@Article{BFPRT73, author = { Manual Blum and Robert W. Floyd and Vaughan Pratt and Ronald L. Rivest and Robert E. Tarjan }, title = { Time Bounds for Selection }, journal = { Journal of Computer and System Sciences }, OPTyear = { 1973 }, OPTmonth = { August }, date = { 1973-08 }, volume = { 7 }, number = { 4 }, pages = { 448--461 }, doi = { 10.1016/S0022-0000(73)80033-9 }, url = { http://www.sciencedirect.com/science/article/pii/S0022000073800339 }, abstract = { The number of comparisons required to select the $i$-th smallest of $n$ numbers is shown to be at most a linear function of $n$ by analysis of a new selection algorithm---PICK. Specifically, no more than $5.4305 n$ comparisons are ever required. This bound is improved for extreme values of $i$, and a new lower bound on the requisite number of comparisons is also proved. }, }