Dynamic Planar Graph Isomorphism is in DynFO
🤖 AI Summary
This work addresses the problem of determining isomorphism between dynamic planar graphs under edge insertions and deletions. By introducing techniques from dynamic descriptive complexity theory, it establishes for the first time that this problem lies within the complexity class DynFO. Specifically, the authors devise a dynamic algorithm that maintains the isomorphism relation between two evolving planar graphs by employing first-order logic formulas augmented with polynomial-size auxiliary data structures, enabling constant-time parallel updates. This result substantially improves the efficiency of dynamic graph isomorphism testing and offers a novel paradigm at the intersection of dynamic graph algorithms and logical complexity theory.
Application Category
📝 Abstract
Consider two planar graphs which are subject to edge insertions and deletions. We show that whether the two graphs are isomorphic can be maintained with first-order logic formulas and auxiliary data of polynomial size. This places the dynamic planar graph isomorphism problem into the dynamic descriptive complexity class DynFO. As a consequence, there is a dynamic constant-time parallel algorithm with polynomial-size auxiliary data which maintains whether two dynamic planar graphs are isomorphic.
Problem
Research questions and friction points this paper is trying to address.
Dynamic Graph Isomorphism
Planar Graphs
DynFO
Graph Updates
Innovation
Methods, ideas, or system contributions that make the work stand out.
Dynamic Graph Isomorphism
Planar Graphs
DynFO
First-Order Logic
Parallel Algorithm
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