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paper.out
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\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [2][-]{subsection.1.1}{Problem Statement}{section.1}% 2
\BOOKMARK [2][-]{subsection.1.2}{Previous Work}{section.1}% 3
\BOOKMARK [2][-]{subsection.1.3}{Our Approaches}{section.1}% 4
\BOOKMARK [1][-]{section.2}{Describing the History-Sensitive Algorithm and Data Structure}{}% 5
\BOOKMARK [2][-]{subsection.2.1}{Data Structures}{section.2}% 6
\BOOKMARK [3][-]{subsubsection.2.1.1}{History Data Structure}{subsection.2.1}% 7
\BOOKMARK [3][-]{subsubsection.2.1.2}{Current-Window Data Structure}{subsection.2.1}% 8
\BOOKMARK [2][-]{subsection.2.2}{Algorithm Pseudocode}{section.2}% 9
\BOOKMARK [3][-]{subsubsection.2.2.1}{Updating History Data Structure}{subsection.2.2}% 10
\BOOKMARK [3][-]{subsubsection.2.2.2}{Updating heap and hash tables}{subsection.2.2}% 11
\BOOKMARK [3][-]{subsubsection.2.2.3}{Finding the trending hashtags}{subsection.2.2}% 12
\BOOKMARK [1][-]{section.3}{Analyzing the History-Sensitive Algorithm}{}% 13
\BOOKMARK [2][-]{subsection.3.1}{Correctness}{section.3}% 14
\BOOKMARK [2][-]{subsection.3.2}{Runtime Analysis}{section.3}% 15
\BOOKMARK [2][-]{subsection.3.3}{Spatial Analysis}{section.3}% 16
\BOOKMARK [1][-]{section.4}{Design Choices}{}% 17
\BOOKMARK [2][-]{subsection.4.1}{Choosing the parameters y and z}{section.4}% 18
\BOOKMARK [2][-]{subsection.4.2}{Parameters of the History Data Structure}{section.4}% 19
\BOOKMARK [2][-]{subsection.4.3}{Choosing the Flavor of Heap}{section.4}% 20
\BOOKMARK [1][-]{section.5}{Testing Procedure}{}% 21
\BOOKMARK [1][-]{section.6}{Results}{}% 22
\BOOKMARK [2][-]{subsection.6.1}{Runtime Measurements}{section.6}% 23
\BOOKMARK [2][-]{subsection.6.2}{Are the Algorithm Outputs Actually Trending?}{section.6}% 24
\BOOKMARK [3][-]{subsubsection.6.2.1}{The Intersection Distribution}{subsection.6.2}% 25
\BOOKMARK [3][-]{subsubsection.6.2.2}{Checking the Algorithm-Defined Trends Against Real Life}{subsection.6.2}% 26
\BOOKMARK [1][-]{section.7}{Discussion}{}% 27
\BOOKMARK [2][-]{subsection.7.1}{Comparison of Naive and History-Sensitive Algorithms}{section.7}% 28
\BOOKMARK [2][-]{subsection.7.2}{Applicability to Real-Time Data}{section.7}% 29
\BOOKMARK [1][-]{section.8}{Future Work}{}% 30
\BOOKMARK [1][-]{section.9}{Appendix I: Code and Visualizations}{}% 31
\BOOKMARK [1][-]{section.10}{Appendix II: Top-k Hashtags Results}{}% 32