Optimal Node Placement in Multi-Hop Networks
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Solution Overview
Problem
Conventional methods for identifying optimal node placement in multi-hop networks to form redundant paths around critical nodes and links are time-consuming and computationally intensive, especially in dynamic topologies, which can lead to network failures and disruptions.
Innovation Solution
The method involves identifying critical nodes and links using Eigenvectors of a matrix defining the network topology, generating lists of orphaned nodes that lose connectivity when these critical elements fail, and determining optimal locations for additional nodes to reduce the number of critical nodes and links by simulating node and link removals, thereby ensuring network self-healing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a brute-force approach is used to identify critical nodes and links by simulating node removal, then network reliability can be assessed, but the computational time and complexity increase significantly
Solution Approach 1:
The patent extracts the essential characteristics of critical nodes and links by using spectral graph theory to identify dominant eigenvectors of the network adjacency matrix. This extraction method identifies critical elements without requiring exhaustive simulation of every possible node removal, thereby reducing computational time while maintaining reliability assessment accuracy.
Solution Approach 2:
The patent transforms the network topology into a mathematical representation using an adjacency matrix and analyzes its eigenvalues and eigenvectors. By changing the parameter representation from physical node connections to spectral properties, the system can identify critical nodes and links efficiently without brute-force simulation, resolving the contradiction between reliability assessment and computational time.
2Reliability
If the network topology is constantly monitored and reorganized to maintain connectivity, then network resilience improves, but the system complexity and computational requirements increase
Solution Approach 1:
The patent enables the network to automatically identify critical nodes and links and determine optimal replacement node locations using spectral analysis. This self-service capability allows the network to maintain resilience through automated topology analysis and reconfiguration without requiring complex external management systems, thereby improving reliability while controlling system complexity.
Solution Approach 2:
The patent performs preliminary identification of critical nodes and links using eigenvector analysis before actual failures occur. By proactively identifying vulnerable network elements and pre-determining optimal replacement locations, the system can quickly respond to failures without complex real-time decision-making, thus improving resilience while managing system complexity.
3Reliability
If additional nodes are strategically placed to form redundant paths, then network connectivity and self-healing capability improve, but the network cost and node density increase
Solution Approach 1:
The patent identifies and addresses only the critical nodes and links that most significantly impact network connectivity, rather than attempting to create redundant paths throughout the entire network. By focusing spectral analysis on dominant eigenvectors that represent the most critical network structures, the system achieves effective self-healing capability with a minimal number of additional nodes, resolving the contradiction between reliability improvement and quantity increase.
Data Source
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AI summary
A method includes obtaining (902, 1002, 1104) information identifying one or more critical nodes (102) and/or one or more critical links (104) in a multi-hop network (100). Each critical node or critical link represents a node or link whose failure isolates at least part of the network. The method also includes generating (906, 1006, 1108) a list identifying one or more orphaned nodes that lose connectivity to a gateway when a specified critical node or critical link fails. The list is generated using an Eigenvector of a matrix defining a topology of the network without the specified critical node or critical link. The method further includes identifying (916, 1016, 1118), using the list, at least one location where an additional node (102) can be inserted into the network in order to reduce a number of critical nodes and critical links in the network. The gateway and the orphaned node(s) can be associated with different values in the Eigenvector.