Notes on searching in multidimensional monotone arrays

Author

Aggarwal, Alok ; Park, James

Author_Institution

IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA

fYear

1988

fDate

24-26 Oct 1988

Firstpage

497

Lastpage

512

Abstract

A two-dimensional array A={a_i,j} is called monotone if the maximum entry in its ith row lies below or to the right of the maximum entry in its (i- 1)-st row. An array A is called totally monotone if every 2×2 subarray (i.e., every 2×2 minor) is monotone. The notion of two-dimensional totally monotone arrays is generalized to multidimensional arrays, and a wide variety of problems are exhibited involving computational geometry, dynamic programming, VLSI river routing, and finding certain kinds of shortest paths that can be solved efficiently by finding maxima in totally monotone arrays

Keywords

computational complexity; graph theory; search problems; (i- 1)-st row; 2×2 minor; 2×2 subarray; VLSI river routing; computational geometry; dynamic programming; ith row; maximum entry; multidimensional monotone arrays; searching; shortest paths; totally monotone; two-dimensional array; two-dimensional totally monotone arrays; Clocks; Computational geometry; Computer science; Contracts; Euclidean distance; Multidimensional systems; Rivers; Routing; Springs; Very large scale integration;

fLanguage

English

Publisher

ieee

Conference_Titel

Foundations of Computer Science, 1988., 29th Annual Symposium on

Conference_Location

White Plains, NY

Print_ISBN

0-8186-0877-3

Type

conf

DOI

10.1109/SFCS.1988.21966

Filename

21966