in reply to Re^3: Help required in optimizing the output (PERL)
in thread Help required in optimizing the output (PERL)

This uses bitstrings to represent the keywords contained within each para. This means:

It may make some sense to perform a second filtration to attempt to exclude further paras where a later inclusion covered the additions of an earlier inclusion. This might even be made iterative until no further exclusions can be made.

For my testcase this refinement made no difference, so I removed the code. 

#! perl -slw
use strict;

## Load the words list
my @idx;
{
    local( @ARGV ) = '845818.idx';
    @idx = <>;
};
chomp @idx; print "Words: ", ~~@idx;

$/ = ''; ## Paragraph mode

## hash of bitstrings; keyed by para number; 
## each bit represents one word in @idx
my %paras; 
while( <> ) {
    $paras{ $. } //= ''; ## Initalise bitstring
    for my $i ( 0 .. $#idx ) { ## for each word index
        my $word = $idx[ $i ];  ## get the word
        if( m[\b\Q$word]i ) { ## If it is found in the paragraph
            ## Set the bit for this word in the bit string for this pa
+ra
            vec( $paras{ $. }, $i, 1 ) = 1;
        }
    }
}
print "Paras: ", scalar keys %paras;

## Order keys (para numbers) by the bits set 
## (words found) in bitstring (descending)
my @parasByWordCount = sort {
    unpack( '%32b*', $paras{ $b } ) <=> unpack( '%32b*', $paras{ $a } 
+)
} keys %paras;

## Initialise the minimal set with the para 
## that contains the most words
my @set = shift @parasByWordCount;

## And initalise the mask to its bitstring
my $mask = $paras{ $set[ 0 ] };

## While there are still paras to consider
## (considering them in descending order)
while( @parasByWordCount ) {
    ## Get the next one to be considered
    my $next = shift @parasByWordCount;

    ## If adding (ORing) the next bitstring with the mask makes a diff
+erence
    if( ( $mask | $paras{ $next } ) ne $mask ) {
        ## $next contains new paras not yet covered, 
        ## so add it to the set and the mask
        push @set, $next;
        $mask |= $paras{ $next }
    }
    ## otherwise just discard it
}

## Now we have a set of paras that covers all the words
## Is it minimal? For my artificial testcase it appears to be
## But I offer no proof. That's for others (probably to discount).

printf "All the words are covered by %d paras:\n", scalar @set;
printf "%3d : %s\n", $_, unpack 'b*', $paras{ $_ } for sort{ $a<=>$b }
+ @set;
printf "All : %s\n", unpack 'b*', $mask;

