ExSan's Novel Data Structure
ExSan Abstract Data Structure
Not Afraid Of Pointers
The ExSan Abstract Data Structure is built upon a node design that incorporates eight directional pointers. Specifically, these pointers are divided into two groups:
- Cardinal Directions: North, South, East, and West
- Diagonal Directions: Northeast, Northwest, Southeast, and Southwest (45-degree intervals)
This design enables the creation of a highly interconnected and spatially comprehensive graph structure, suitable for modeling multidimensional relationships or spatial data.
Integration with Red-Black Binary Search Tree
Each node in the ExSan structure is further integrated into a master Red-Black Binary Search Tree (RB-BST), ensuring the overall structure remains balanced and efficiently searchable. The Red-Black Tree provides O(log n) time complexity for operations such as insertion, deletion, and lookup. This hierarchical design supports:
- The dense, grid-like connectivity of the eight-pointer nodes
- The global balancing properties of the Red-Black Tree
ExSan is centered on a single master Red-Black Tree template, implemented (coded) only once. This template provides a consistent and reusable structure for organizing and managing all nodes within the system, reducing redundancy and enhancing maintainability.
Applications
By combining local traversal capabilities and efficient global data management, the ExSan Abstract Data Structure is well-suited for applications that require:
- Rapid local traversal
- Efficient handling of large-scale hierarchical data
- Dynamic clustering of spatial or multidimensional data
This is the rendering of a 3*3 net
Each diagonal, column, and row within the mesh network is represented as a circular doubly linked list embedded within a corresponding Red-Black Tree, enabling efficient traversal and modifications while maintaining the structure's integrity.
The ExSan abstract data structure is constructed using a Red-Black Tree as its foundational layer. Within this structure, the central node of the linked list functions as the root of the binary tree, allowing direct access for efficient operations.
In terms of accessibility, both the central node and the corner nodes can be accessed in constant time, O(1),
as they do not require traversal through intermediate nodes. Accessing other nodes, however, may involve multiple transitions
or hops. The maximum number of hops required is bounded by h ≤ 2 · log2(n + 1), where
n represents the total number of nodes in the structure. This logarithmic bound ensures scalable
performance as the structure grows.
This is the rendering of a 3*4 net
Clustering
ExSan's core node has been enhanced to integrate a Red-Black Tree as a dynamic pointer, representing the corresponding cluster for a specific time lapse. This design enables the structure to adapt by dynamically shrinking or expanding as data is collected within the cluster, effectively addressing the requirements of advanced clustering techniques for high-frequency and low-latency analysis. The self-balancing properties of the Red-Black Tree ensure efficient data handling, optimal resource usage, and scalability, making it well-suited for real-time processing and large-scale datasets.
The core node of ExSan also supports the incorporation of any abstract data structure, such as hash tables, tries, or user-defined structures, in a manner similar to what was described above. This added flexibility significantly enhances the versatility and adaptability of the ExSan architecture.
ExSan was conceived 35 years ago, when it first started as a coding project. The original version was written in C and was later rewritten in C++. From the very beginning, the project was based on Red-Black Trees.
The Role of Red-Black Trees in Quantitative Finance
A recent LinkedIn post highlights the foundational significance of Binary Red-Black Trees in the development of Quantitative Finance software. From its inception, ExSan's architecture was purposefully built on Binary Red-Black Trees, valued for their proven efficiency, reliability, and scalability.
Remarkably, during ExSan’s development, it was not yet apparent that other firms were independently pursuing similar approaches. The post also reveals how a leading institution employs the same abstract data structure in its Quant Finance solutions, further validating the robustness of ExSan’s design principles. This convergence with industry practices underscores the enduring relevance of ExSan's foundations in solving the intricate challenges of financial engineering.
ExSan's codebase now surpasses 100,000 lines of C++ source code.
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