An Efficient Algorithm for Row Minima
Computations on Basic Reconfigurable
Meshes
Koji Nakano, Member, IEEE, and Stephan Olariu, Member, IEEE
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED
SYSTEM, VOL. 9, JUNE 1998, pp. 561-569
Abstract
The problem of computing the minima of monotone matrix is import
in image processing, pattern recognition, text editing , facility location,
optimization , and VLSI. Our row-minima algorithm runs in O( l o gn )
t i me i f 1 ≦ m≦ 2 a n d i n O(
log n
log log m ) t i me i f m > 2 .
log m
1. Introduction
Matrix A is termed monotone if ,for every i , j ,1≦ i ≦ j ≦m, the
smallest value in row j lies below or to the right of the smallest value in
row i .
2
13
5
10
20
16
3
6
9
21
6
10
9
4
10
9
8
8
17
9
11
5
22
17
19
2. Prefix-Maxima-1
2-1. O(1) time for computing the prefix maxima of n items on a BRM
of size n x n .
2-2. O(
log n
) time for computing the prefix maxima of n items in one
log m
row of a BRM of size m x n with 2≦ m≦ n .
3. Selective-Row-Minima
Step1.
6
4
4
2
3
6
1
5
3
8
9
9
R 1 ,1
5
R 2 ,1
3
4
5
10
11
7
13
R2
R1
1
10
4
6
9
8
8
10
12
R 1 ,2
2
R 2 ,2
13
15
Step2.
a1,1
a2,1
a1,2
a2,2
Step3.
T1
T2
Step4. Using the 2-2. ,the compute the minimun in the first row of each
Ti in O(
log N  log K
)
log M  log K
= O(
log N
) time.
log M
4. Row-Minima
2
Step1.
3
T1
6
4
9
T2
8
7
9
T3
8
Step2.
Using selective Row
Minima compute the
minima of the itms in
the first row in
log n
O(
) time.
log m
T1
T2
T3
Step3.
c1
T1
R1
c2
R2
T2
c3
T3
R3
Step4. For log log m iterations ,repeat Step 1-3 above in each submesh.
5. Concluding Remarks
Created by :Kuen-Feng Huang
Date : Feb. 22, 2000