(Supplement of Page 5) Four techniques for finding lower bounds. (1) - PDF document

(Supplement of Page 5) Four techniques for finding lower bounds. (1) Comparison tree. (2) A particular problem instance. (3) State transition. (4) Problem reduction.

(Supplement of Page 7) The progress of any comparison-based searching algorithm can be described by a path in a binary comparison tree. Each internal node of the tree represents a comparison between x and some A [ i ]. Since the tree contains at least n internal nodes, which represent the n possible successful occurrences of x in A , the tree depth is � (log n ). ⇒ Comparison-based searching has a lower bound of � (log n ).

(Supplement of Page 19) For example, n = 5. There are five node-disjoint paths from 00000 to 01111 whose maximal length is n + 1 = 6. (00000, 01000, 01100, 01110, 01111) (00000, 00100, 00110, 00111, 01111) (00000, 00010, 00011, 01011, 01111) (00000, 00001, 01001, 01101, 01111) (00000, 10000, 11000, 11100, 11110, 11111, 01111)