Multiway In-Place Merging

Abstract. We present an algorithm for asymptotically efficient multiway blockwise in-place merging. Given an array A containing sorted subsequences A1, . . . , Ak of respective lengths n1, . . . , nk, where k i=1 ni = n, we assume that extra k·s elements (so called buffer elements) are positioned at the very end of array A, and that the lengths n1, . . . , nk are positive integer multiples of some parameter s (i.e., multiples of a given block of length s). The number of input sequences k is a fixed constant parameter, not dependent on the lengths of input sequences. Then our algorithm merges the subsequences A1, . . . , Ak into a single sorted sequence, performing Θ(log k·n) + O((n/s)2 ) + O(s· log s) element comparisons and 3·n + O(s·log s) element moves.1 Then, for s = n2/3 /(log n)1/3 , this gives an algorithm performing Θ(log k·n) + O((n·log n)2/3 ) comparisons and 3·n + O((n·log n)2/3 ) moves. That is, our algorithm runs in linear time, with an asymptotically optimal...

• Type: Conference
• Year: 2009
• Where: FCT
• Authors: Viliam Geffert, Jozef Gajdos
• Keywords: Algorithm, Blockwise In-place Merging, FCT 2009, Input Sequences