__END__
c:\test>845818 fannyhill.txt
Words: 599
Paras: 612
All the words are covered by 34 paras:
 62 : 1100001001100000100011100000111000000110010000000000000000000110
+110100000100000000000000000010110000001000100000000010000001100000000
+000000100010000000000100000001001000000010011000000000100010100000000
+111001000001011001000111100000001000110000100101100110000000110010000
+000000000010000010000000000000000000000001000000000101000001111000010
+100000011010000000101011000101101100000000000000100000010110001010000
+100000000101100001000000001000000100101000000010010000000100011100001
+001001000000000000100001000000100011000101001110000101000100011100000
+0010001000001000011101101110110100100001110100001000
 82 : 1110000000001000101011100011011011010100000000100000011000000110
+110000000010000000000100000010000110101000111000100000100010000001000
+000000101011000000000100110000000001010000110000000000000000100010000
+011001110010011100100000001010000001101000110000000010000001011001100
+010000000010000000100000000100010000001001000000000000010000011101100
+001000101110000000110110011100011000010010000000000000000000010001000
+000100000001000000000000010000000000000100001001010000000000000100000
+000011001000000001100000000001000011010110010010010010010101100010000
+0001110000010000000101001100001101000001101000111000
139 : 1110000001101000100011111000011011010110000010000010011000100110
+100000000000100000001000000001000000000000000100000100000000010001000
+000000101000000000000000000011000001010000010011001100000010110000000
+011011100001011001000110001110000000101000100000000111011000011000000
+010000001100000010101000000010000000000001000000000001001001000000010
+000000001100100100100010100110010001000000000000000000010000001010000
+000000000000000000000000000000000101100000000000011000001010000100101
+000000001000000010000100000000100111111110010010000000001100110000000
+0000111000001010000111001100000100010000100000101100
197 : 1100000000000000100011100000011011000100010100001010000100100110
+100000010000000010000100000000010000001000100000000001000000000000011
+000000100000010000100000000110001001000000110001000000000010100000000
+011001101000011001000000011110001000101000100000000011001000111000000
+010000000000000010100000000111100000001001100000000000000000010100010
+000000001010110000110010111000001000010010000001010010010000001010000
+011010000000000001000000000110100101011000000000000010000000000000000
+000001010000000000000000000000100011011110000010000000001100011010001
+0101100000000000000001001100100101110000100100110000
248 : 1101000101100000100011111000011011000101001100000000000000000100
+000000001000000000000100110000100000000000000001000000010000001000011
+000000010010000000000000110000000001110100011000001000001100100100000
+011000000001011010000110101110101000100000110001001000000000000000010
+001000000001000100101100010000000011000001000000000000000011010000000
+000000001011000000110010100110000100011000001101000000000000001000000
+001000100000010000100000000001000100000000000000011000010000000100000
+000000000000000001000000011100000111000110001010000000010101011010000
+0000110000000000000100000000000100011000100000101001
253 : 1110000001100000001011100011011011000100111100000011010000000110
+001000000100000010000100000000000111101000100100000000000000000001011
+000000000000010010000000110001000001000010010000001100000000100010000
+011101100001111000000000001110001100100000100010000010000000010010000
+111100000100111001001010000000000000001001000000100011000001011000001
+000101001110100000110010000100000000010011000000000011010000001010010
+000110000000010010000000000100100000000100000010000000010000000100001
+010100001001000000100000000001101111000100101010011000110100011000000
+000100000010100000010000001110010101100010110
290 : 1100000001100001101011100000011011000100000000000000010000010010
+110000000000110000001110000010000001001110100000000001000000100000000
+000000010000000000000000100001000011000000010101001010101000100110000
+011001100000111000000110101111000000100000110010000010000000000000000
+000000100110000001001100000001000000000011000000100100001101110000000
+000000001011100000100010010000011000100000000010010000000001000001000
+000000000000000000001010000000100101000000010000011100000100001100100
+010000000010101010100010000100000111010000010010011000001100000010001
+0000110000010100000111000000010100110001100000101010
307 : 1100000000000000100011100011011011010110000010100001011000100111
+100000000010000000000000000000001000001000100000000001100001001001011
+010000101100010100000100000010000001000000010001000010000000100000000
+011100000000011000000000001110000000100000100001001011011001000010000
+010000001010100001111000010001100100000001001001100001001000010000010
+000001001010100000110011101000111000010010001100000000010000000000100
+000000000000000000000000000000100101000100000000110000101000000110101
+000010011000100000000001000000000011000101001000100000110110000000000
+0001100000010000011111101100000111011000111000111001
326 : 1101000010000010100011100000100011000100001000000000110000000110
+000000000000000010000100000000001001000000000000010000000010000001000
+000100100000010100001000000000000001001000110000000000000010000001010
+011001110011011000010111001010000000100000110000000011000000000000000
+001000000010101000001000000001000000000011000000000001000001010001010
+000000001110000000100010100100000001000000010011000000110000010000000
+110010000001100010010000000000100000000100000000011000010000000100000
+000000000000110010010000011110000001110000100010000001000100010000000
