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Electronic Colloquium on Computational Complexity

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All reports by Author Kilian Risse:

TR21-021 | 18th February 2021
Per Austrin, Kilian Risse

Average-Case Perfect Matching Lower Bounds from Hardness of Tseitin Formulas

We study the complexity of proving that a sparse random regular graph on an odd number of vertices does not have a perfect matching, and related problems involving each vertex being matched some pre-specified number of times. We show that this requires proofs of degree $\Omega(n/\log n)$ in the Polynomial ... more >>>

TR19-174 | 2nd December 2019
Susanna de Rezende, Jakob Nordström, Kilian Risse, Dmitry Sokolov

Exponential Resolution Lower Bounds for Weak Pigeonhole Principle and Perfect Matching Formulas over Sparse Graphs

We show exponential lower bounds on resolution proof length for pigeonhole principle (PHP) formulas and perfect matching formulas over highly unbalanced, sparse expander graphs, thus answering the challenge to establish strong lower bounds in the regime between balanced constant-degree expanders as in [Ben-Sasson and Wigderson '01] and highly unbalanced, dense ... more >>>

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