Searching Monotone Multi-dimensional Arrays
  In this paper we investigate the problem of searching monotone multi-dimensional arrays. We generalize Linial and Saks' search algorithm \cite{LS1} for monotone 3-dimensional arrays to $d$-dimensions with $d\geq 4$. Our new search algorithm is asymptotically optimal for $d=4$. 
Yongxi Cheng, Xiaoming Sun, Yiqun Lisa Yin