[Paper Review] On Stability Problems of Omega and 3-Disjoint Paths Omega Multi-stage Interconnection Networks

Ravi Rastogi, Nitin Nitin+2 more|arXiv (Cornell University)|Feb 6, 2012

Interconnection Networks and Systems27 references3 citations

TL;DR

This paper analyzes the stability of Omega Multi-stage Interconnection Networks (OMIN) and a proposed 3-Disjoint Paths Omega Network (3DON) by modeling them as stable matching problems, using the Stable Marriage Problem as a framework. It finds that OMIN exhibits higher stability than 3DON due to its structural properties, demonstrating that regular, symmetric interconnection topologies inherently support more stable configurations under matching-based analysis.

ABSTRACT

The research paper emphasizes that the Stable Matching problems are the same as the problems of stable configurations of Multi-stage Interconnection Networks (MIN). We have discusses the Stability Problems of Existing Regular Omega Multi-stage Interconnection Network (OMIN) and Proposed 3-Disjoint Paths Omega Multi-stage Interconnection Network (3DON) using the approaches and solutions provided by the Stable Matching Problem. Specifically, Stable Marriage Problem is used as an example of Stable Matching. On application of the concept of the Stable Marriage over the MINs states that OMIN is highly stable in comparison to 3DON.

Motivation & Objective

• To investigate the stability characteristics of existing regular Omega Multi-stage Interconnection Networks (OMIN).
• To evaluate the stability of a proposed 3-Disjoint Paths Omega Network (3DON) using matching theory.
• To apply the Stable Marriage Problem as a theoretical framework for analyzing stable configurations in MINs.
• To compare the relative stability of OMIN and 3DON under the same theoretical model.

Proposed method

• Modeling OMIN and 3DON as stable matching problems using the Stable Marriage Problem framework.
• Applying matching theory to assess the existence and robustness of stable configurations in both network types.
• Analyzing structural differences between OMIN and 3DON to explain variations in stability outcomes.
• Using the concept of stable configurations to evaluate network resilience and routing consistency.
• Mapping network connection patterns to preference lists in the Stable Marriage Problem to simulate stability.
• Comparing the number and quality of stable matchings between OMIN and 3DON to infer relative stability.

Experimental results

Research questions

• RQ1 How does the structure of OMIN influence its stability in multi-stage interconnection networks?
• RQ2 To what extent does the 3-Disjoint Paths Omega Network (3DON) achieve stable configurations under matching-based analysis?
• RQ3 Why does OMIN demonstrate higher stability compared to 3DON when modeled as a stable matching problem?
• RQ4 Can the Stable Marriage Problem effectively model and predict stability in MIN architectures?
• RQ5 What structural features of a network topology enhance or diminish stability in interconnection networks?

Key findings

• OMIN exhibits higher stability than 3DON when analyzed through the lens of the Stable Marriage Problem.
• The regular, symmetric structure of OMIN supports more stable matchings compared to the more complex 3DON topology.
• The 3DON network, despite its improved disjoint path diversity, suffers from reduced stability due to structural asymmetries.
• Stable matching theory provides a valid and insightful framework for evaluating stability in multi-stage interconnection networks.
• The analysis confirms that structural regularity in MINs correlates strongly with enhanced stability in routing configurations.
• The study establishes that OMIN is more resilient to instability-induced routing conflicts than 3DON under the same theoretical model.