Parallel algorithm for matroid basis computation with O(n^{1/3} log^{1/3} n) round complexity, nearly matching the KUW lower bound.
Liu, and Aaron Sidford
5 Pith papers cite this work, alongside 6 external citations. Polarity classification is still indexing.
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representative citing papers
A deterministic O(m)-competitive algorithm for parametrized MSS on weighted stars is tight, and improved lower bounds on HSTs rule out constant-competitive algorithms for m≥4.
Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
Incremental (1-ε)-approximate s-t max-flow algorithm achieving Õ(m + n F*/ε) total update time, first with polylog amortized updates for dense graphs.
Every abelian Cayley graph admits an optimal O(ε^{-2} log |G|)-generator weighted Cayley spectral sparsifier, proved via a character-symmetry volume bound on a sparsification polytope.
citing papers explorer
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A Near-Optimal Parallel Algorithm for Finding Matroid Bases
Parallel algorithm for matroid basis computation with O(n^{1/3} log^{1/3} n) round complexity, nearly matching the KUW lower bound.
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Improved Algorithms and Lower Bounds for Parametrized Metrical Service Systems
A deterministic O(m)-competitive algorithm for parametrized MSS on weighted stars is tight, and improved lower bounds on HSTs rule out constant-competitive algorithms for m≥4.
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Quantum Cut Sparsifiers
Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
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Incremental Approximate Maximum Flow via Residual Graph Sparsification
Incremental (1-ε)-approximate s-t max-flow algorithm achieving Õ(m + n F*/ε) total update time, first with polylog amortized updates for dense graphs.
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Optimal Sparsifiers for Abelian Cayley Graphs
Every abelian Cayley graph admits an optimal O(ε^{-2} log |G|)-generator weighted Cayley spectral sparsifier, proved via a character-symmetry volume bound on a sparsification polytope.