Cluster Network Topology Using Singer Difference Sets
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Solution Overview
Problem
Existing cluster networks face challenges in achieving symmetric connections, reducing the number of required connections, and ensuring cost-effective, scalable, and conflict-free communication, particularly in large-scale computer clusters where all-to-all connectivity is prohibitively expensive and asymmetric.
Innovation Solution
The method involves using Singer Difference Sets to connect nodes in a cluster such that each node is connected to at most n+1 other nodes, creating symmetric connections and optimizing the number of edges between nodes, with a maximum distance of two hops, and utilizing switches to facilitate efficient data transfer and permutation-based communication.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If an all connect network is used to allow any combination of computers to talk to each other, then connectivity and communication capability are improved, but the number of connections required becomes prohibitively expensive for large N
Solution Approach 1:
The patent segments the all-connect network into multiple cycles, where each cycle provides a subset of connections. Instead of implementing all N*(N-1)/2 connections directly, the network is divided into manageable cycle segments that collectively provide the desired connectivity with fewer total connections.
Solution Approach 2:
The patent introduces a temporal dimension to the network connectivity by using permutation sequences. Data communication is achieved through time-multiplexed connections where different connection patterns are activated in different time slots, effectively adding a time dimension to the spatial network structure.
2Power
If the number of processors accessing a large shared memory is increased, then computational power is improved, but the performance is limited by memory bandwidth
Solution Approach 1:
The shared memory system is segmented into multiple memory modules that can be accessed by different processors simultaneously. The memory access network is divided into multiple independent paths, allowing parallel memory operations that increase effective bandwidth without increasing the size of a single memory unit.
Solution Approach 2:
The patent pre-arranges memory access patterns and data placement strategies before computation begins. By anticipating memory access requirements and pre-positioning data in optimal locations, the system reduces memory access conflicts and maximizes bandwidth utilization during actual computation.
3Speed
If more connections are added to reduce the maximum distance between nodes, then communication speed is improved, but the cost and complexity of the network increases
Solution Approach 1:
The patent employs periodic connection patterns where nodes are connected in regular intervals rather than to all other nodes. This periodic structure achieves good communication performance by ensuring that every node can reach any other node within a bounded number of hops, while maintaining a manageable connection density that scales efficiently.
Data Source
AI summary
A method for arranging a plurality of nodes in a cluster is disclosed. The invention proposes a scheme for creation of a cluster having optimum number of connections and with a diameter of two, meaning any two nodes are at most two edges away from each other. The present invention uses Singer Difference Set for deriving networks with a smaller number of connections per node for clusters of the same size. Further, the method envisaged by the present invention allows multiple computers to be placed at each node with the computers sharing the network in a non-conflicting manner, resulting in a powerful cluster at reduced cost.