2008/12/15 by Pawel Gawrychowski, Gawrychowski, Pawel, Travis Gagie +1
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.0812.2868
arxiv created 2009/01/28 · arxiv updated 2009/12/01
A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves' depths, it minimizes the maximum of any leaf's weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, \Ohn log n-time algorithm for building them. Drmota and Szpankowski (2002) gave another \Ohn log n-time algorithm, which checks the Kraft Inequality in each step of a binary search. In this paper we show how Drmota and Szpankowski's algorithm can be made to run in linear time on a word RAM with (Ω(log n))-bit words. We also discuss how our solution applies to problems in data compression, group testing and circuit design.