## Data Structure Name: Quad Trees ### Description: Quad Trees are... #flashcard hierarchical data structure that is used for storing location data. The structure works by dividing a map region into 4 sections and defining a max number of entities that can exist in a region (*k*). For any region that exceeds *k*, the region is further divided into 4 sections. This repeats until the map contains only regions with less than *k* entities. The resulting map can then be represented as a graph where each node is a region. Each node then contains the values of all entities within the region. <!--ID: 1751507777636--> ### Variations: ### Diagram: ![[Drawing 2024-09-09 13.27.11.excalidraw.svg]] ### General Use of Quad Trees #flashcard The Quad Trees structure makes it well-suited for bounding box searches and spatial queries. It is preferred over a [[Geohash]] when there is an uneven distribution of density across locations. This is because the sparse regions are represented in the higher levels of the tree. Conducting a search into dense regions would require traversing many levels of the graph. <!--ID: 1751507777638--> ## Key Considerations ### Properties: ### Strengths of Quad Trees: #flashcard - Hierarchical structure is efficient for spatial data indexing, supporting fast retrieval - Precision is consistent across the map <!--ID: 1751507777642--> ### Weaknesses of Quad Trees: #flashcard - Potentially higher computation overhead when compared to [[Geohash]] - Requires more space for storage due to the structure and pointers - Not as straightforward for sharing location data as compared to a single string representation - ### Implementation Details: <!--ID: 1751507777644--> | | [[Big O - Time Complexity]] | [[Big O - Space Complexity]] | | ------ | --------------------------- | ---------------------------- | | Access | | | | Add | | | | Delete | | | | Search | | | ### Implementation Tips of Quad Trees #flashcard - **Load Balancing**: In a real-world scenario, business locations are not evenly distributed. Some areas may have a high density of businesses, leading to deep QuadTree nodes. Balancing the tree to prevent very deep or unbalanced trees is important for performance. - **Memory Usage**: Each node in the QuadTree stores a list of points and child nodes, which can lead to high memory usage. Pruning and garbage collection strategies may be necessary to manage memory. - **Concurrency**: In a high-traffic system like Yelp, multiple read and write operations may occur simultaneously. Implementing concurrency control, such as read-write locks, can ensure data consistency. <!--ID: 1751507777647--> ### Special Properties ## Specific Use Cases - Bounding box searches - Spatial Queries ## Reference #### Working Notes #### Sources