How to optimize the following algorithm?

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C Zeng 2013-6-6

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https://ww2.mathworks.cn/matlabcentral/answers/78220-how-to-optimize-the-following-algorithm

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)=[];