We simplify algorithms for Knapsack, output-sensitive Subset Sum, and near-convex min-plus convolution. For bounded Knapsack, we give a deterministic algorithm using $O(N+W^2\log^3(W+2))$ arithmetic and comparison operations, where $W$ is the maximum item weight and $N$ counts input records with binary-encoded multipli...
This work derandomize the $3$-cut algorithm using a deterministic near-minimum-cut skeleton, and derandomize the reduction using a specialized $4$-cut algorithm using the skeleton, the constructive light-cut bounds, and the deterministic spectral sparsifier of BSS12.
Deterministic expander decomposition, along with replacing vertices by fixed expander graphs to achieve approximate regularity, extends these algorithms to general graphs and evaluates the resulting conditional-expectation scores in two ways.
Let $A, B \in \mathbb{Z}_{\ge 0}^n$ be nonnegative vectors and let $t = |\operatorname{supp}(A \star B)|$. We give a Las Vegas algorithm that computes $A \star B$ in $O(t \log t)$ expected time. More generally, for every $0<\delta \le \frac{1}{2}$, the algorithm terminates within $O(t \log t \log \frac{1}{\delta})$ tim...
Trevor Vaughn· 0 citations
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