Problem
Research questions and friction points this paper is trying to address.
Label Propagation
Graph Transformation
Robustness Analysis
On Approximate Reconfigurability of Label Cover
🤖 AI Summary
This paper investigates the approximate reconfigurability of Label Cover: given two satisfying label assignments, can one be transformed into the other via a sequence of local, single-vertex relabelings—each preserving a high fraction of satisfied constraints (“looking correct” for as long as possible)? We formally define and characterize approximate reconfigurability thresholds for structured instances, including biregular graphs, balanced bipartite graphs, and graphs with high average degree. Our approach integrates PCP-based hardness techniques, spectral and combinatorial graph expansion analysis, coupling of random walks, and combinatorial reconfiguration theory. The main result establishes NP-hardness of approximate reconfigurability under the assumption NP ≠ RP, thereby pinning down its exact computational complexity. This resolves a fundamental question in constraint satisfaction reconfiguration and reveals deep connections to the PCP Theorem and the theory of approximation hardness.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Robust Errors
Estimation Methodology
Graph Reconstruction
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