Sparsity helps for k-independent set only below certain density thresholds, with new algorithms achieving O(min(n^{ωk/3} + m^{k/3}, n^k)) time and conditional lower bounds showing brute-force necessity above thresholds for many binary constraint families.
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Algorithms for LS Vertex Cover achieve ℓ^{f(k)} n^{O(1)} time for ℓ equal to h-index, treewidth, modular-width, or a new modular-decomposition degree parameter, and extend to weighted d-improving swaps.
Approximates large matrix multiplication via truncated SVD and circulant decompositions with O(n^2 log n) complexity and ~1% relative error, including LLM operation demonstrations.
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When Does Sparsity Help for k-Independent Set in Hypergraphs and Other Boolean CSPs?
Sparsity helps for k-independent set only below certain density thresholds, with new algorithms achieving O(min(n^{ωk/3} + m^{k/3}, n^k)) time and conditional lower bounds showing brute-force necessity above thresholds for many binary constraint families.
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Parameterized Local Search for Vertex Cover: When only the Search Radius is Crucial
Algorithms for LS Vertex Cover achieve ℓ^{f(k)} n^{O(1)} time for ℓ equal to h-index, treewidth, modular-width, or a new modular-decomposition degree parameter, and extend to weighted d-improving swaps.
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Efficient approximations of matrix multiplication using truncated decompositions
Approximates large matrix multiplication via truncated SVD and circulant decompositions with O(n^2 log n) complexity and ~1% relative error, including LLM operation demonstrations.
- Deterministic Monotone Min-Plus Product and Convolution