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.
Listing, Verifying and Counting Lowest Common Ancestors in DAGs: Algorithms and Fine-Grained Lower Bounds , booktitle =
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Global lca-DAGs are characterized via join semi-lattices and forbidden topological minors, with a polynomial-time recognition algorithm.
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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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Global Least Common Ancestor (LCA) Networks
Global lca-DAGs are characterized via join semi-lattices and forbidden topological minors, with a polynomial-time recognition algorithm.