Reproduce “Hardness Results for Approximate Distance Labeling in Sparse Graphs” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Tsvi Kopelowitz, Ariel Korin, Liam Roditty
The authors prove a lower bound for distance labels in sparse, unweighted undirected graphs, where a decoder estimates vertex distance from two local labels. They construct graphs with unique short paths that encode bits, so deleting a path forces a larger distance. For infinitely many graph sizes, stretch strictly below 1.5 requires labels of size Ω(SumIndex(n)/2^(C₂√log n)) when k=2; near-linear size is conditional on a SumIndex conjecture.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.