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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DSQ is W[1]-hard on degeneracy-2 and K_{3,3}-free graphs but FPT parameterized by solution size plus treewidth, FPT on nowhere dense classes, and admits subexponential algorithms on apex-minor-free graphs via bidimensionality.
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
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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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Dominating Set with Quotas: Balancing Coverage and Constraints
DSQ is W[1]-hard on degeneracy-2 and K_{3,3}-free graphs but FPT parameterized by solution size plus treewidth, FPT on nowhere dense classes, and admits subexponential algorithms on apex-minor-free graphs via bidimensionality.
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Lower overhead fault-tolerant building blocks for noisy quantum computers
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.