Range Mode and Range Median Queries on Lists and Trees 1st edition by Danny Krizanc, Pat Morin, Michiel Smid ISBN 3540206958  9783540206958

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Product details:

ISBN 10:       3540206958 
ISBN 13: 978-3540206958 
Author:         Danny Krizanc, Pat Morin, Michiel Smid
 

Range Mode and Range Median Queries on Lists and Trees 1st  Table of contents:

1. Introduction

   • 1.1 Overview of Range Queries
   • 1.2 Mode and Median Queries: Definitions and Applications
   • 1.3 Challenges in Efficiently Answering Range Mode and Median Queries
   • 1.4 Motivation and Importance of Range Mode and Median Queries
   • 1.5 Structure of the Paper

2. Background and Preliminaries

   • 2.1 Basics of Range Queries and Data Structures
   • 2.2 Mode Queries: Definition, Characteristics, and Challenges
   • 2.3 Median Queries: Definition, Properties, and Techniques
   • 2.4 Introduction to Lists, Arrays, and Trees as Data Structures
   • 2.5 Previous Work on Range Mode and Median Queries

3. Range Mode Queries

   • 3.1 Problem Formulation for Range Mode Queries
   • 3.2 Naive Approaches for Mode Queries on Lists and Trees
   • 3.3 Efficient Algorithms for Range Mode Queries
   • 3.4 Data Structures for Fast Mode Queries (e.g., Segment Trees, Fenwick Trees)
   • 3.5 Optimal Time Complexity for Range Mode Queries

4. Range Median Queries

   • 4.1 Problem Formulation for Range Median Queries
   • 4.2 Naive Approaches for Median Queries on Lists and Trees
   • 4.3 Efficient Algorithms for Range Median Queries
   • 4.4 Data Structures for Fast Median Queries (e.g., Segment Trees, Balanced BSTs)
   • 4.5 Optimal Time Complexity for Range Median Queries

5. Advanced Techniques for Range Mode and Median Queries

   • 5.1 Augmented Data Structures for Both Mode and Median Queries
   • 5.2 Range Queries with Multiple Mode and Median Values
   • 5.3 Combining Mode and Median Query Solutions
   • 5.4 Approximation Techniques for Mode and Median Queries
   • 5.5 Parallel and Distributed Approaches for Large-Scale Queries

6. Applications of Range Mode and Median Queries

   • 6.1 Range Queries in Data Analysis and Databases
   • 6.2 Mode and Median in Time-Series and Streaming Data
   • 6.3 Range Queries in Computational Biology (e.g., Genome Data)
   • 6.4 Mode and Median Queries in Geospatial and Sensor Networks
   • 6.5 Real-Time Applications: Querying Dynamic Data Structures

7. Experimental Evaluation

   • 7.1 Experimental Setup and Test Cases for Mode and Median Queries
   • 7.2 Performance Comparison of Different Algorithms
   • 7.3 Impact of Data Structure Choice on Query Efficiency
   • 7.4 Empirical Results for Large-Scale Range Mode and Median Queries
   • 7.5 Scalability of Algorithms in Practical Scenarios

8. Challenges and Open Problems

   • 8.1 Difficulties in Handling Dynamic and Streaming Data
   • 8.2 Space and Memory Efficiency of Range Query Algorithms
   • 8.3 Trade-offs Between Preprocessing and Query Time
   • 8.4 Open Problems in Optimizing Range Mode and Median Queries
   • 8.5 Directions for Future Research in Range Query Optimization

9. Conclusion

   • 9.1 Summary of Key Findings
   • 9.2 Contributions to Range Mode and Median Query Algorithms
   • 9.3 Practical Implications of Efficient Range Queries
   • 9.4 Final Thoughts on Future Developments in Range Queries
10.  

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