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# How to optimize the following algorithm?

Asked by C Zeng on 6 Jun 2013

I have a large matrix-M, and the rows have been sorted based on the value on some entry. Next I want to identify all rows that can be dominated, i.e., row #i is dominated by #j if j<i and M(j,:)<=M(i,:).

If rows #i is dominated, we can remove row i. I notice that remove row #i takes a lot of time for a large matrix so I set a index() and each time if it is dominated then index(i)=1. At last, M(index)=[]. (remove those dominated rows at last)

I run my code several times, and find out there is a bottleneck-N loops. Below I show some code:

```for i=3:N
j=2; %j from i-1 to may be faster!
while j<=i-1
if all(M(j,1:N)<=M(i,1:N))
idx(i)=1;
break;
else
j=j+1;
end
end
end
```
`    M(idx)=[];`

I am thinking if someone can help me to optimize the code? Can we do better here? Thanks.

Sean de Wolski on 6 Jun 2013

Is idx preallocated?

```idx = zeros(N,1);
```
C Zeng on 6 Jun 2013

Yes, Sean, you are right. That is the index that records which row is dominated, I will delete them at last.

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