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This work proves a new upper bound of $\widetilde{O}\!\left(\frac{q\rho^{2q-3}}{\varepsilon^2 (q-2)!^2}\right)$ on the sample complexity of testing the $\rho$-independent set property.
We present a simple linear-time algorithm that outputs an Eulerian tour of an undirected multigraph with $n$ vertices and $m$ edges, if one exists, in $O(m)$ time and using $O(n)$ words of working memory. The input is given as read-only adjacency lists, and the output is written to an append-only stream in traversal or...
This paper provides the first truly linear-time approximation scheme for the Densest Subgraph Problem, and uses assignments arising from a flow-based formulation together with a structural carving lemma to progressively carve "sparse" parts of the graph while nearly preserving the densest subgraph.
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