algorithms-optimization / Randomized algorithms

The Arborescence-Sampling Barrier for Eulerian Tours

Sampling a nearly uniform Eulerian tour of a directed Eulerian multigraph was stuck at $mn$-type running times coming from arborescence sampling. A randomized algorithm achieves $\widetilde{O}(m^{3/2})$ worst case, breaking that barrier on sparse graphs.

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algorithms-optimizationMay 28, 2026Significance 15/100Registry: unreviewed

The Arborescence-Sampling Barrier for Eulerian Tours

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Sampling a nearly uniform Eulerian tour of a directed Eulerian multigraph was stuck at $mn$-type running times coming from arborescence sampling. A randomized algorithm achieves $\widetilde{O}(m^{3/2})$ worst case, breaking that barrier on sparse graphs.

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Sampling a nearly uniform Eulerian tour of a directed Eulerian multigraph was stuck at $mn$-type running times coming from arborescence sampling. A randomized algorithm achieves $\widetilde{O}(m^{3/2})$ worst case, breaking that barrier on sparse graphs.

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