+0000000000010000100101001100000101010010100000101100
335 : 1100000000001000100011110011111011011100001100100010000000010110
+001000000110100100000100000000111000001000100000010000100011100000011
+001100001000100010110000111000001001100000011011000100001000110001000
+011001000010111101001000011111001100101000110001001111110111011000000
+010110011000101011110000000001011000001001001000100101011000011100011
+000000001111100000110010110000101000010110000000000100110110011000000
+001000000111010001100010000100001000000001101000010000011000001111001
+000000001100000000000001011100100111110111110010110000100100011100000
+0001111100100100011111111100100111010011111000010000
383 : 1111010000000010100011111100011011001100000100001000001001100110
+100000000100100100000110000000000000001000100000000000000010100100011
+000000010010010010000010000000000011100000010000000000001100110010000
+011101100001011011000000001110011000110001100101000100000100000010000
+001000101000101001000000100001000000000001000010001001010000011000000
+000100001110000000100010110100101000000000001000000000000000000000010
+000000100000000000000000000101000100000000000000000000100000000100100
+000000001000000000000000000001101101110010100010100001111110011001000
+0001000000000000000101101110100100011100101000011000
384 : 1100010001100010100011111000011011000100110000000000010000000111
+100000000000000000100101000000000000001010000100000000000010000001000
+000011001000000000001001001001000011000000010000000000000000110000000
+011000000001111100000000001010011000101000100100001010000000000000010
+000000100000010000101000000000000010000000000000000001000001010001000
+000110011110000001100111100101110000010010000010000000000000001010000
+001000000000000000001000000000000111000000000000010000010000000100100
+000001000010000010100000010100000111010110001110111001110110000000000
+0000111000000000000101011110100101010000101010001100
385 : 1100000000000000110111110100011011001100010100000010010100000110
+100000000110000010100100000000000100011000100100000000010000000001000
+000111000010000010110100000011001001000010010100000100000001100010000
+011001000000011000101000001110001101101000110011001111000100111010000
+111000001010000001000000000001101010000001000000001000000001010000010
+010011001010100000110011111000110001010010000000000010010100011000000
+011000100000000000100000000000000000000100001010000000001000000100100
+000000000001000000000100000100000111010110010010011000010101011110000
+0001111101000001010111001110010101000000101000111100
392 : 1101000001100000100011101111011011111100001010100010000000000110
+110010000000000001000101000100001110011001000000000000000000000100011
+001000110011100011100000001011001001001010110001100010000000000001000
+011100000001011100000000001010000000100000100010000011000000100000000
+011000010000000000101000000001001010000001000000000010000000010111010
+001001001011110010110011100100011100010000001100010100000000010000000
+000000000000000000000110100000000110000000101010000000010100010110110
+000000000001001000000000000000000111010110110010100000001100011010100
+0000111000010000000111100000110101110010101000101001
393 : 1100001011111000110011100011011011010100001100101000100000000110
+100010001000100010100100000001000111001110110000000010100000100001010
+000010100010000011000110110000000101010010010000001010001110000000000
+011001000001011011100000001010001000100000100001011110001000010100001
+010100000000101001001010000000001010000001110001111000010001111000010
+000100001110110001110010011100011001010011000010000000000101010000000
+000110001100000000000010001000100110100110100000000000000101000110100
+000000001000101011100001011001000011110111001010011000011101011000001
+1001110000010100000111110010110100000000100000101101
395 : 1110000001101100100011100011111011000110000100101001000010000110
+001100001000000000001100000000000100001010100001001000000010100001010
+000010100000100000001110110011010001010000010000001000000001110101001
+111001101011111011000000001010010000110001100000011011001001010100100
+001010101100110010111000010000001010001001111111000011010000011100001
+000001001011110100100010111101011101010111000001010001110001011000000
+001010100001010000100100010000100110011101000100000000000100100110111
+000000011000110110000011000000110111010110001110000000011100111100010
+0000110000010000000101001110100101010000101100011100
398 : 1100000001100000100111101000011011000100001100100100000000001111
+001000001000101000110110000000000101001000100000000000000000000000000
+000000100000010000100000000001000011000010000000000000101100100010000
+111000000000011000000111001111000000100010100000001011000101100010000
+000000101000100001000000100101101000011011110000101001000001010001010
+000001001010100000101111000100111000010011000000010110011101100000000
+101001000000000000000000000000100100000000001000010000010011000110001
+000001000000110000000000011000000111010000001110000000000101011100010
+0001100000000000100111001110110110010100101100011000
404 : 1100000001110010100011110000011011011100011100101111010010001111
+000011000000010100000101000111011111101000100001000000000111000001011
+000110100010100011111100110001000001100000011001101011101000101101000
+011001110001011111000110001011001110100101110011101111011000011110100
+110000001100000010101000000101001010000001001011110011011001011101111
+000000011011110001100011111101011111010000001101000010110100101000000
+001000010000000011101110001000100101001110000001000010001100000110101
+001000101000000010001000011000101111110111011010111011110101111101001
+0001111000111100011101101110110101011001101000111101
