Author

Edward Pyne

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Preprint Aug 2026

Graph Spectral Sparsification is in Catalytic Logspace

This work analyzes effective-resistance sparsification using a pessimistic estimator that can itself be computed in catalytic logspace and shows that such a pessimistic estimator can be transformed into an algorithm that performs an in-place compression of a string with bad potential.

Cassandra Marcussen, Edward Pyne, R. Rubinfeld · 0 citations

Jul 2026

Graph k-Coloring in Average Sublinear Time

The main result shows that the exact average-case complexity of this fundamental problem is $\Theta(nk)$ for every $k \leq n^{c'}$ and some $c'\in (0, 1)$, and reveals the average sublinear nature of $k$-colorability: the average-case complexity is linear in $n$, and thus sublinear in the size of the input.

Cassandra Marcussen, Edward Pyne, R. Rubinfeld et al. · arXiv.org · 0 citations