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For example, if I have a cell with arrays listed inside:

C = {[1,2,3,4], [3,4], [2], [4,5,6], [4,5], [7]}

I want to output: 

D = {[1,2,3,4], [4,5,6], [7]}

What is the most efficient way to remove cell elements that are already included/subset in another larger element?

My existing algorithm loops through each element, compares it to each element in the new cell list and updates the new cell list accordingly but it is extremely slow and inefficient (my original cell contains >200 array elements).

ru111
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1 Answers1

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Here is an approach using ,very fast, matrix multiplication. You can convert C to a ,sparse, binary matrix b that each element of C is related to each row of the matrix. So columns [1 2 3 4] of the first row and columns [3 4] of the second row are set to 1 and so on. Multiplying the matrix by its transpose we can find the number of corresponding elements between all pairs of rows. using that information we can find cell elements that are subset of others.

C = {[1,2,3,4], [3,4], [2], [4,5,6], [4,5], [7]};
n = cellfun(@numel,C);      % find length of each element.
v = repelem(1:numel(C),n);  % generate indices for rows of the binary matrix
[~,~,u] = unique([C{:}]);   % generate indices for rows of the binary matrix
b = accumarray([v(:),u(:)],ones(size(v)),[],@max,[],true); % generate the binary matrix
s = b * b.';                % multiply by its transpose
s(1:size(s,1)+1:end) = 0;   % set diagonal elements to 0(we do not need self similarity)
result = C(max(s)<n)        % remove an element if it is a subset and preserve others
rahnema1
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    @SardarUsama Thanks! Answer updated! I tested `sparse` in Octave but MATLAB doesn't have such a signature. – rahnema1 Oct 21 '17 at 10:07
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    That is some serious clever magic - I'm curious as to how you got to this solution so quickly. Are some of these concepts common knowledge in computer science? e.g. "Multiplying the matrix by its transpose we can find the number of corresponding elements between all pairs of rows"? – ru111 Oct 21 '17 at 12:40
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    It requires basic knowledge of math but also needs some experiences in programming and playing with code. I have learned very things from Q/A in SO and other communities. – rahnema1 Oct 21 '17 at 13:08
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    @ru111. The concept of multiplying a matrix by its transpose is fairly common. I found the matrix construction to be the clever part here. – Mad Physicist May 06 '20 at 00:10