Hierarchy of Graph Isomorphism Testing
Read PDF →Chen, 1984
Category: Computer Science
Overall Rating
Score Breakdown
- Cross Disciplinary Applicability: 4/10
- Latent Novelty Potential: 3/10
- Obscurity Advantage: 3/5
- Technical Timeliness: 2/10
Synthesized Summary
...its reliance on fundamentally weak vertex invariants and transforms with non-guaranteed termination presents significant limitations.
The dependence on expensive backtracking for hard cases suggests the core deterministic methods are insufficient.
Modern computing power doesn't fix these theoretical weaknesses...
...contemporary graph algorithms and machine learning approaches provide more robust and efficient ways to tackle symmetry and structural comparison challenges, rendering this paper's specific techniques largely obsolete.
Optimist's View
...its most promising latent potential for modern, unconventional research lies in its proposed hierarchical graph transform approach (Algorithms H/HA) designed to tackle "hard" graph instances like Strongly Regular Graphs (SRG) and Balanced Incomplete Block Design (BIBD) graphs.
The unconventional direction inspired by this paper is to create a conditional, multi-stage graph processing pipeline that leverages modern graph learning models but incorporates the concept of dynamic graph transformation triggered by the failure of an initial test.
Instead of just refining partitions ..., the system applies a graph transform ... to the graph or its ambiguous parts. This transformation aims to break symmetries and expose structural differences that were previously hidden.
The efficiency challenges of high-order transforms mentioned in 1984 are more manageable with modern hardware and distributed computing...
Skeptic's View
While the graph isomorphism problem remains relevant, the core methodology based on specific, relatively simple layer-based vertex invariants ... is fundamentally limited.
This paper likely faded into obscurity due to inherent limitations in the power and efficiency of its proposed heuristics, particularly when faced with known hard instances...
The attempt to overcome this via a hierarchy using graph transforms ... introduces its own set of problems, including non-guaranteed termination and potential graph size explosion...
Modern graph isomorphism solvers have significantly surpassed the techniques presented here...
Final Takeaway / Relevance
Ignore