Math Engine Collaboration System for Low-Latency Expression Manipulation
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Solution Overview
Problem
Existing mathematical platforms are not suitable for real-time, low-latency collaboration on mathematical expression manipulation across multiple computing devices, and traditional multiplayer gaming platforms suffer from latency issues that hinder effective collaboration.
Innovation Solution
A method for low-latency math expression manipulation collaboration across multiple client devices, utilizing a math engine that generates and updates local mathematical expression trees on each device, with a peer-to-peer system that minimizes data transfer by sending only necessary information, such as node IDs and timestamps, to maintain synchronized displays and enable real-time manipulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If traditional multiplayer gaming platforms are used for collaboration, then real-time interaction is achieved, but latency issues hinder effective collaboration
Solution Approach 1:
The mathematical expression is segmented into a tree structure with nodes representing individual elements (numbers, operators, variables). This segmentation allows independent manipulation of specific nodes without affecting the entire expression, enabling precise real-time collaboration where multiple users can work on different parts simultaneously with minimal conflict and latency.
Solution Approach 2:
The system implements dynamic role assignment where users can switch between controller and observer roles. The controller user can manipulate expressions while observers watch, and roles can be transferred dynamically. This dynamic structure optimizes real-time collaboration by allowing one user to lead manipulations while others follow, reducing simultaneous conflicts and improving overall collaboration effectiveness.
2Stability of the object's composition
If full expression data is transmitted between devices, then synchronization is maintained, but bandwidth consumption increases
Solution Approach 1:
The system extracts and transmits only the essential structural information needed for synchronization: node identifiers, parent-child relationships, and sibling indices. Rather than transmitting complete expression data, only the minimal necessary information is sent to reconstruct the expression tree on remote devices, dramatically reducing bandwidth consumption while maintaining synchronization.
Solution Approach 2:
Each device creates a local copy of the mathematical expression tree and maintains it independently. Instead of continuously syncing full data, devices exchange only the structural metadata (node IDs, parent IDs, sibling indices) needed to keep local copies synchronized. This copying approach with selective data exchange reduces bandwidth usage while preserving expression integrity.
3Loss of information
If complex data structures are transmitted for expression manipulation, then complete information is shared, but data transfer complexity increases
Solution Approach 1:
The system assigns unique local identifiers (node ID, parent ID, sibling index) to each node in the expression tree. These local quality markers allow devices to reference specific nodes without transmitting the entire node structure or expression data. The simplified identifier trio preserves complete expression information while dramatically reducing data transfer complexity.
Solution Approach 2:
The system transforms the complex expression data structure into a simplified parameter representation. Instead of transmitting nested data structures representing the full expression, only three integer parameters per node (node ID, parent ID, sibling index) are transmitted. This parameter transformation maintains complete expression information while reducing data complexity and transfer overhead.
Data Source
AI summary
This disclosure describes systems, methods, and apparatus for low-latency math expression manipulation, communication, and collaboration across multiple peer devices. A controlling peer device can detect a drag node event, pass a network ID of a selected node to at least a second peer device, where the second peer device can locally process the network ID and update a local instantiation of an expression tree and UI rendered from the local expression tree. The controlling device can generate drop regions based on the selected node and the existing tree structure and pass an indication of the drop region to the second peer device. The controlling peer device can detect release of the dragged node within a drop region and pass a network ID of the drop region to the second peer device, which then locally updates its expression tree and UI based on the network ID of the drop region.