Alphabetic Minimax Trees of Degree at Most t

Problems in circuit fan-out reduction motivate the study of constructing various types of weighted trees that are optimal with respect to maximum weighted path length. An upper bound on the maximum weighted path length and an efficient construction algorithm will be presented for trees of degree at most t, along with their implications for circuit fan-out reduction. Key words, optimal weighted tree, minimax tree, t-ary tree, fanout reduction, logical circuits In this paper we consider the problem of constructing, for any list w1,. W of integers, a tree T with maximum degree at most (where _-> 2 is a fixed integer) and leaves vl, , vn in left to right order such that fT(wl,’", w,) maxl= 1 and w_- 1 +max (wi+l, , wi+) for some s <and with 0 <<n-s, then replace the s weights W+l," , w+ by the single weight 1 max (wi+, ", wi+). * Received by the editors May 2, 1983, and in revised form May 21, 1984. t IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598. $ IBM Research Laboratory, San Jose, California 95193.