By Topic

An efficient algorithm for row minima computations on basic reconfigurable meshes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Nakano, K. ; Dept. of Electr. Eng. & Comput. Sci., Nagoya Inst. of Technol., Japan ; Olariu, S.

A matrix A of size m×n containing items from a totally ordered universe is termed monotone if, for every i, j, 1⩽i<j⩽m, the minimum value in row j lies below or to the right of the minimum in row i monotone matrices, and variations thereof, are known to have many important applications. In particular, the problem of computing the row minima of a monotone matrix is of import in image processing, pattern recognition, text editing, facility location, optimization, and VLSI. Our first main contribution is to exhibit a number of nontrivial lower bounds for matrix search problems. These lower bound results hold for arbitrary, infinite, two-dimensional reconfigurable meshes as long as the input is pretiled onto a contiguous n×n submesh thereof. Specifically in this context, we show that every algorithm that solves the problem of computing the minimum of an n×n matrix must take Ω(log log n) time. The same lower bound is shown to hold for the problem of computing the minimum in each row of an arbitrary n×n matrix. As a by product, we obtain an Ω(log log n) time lower bound for the problem of selecting the kth smallest item in a monotone matrix, thus extending the best previously known lower bound for selection on the reconfigurable mesh. Finally, we show an Ω(√loglogn) time lower bound for the task of computing the row minima of a monotone n×n matrix. Our second main contribution is to provide a nearly optimal algorithm for the row-minima problem: With a monotone matrix of size m×n with m⩽n pretiled, one item per processor, onto a basic reconfigurable mesh of the same size, our row-minima algorithm runs in O(log n) time if 1⩽m⩽2 and in O(logn/logm loglog m) time if m>2. In case m=nε for some constant ε, (0<ε⩽1), our algorithm runs in O(log log n) time

Published in:

Parallel and Distributed Systems, IEEE Transactions on  (Volume:9 ,  Issue: 6 )