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.
Tight Hardness for Shortest Cycles and Paths in Sparse Graphs , booktitle =
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Partition ranks bound multiplicative complexity from below for constant-degree multilinear arithmetic circuits, generalizing Strassen's tensor-rank characterization.
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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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Partition Rank and Algebraic Circuit Lower Bounds
Partition ranks bound multiplicative complexity from below for constant-degree multilinear arithmetic circuits, generalizing Strassen's tensor-rank characterization.