arXiv subjects

Yusong Du

Publications and source records attributed to Yusong Du.

2 recordsLinked to original sources

arXiv2026

Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs

We refine Radhakrishnan's entropy proof of the Br\'egman-Minc bound by introducing a terminal-set framework in which selected vertices are revealed last. This gives new degree-sensitive upper bounds for the number of perfect matchings in bipartite graphs and an explicit formula for single-vertex terminal sets. The bounds recover the standard Br\'egman equality family and improve the estimate for certain nonuniform degree sequences. We also obtain a $C_4$-free refinement complementary to the edge-count bound of Araujo, Balogh and Wang.

math.CO↗

arXiv2020

An Improved Exact Sampling Algorithm for the Standard Normal Distribution

In 2016, Karney proposed an exact sampling algorithm for the standard normal distribution. In this paper, we study the computational complexity of this algorithm under the random deviate model. Specifically, Karney's algorithm requires the access to an infinite sequence of independently and uniformly random deviates over the range (0,1). We give an estimate of the expected number of uniform deviates used by this algorithm until outputting a sample value, and present an improved algorithm with lower uniform deviate consumption. The experimental results also shows that our improved algorithm has better performance than Karney's algorithm.

cs.DS↗