Cache-Oblivious Selection in Sorted X+Y Matrices

TL;DR

This paper presents a cache-oblivious algorithm for selecting the k-th smallest element in a matrix formed by adding two sorted arrays, significantly reducing input/output operations and improving efficiency.

Contribution

It extends Frederickson and Johnson's selection algorithm to be cache-oblivious, achieving optimal IO efficiency without prior knowledge of memory block size.

Findings

Achieves O((m+n)/B) IO complexity

Improves practical efficiency of selection in sorted matrices

Extends existing algorithms to cache-oblivious model

Abstract

Let X[0..n-1] and Y[0..m-1] be two sorted arrays, and define the mxn matrix A by A[j][i]=X[i]+Y[j]. Frederickson and Johnson gave an efficient algorithm for selecting the k-th smallest element from A. We show how to make this algorithm IO-efficient. Our cache-oblivious algorithm performs O((m+n)/B) IOs, where B is the block size of memory transfers.