415 : 1110000000000001100011100000011011000100000000001010001001000111
+001000000110000100001100000000111000001000000100101010000001000000011
+100000100000010100110000001001001001010000011001000000100010100100000
+110101000001111101000110111110000000100010100001111011011111011000000
+101001011000011000000000011101000000000001001000100000010000000000000
+000010001011100100100011101100111001010000000000000000110000001110000
+000100001010000001000001000000000100100000000000011111101011000110001
+000100000010000001000011000010000111110100110000000010011100000010101
+101011100010101000010100111011010101000011100
421 : 1110100000001100100011100011011011000101000001110010000001000111
+000000000010000000000100000011011110001000100000111000100001100000011
+000000101100000010000100000110000001010000010001101100111000000000000
+111001000000011101000110101111000010101000100000011011111001010000001
+010101011000100011100000010111000000001001101001100101001000000001111
+000000001010100000110010101001111100000010000000001100010100000000001
+000010000001100011000000000101000000000000000000011000001110100110000
+000110011010110000000001011000100111100110110010000011011110011110100
+0010111000000000000101001100100101111010100100101001
424 : 1110100001101000100011100000011011001101100010100010011110010111
+001100000010010000001100000001001001001000100110100001100011000001011
+000110111110010000000100001001101011011000011001001100001001000001000
+011001101000011100000110011111000000111000110001001111010101011000000
+010011011001110001100000000101000100000001000001100011000001000101010
+111001001011100000111010100100011000110110001101001101110000001101000
+000000101000000111011111000110000100101000001000011010001100001110101
+110010000010100010000011100000100111110110110010111001111110011100001
+0100111000001100010101111100110101110010101000101001
433 : 1100100000001100100011100100011011000110001110101100001000000111
+100100000010000000001000000001011101101001100000000000100010100101011
+000110110010110000110110110010000101000010010001110000000001000001101
+011100000001011100100000001011001100100001110001011011011000011010100
+010000000000101000000001000001000000001001000001000001011001010100000
+001000011010100000110011100100111000010010010000001110011100011000001
+000101100101000000011010000111110000000100100000111101000100000100001
+101000011010000010000001000010100111100101110010100010110110010110100
+0001111000101000011101101110111100011000111000010000
435 : 1110001001100000000011111000011011100100110110000000000000100101
+000011100001100100000101000000000000000000001000000000000010110011011
+010000000000000000001000000000000001001010010000101011000000100010000
+011000000001011000000110000010000000100100100000000011001100000010000
+000000100100000000000000000001000010000001000000000000100011010001100
+000000011010100101110010100110011010111010000001010010111000001000100
+011000010001001001000000000000000100001000000000110000110000000100000
+000000000000000010000001000000100011000010001000000000010100000001000
+0000101000010000000101010011010100010100101000100000
442 : 1101000001100011100011100100111111000100001010000100000000100111
+000011000000100011100100000010000001000000001000000001000000000011000
+000000100000010000000001000001000011000010010001001000100010100010000
+011000000001111000000000001111000000100000110100001110000110000000001
+000000010000100101000000000001001010100001000000100111010001011011000
+000110101111101001111011101101110100000011000001010000000000000000010
+001001100000000001000000001000000100001000111000000000101010000100000
+010000001011000000000000000000000011110010100110111000010101010001010
+0001110000010000100111011110101101110011101100101100
448 : 1101000001100001100011100000111011000100000100000100000000011110
+001000100001010001000100000000000000000000000000000001100010100101011
+000000000000011000000000001110000001000011010000000011000000100101000
+011000000000011000000111001110001100100000100100001110000001000100001
+001000001010000000100000000001000011000001000010100000000011010001110
+000010001011100000100111100101111001000011000001011000010100000000100
+010000001000001000000000010000000000000000001000010000000000000100000
+010000000000000010001000000010000111000111001000111100001100011000000
+000111000001101100011101110010010101000010110
456 : 1110000101101100110011101000111011010110011110101001011100000111
+000011101101000011000100111011010001001110000000001111000010010001011
+000000001110100000111100110011000011010000011111000010101010100101000
+011011001001011001010110011110001101101000110101011010001101011010000
+011000001110001001100000000011011010010001100010110001111011011100010
+000011101010100100110011111100011101010010101100000101010100011011101
+001000000001001101100100101110100111100001010000011010010110100110111
+100001010000000110100100000010101111110110011110111011101100110110010
+0000111110000100010111101110111111011000111010110000
458 : 1110000001101000100011101000111011000110001010100000100000000110
+001011000100000000000101100001000001001100100000101101000010010000011
+101000000000000010000000000000000001000000010000001010000010100111010
+011010000000111100000000001111001101111000100010000010011001010000001
+010000001011001001110000000001110110000001001000101100010000011000000
+000010001011100010100011010101011001000000100000001000010100001010010
+001000011000000011000100010001000000000111001000010010011000000100001
+000000001100100010100010000000101011010100011010011000011100011010001
+0100110000101100000111101110100111010000110001010000
467 : 1100000010001101100011101011011011011100011001101010110100010110
