7 papers
Asymptotically sharp bounds for affine subspace statistics in
Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov
Given a subset , we can consider the distribution of the intersection size of with a uniformly random -flat . Motivated by the edge statistics…
A GPU-Accelerated Framework for Multi-Attribute Range Filtered Approximate Nearest Neighbor Search
Zhonggen Li, Haoran Yu, Zixuan Xu +2
Range-filtered approximate nearest neighbor search (RFANNS) is increasingly critical for modern vector databases. However, existing solutions suffer from severe index inflation and…
Vertex-minor universality of a random graph
Ting-Wei Chao, Zixuan Xu
Given a graph and a vertex , a local complementation at on is an operation that replaces the induced graph on the neighborhood of by its complement. A gr…
Even-degeneracy of a random graph
Ting-Wei Chao, Dingding Dong, Zixuan Xu
A graph is even-degenerate if one can iteratively remove a vertex of even degree at each step until at most one edge remains. Recently, Janzer and Yip showed that the ErdÅs--Renyi…
Affine Subspace Statistics in the Hypercube
Zixuan Xu
We study the intersection statistics of affine subspaces in the hypercube , motivated by recent work of Alon, Axenovich, and Goldwasser on the intersection statisti…
Nondegenerate hyperplane covers of the hypercube
Lisa Sauermann, Zixuan Xu
We consider collections of hyperplanes in covering all vertices of the -dimensional hypercube , which satisfy the following nondegeneracy condition: Fo…