queries practically much faster compared to the standard segment trees.

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Quantum computing is an emerging field of study and gains importance due to the fact that with the introduction of quantum computers, many challenges and changes are presented for the existing algorithms. The main reason for this is the exponential speed of such computers. This study analyzes some of the benefits and implications of quantum computing on geometrical problems such as the multidimensional search for window queries with R-Trees. A review of the window query on R-Trees in classical computing is done to consider its adaptability to quantum computers by applying the Grover's quantum search algorithm from a theoretical point of view. Thereby, the query time complexity in worst-case scenarios could be improved to quadratic search time.

We present a kinetic data structure named Kinetic Interval Graph (KI-Graph) for performing efficient range search on moving one dimensional axis-parallel segments. This finds applications in Artificial Intelligence such as robotic motion. The structure requires O(n) storage. The time taken per update when a critical event occurs is O (1) thereby improving responsiveness when compared to the kinetic segment trees, while the overall updates across all segments at a time instance is at most n/2. Also, range query is performed efficiently in θ (k) time, where k segments are reported.