Abstract
In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees, 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.
Highlights
Solving geometrical problems computationally seems to be difficult due to its complex nature such as varying dimensionality and shape
The static segment tree requires O(n log n) space, and the stabbing query processing time is O(k+log n), where n is the number of segments and k is the number of output segments
A novel data structure, BITS-tree (Balanced Inorder Threaded Segment Tree), is proposed to dynamically insert and delete segments, with interval range of the node is only based on the end points of segments stored in the tree
Summary
Solving geometrical problems computationally seems to be difficult due to its complex nature such as varying dimensionality and shape. The range of the tree is predefined, and one can insert or delete the segments whose interval contained in this range, in those cases where the range of the segment falls beyond the range of the segment tree, reconstruction of the tree is the only possibility, which is not advisable This may practically increase the time as the number of nodes to be traversed get increased. Variants of segment trees are used in packet classification problem One such data structure is the Fat Inverted Segment Trees (FIS-trees) [5][9] with space requirements of O(n1+1/l) and having complexity for insertion/deletion as O(n1/l log n), where l is the height of the tree. A novel data structure, BITS-tree (Balanced Inorder Threaded Segment Tree), is proposed to dynamically insert and delete segments, with interval range of the node is only based on the end points of segments stored in the tree. Unlike in the dynamic version of the standard segment trees, the root of the BITS-tree does not have the information of overall interval range of nodes in the tree, the BITS-tree permits insertion of segment with any interval range, and it is a real dynamic tree suitable for all situations
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