Peer-to-Peer Overlay Graph Construction via Edge Reconnection
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Solution Overview
Problem
Existing methods for constructing peer-to-peer overlay graphs struggle to maintain resilience, low latency, and bounded resource usage in dynamic network environments, especially when nodes join, leave, or fail, as they often require offline computations and lack guarantees for resilience and connectivity.
Innovation Solution
A method and apparatus for constructing resilient random regular (r3) graphs by iteratively adding nodes to the overlay graph, breaking and reconnecting edges to ensure high connectivity and resilience, with a distributed approach that maintains graph properties even in the presence of node arrivals and failures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If offline techniques are used to construct regular graphs with strict bounds on resilience, then resilience guarantees are improved, but the ability to maintain properties in dynamic environments (node joins, leaves, failures) deteriorates
Solution Approach 1:
The patent transitions from static offline graph construction to dynamic online construction that adapts to node joins, leaves, and failures in real-time. The system maintains resilience guarantees while operating in dynamic peer-to-peer environments through iterative edge breaking and reconnection operations.
Solution Approach 2:
The patent performs preliminary edge breaking before node insertion, preparing the graph structure in advance to accommodate new nodes while maintaining degree constraints and resilience properties. This preliminary action ensures that the graph can dynamically adapt without violating structural invariants.
2Ease of manufacture
If random regular graphs are constructed using distributed approaches, then ease of construction and maintenance is improved, but strict guarantees on resilience deteriorate
Solution Approach 1:
The patent implements self-service through distributed algorithms where each node autonomously participates in graph construction and maintenance by breaking and reconnecting edges according to local rules. This eliminates the need for centralized control while maintaining structural guarantees through probabilistic analysis.
Solution Approach 2:
The patent changes the approach from requiring strict deterministic parameters to using probabilistic parameters that provide high-probability guarantees. By analyzing the expected degree and connectivity parameters of random regular graphs, the system achieves both ease of distributed construction and resilience guarantees with high probability.
3Reliability
If edge breaking and reconnection operations are performed to maintain graph properties, then connectivity and resilience are improved, but computational overhead increases
Solution Approach 1:
The patent segments the graph maintenance task into individual edge breaking and reconnection operations that can be performed locally at each node. This segmentation allows distributed execution with minimal coordination overhead, reducing the computational and communication costs compared to global graph reconstruction.
Data Source
AI summary
Systems and methods for constructing and maintaining a peer-to-peer overlay graph are disclosed herein. The systems and methods include adding a node to the overlay graph. Adding the node includes choosing an edge that is not connected to the node, breaking the edge and connecting the node to broken edge nodes previously connected to the edge. The process is repeating if additional connections are need and node addition data is stored for the node.