Kinetic heap-ordered trees: Tight analysis and improved algorithms
✍ Scribed by Guilherme D. da Fonseca; Celina M.H. de Figueiredo
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 99 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0020-0190
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✦ Synopsis
The most natural kinetic data structure for maintaining the maximum of a collection of continuously changing numbers is the kinetic heap. Basch, Guibas, and Ramkumar proved that the maximum number of events processed by a kinetic heap with n numbers changing as linear functions of time is O(n log 2 n) and (n log n). We prove that this number is actually (n log n). In the kinetic heap, a linear number of events are stored in a priority queue, consequently, it takes O(log n) time to determine the next event at each iteration. We also present a modified version of the kinetic heap that processes O(n log n/ log log n) events, with the same O(log n) time complexity to determine the next event.