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A simple and space efficient segment tree implementation.

Lei Wang1, Xiaodong Wang1

  • 1Fuzhou, China.

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Summary
This summary is machine-generated.

A novel array-based segment tree implementation eliminates node structural information. This efficient data structure optimizes computational geometry problems, including interval union measure and stabbing queries.

Keywords:
AlgorithmsData structuresSegment TreeSegment treeStabbing counting queries

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Area of Science:

  • Computer Science
  • Data Structures
  • Algorithms

Background:

  • Segment trees are versatile data structures widely used in computer science.
  • Existing implementations often rely on complex node structures.
  • Efficiently handling interval-based problems is crucial in computational geometry.

Purpose of the Study:

  • To propose a new, simplified array-based implementation of segment trees.
  • To demonstrate the efficiency of this new implementation for computational geometry problems.
  • To show that structural information can be removed from segment tree nodes.

Main Methods:

  • Developed a novel array-based segment tree implementation.
  • Utilized the new segment tree to solve stabbing counting queries.
  • Applied the implementation to calculate the measure of the union of intervals.
  • Used the segment tree for determining the maximum clique size of intervals.

Main Results:

  • The proposed array-based segment tree implementation successfully removes structural information.
  • Insertions and deletions of intervals into the heap-based segment tree achieve O(log n) time complexity.
  • The implementation efficiently solves primary computational geometry problems.

Conclusions:

  • The new array-based segment tree offers a simplified and efficient approach.
  • This implementation enhances the performance of solving various computational geometry problems.
  • The removal of structural information leads to a more streamlined data structure.