Cache-oblivious selection in sorted X+Y matrices

Authors:
Mark de Berg;Shripad Thite
Affiliations:
Department of Computer Science, Technische Universiteit Eindhoven, The Netherlands;Center for the Mathematics of Information (IST), California Institute of Technology, USA
Venue:
Information Processing Letters
Year:
2008

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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 [G.N. Frederickson, D.B. Johnson, Generalized selection and ranking: Sorted matrices, SIAM J. Computing 13 (1984) 14-30] gave an efficient algorithm for selecting the kth 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.