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.
Faster Combinatorial k-Clique Algorithms , booktitle =
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Constructs infinite 3⁺-parameterized-square-free ternary words and 3⁺-order-preserving-square-free binary words via morphic substitutions, plus reports longest finite ℓ⁺-square-free words under several equivalences.
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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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Relaxation of Square-Freeness
Constructs infinite 3⁺-parameterized-square-free ternary words and 3⁺-order-preserving-square-free binary words via morphic substitutions, plus reports longest finite ℓ⁺-square-free words under several equivalences.