Capacitated Vertex Cover admits no k^{o(k)} n^{O(1)} algorithm under ETH, n^{O(tw)} is optimal even for tree-depth, and vertex integrity admits a vi^{O(vi^2)} n^{O(1)} algorithm via N-fold IP.
Graduate Texts in Mathematics
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Additive εn²-approximation for graph edit distance on VC-dimension-d graphs in n^{O(d/ε²)} time, with extensions to quadratic assignment problems and a Weisfeiler-Leman dimension bound for robust graph isomorphism.
Defines the untangling number for 3-periodic tangles and proves that ground states for infinite open curves are crystallographic rod packings.
In combinatorially sphere-like ranked posets of rank k where rank-(k-2) elements have even covering degree, the maximal elements admit a proper 2-coloring.
Infant daily visual experiences of objects are dominated by repeated instances of few exemplars in lumpy similarity clusters, enabling category generalization from small training sets in computational models.
In finite-depth random linear optical circuits, entanglement grows at most diffusively and robust circuit complexity scales similarly, with depth bounds ensuring near-maximal subsystem entanglement and closeness to Haar unitaries.
citing papers explorer
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Parameterized Capacitated Vertex Cover Revisited
Capacitated Vertex Cover admits no k^{o(k)} n^{O(1)} algorithm under ETH, n^{O(tw)} is optimal even for tree-depth, and vertex integrity admits a vi^{O(vi^2)} n^{O(1)} algorithm via N-fold IP.
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Robust Graph Isomorphism, Quadratic Assignment and VC Dimension
Additive εn²-approximation for graph edit distance on VC-dimension-d graphs in n^{O(d/ε²)} time, with extensions to quadratic assignment problems and a Weisfeiler-Leman dimension bound for robust graph isomorphism.
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The untangling number of 3-periodic tangles
Defines the untangling number for 3-periodic tangles and proves that ground states for infinite open curves are crystallographic rod packings.
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$2$-colourability of the maximum ranked elements of a combinatorially sphere-like ranked poset
In combinatorially sphere-like ranked posets of rank k where rank-(k-2) elements have even covering degree, the maximal elements admit a proper 2-coloring.
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A solution to generalized learning from small training sets found in infant repeated visual experiences of individual objects
Infant daily visual experiences of objects are dominated by repeated instances of few exemplars in lumpy similarity clusters, enabling category generalization from small training sets in computational models.
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Entanglement and circuit complexity in finite-depth random linear optical networks
In finite-depth random linear optical circuits, entanglement grows at most diffusively and robust circuit complexity scales similarly, with depth bounds ensuring near-maximal subsystem entanglement and closeness to Haar unitaries.