+110010000000011000000001000010010111001010101100001000000010000001110
+000000110011100000111001001010000001010010010001000000001010110010000
+011001110001011100001111001111001100101000110000001111000000010010100
+010001000000101101101000000001010010001001101000100001000000011100000
+001000101010100001100011100101111100010110101110001000100100010001000
+010000000000010001111010001000100100000000100000011010111000000110000
+000111011000000010100001000010101111010101001010111110011101111010001
+1011100000011001000111011110110101011001101001001100
472 : 1110000100000010000011111100011011000100000000100000000000001110
+000000000001100000010001110010100100000000000000000100001000110001000
+000000000000010100000010000000000001000000011000111000000000000001001
+011001110001011101000110001110010000100000110000000110001100000000000
+000000000100100001001000001101000000000001000000000001000110010000000
+000000001010100000111110110101000010010100000001000000010100000000000
+000000000000000000000000000100000100010000000000010000000000000100000
+010100001001000010000000000010101011100110100011110001000100000011001
+0001001110000000000111001110110100010100100000111100
499 : 1100000000001100100011100000011011001110101110000000101001010110
+000011000000000010000100000010001100111000100000001000000010010000010
+011010001100010000100001001011000001000000010010000100001000100110000
+011101101010011100100111001010001100100000111001011111001101000100000
+000000010010101000000000000011000011000011000000000001010101010100011
+001001001010110000100010010100111101010110000000000000010100011010000
+000100000010000001000010000111100110000111001000000000010110100110101
+000110001011000010100010000000000111010111010010100010100100011100001
+0100100000100010000111001110111101011000101001011000
506 : 1110001001101101101011101000111011000101011110100010001000110110
+001110000001000001000101100000000001011101111010000000001010010101010
+010110111100010010001001111001100101010000010000001100101000100111000
+011101110001111100000111101111001100111001100011101010000111000000001
+000101101100110001000000001101101100000001100000000001010011010001110
+000000011011100000110111101100010011010010001100010101000111001100000
+011010000000001000011000000001000100010000001010010000001100010110100
+000000001011000110100100010010000111110000101110111101101110011000001
+0111110000010010011111111110111111011000100100100000
517 : 1100000000001111100011101100011011000100001000100100000000000111
+000000100001001001000100000100000000001000000000000000100000000100000
+000000000000000000000000001000000001000000010000100000000000000001000
+011000001101011000000110000001001100100000100000010011100000100010000
+001000000100000011000000000000000011000001000000100001010010000010000
+000000001010001000100010110101111100010011010000000000000000001000000
+101000000000001010000000011000100101000000000010010000010000000100110
+000000000000000000000000010000000111110011101010010000001101000000010
+0001100000010000000101001111100100010110100100110000
525 : 1100000000000000000011100000011000001100001000100000010001000100
+000000000000001010000100000000000000011100001000000000000000000001000
+000000001000000000000100001100001001000000011000110000001000100010000
+011000000001011101011110101010001100100000110000000111010000000001000
+000000001000000001100000000100000110000101000000101001010001010001010
+000000001010100000100010100001110000010100000011000100100001000000001
+000000001100000000000010000000000100100000000001010001100001101100110
+000010001000000010000000000000000111000100110000100001000100010100100
+0001101110010000000101101100010100111000111000001001
557 : 1100000100000000000011101000011011001100000000100000000000000110
+111000100001000000000001000000000000001000101000000000010000000100000
+000000010000000000000000000000100011100100110000001000001000111000000
+011000000000011100000111001010001100101100100011000011000000000010000
+000010010101101000000001000000100000000001000001000000100011010001100
+000011001010101011110010110100111000000000001100001000110000000001000
+010000000000000000100000001000100100100000000000000000000000000100000
+000000000000000011000000000000000101000000000010000000000100000010101
+0101001000001010010111111100111100010110110100001100
All : 1111111111111111111111111111111111111111111111111111111111111111
+111111111111111111111111111111111111111111111111111111111111111111111
+111111111111111111111111111111111111111111111111111111111111111111111
+111111111111111111111111111111111111111111111111111111111111111111111
+111111111111111111111111111111111111111111111111111111111111111111111
+111111111111111111111111111111111111111111111111111111111111111111111
+111111111111111111111111111111111111111111111111111111111111111111111
+111111111111111111111111111111111111111111111111111111111111111111111
+1111111111111111111111111111111111111111111111111111

[download]

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
RIP an inspiration; A true Folk's Guy

Replies are listed 'Best First'.
Re^5: Help required in optimizing the output (PERL)
by choroba (Cardinal) on Jun 22, 2010 at 23:04 UTC
    My script takes 25 secs on an old HP notebook or 10 secs on Mac Mini for 600 words, 612 paragraphs. I don't know how it scales though yet.
    Read more... (2 kB)
[reply]
[d/l]
      I don't know how it scales though yet.

      Projecting from: 

      [ 0:53:04.64] c:\test>845979 1000
Generate fake paragraphs
Sort
Count reversed hash
Solving
999/1000
[0 2 3 4 7 8 9 10 11 12 13 1
[4 6 7 8 10 11 12 13 14 15 1
[0 1 3 4 6 7 8 10 11 12 13 1
[0 5 6 7 8 9 10 12 14 15 18
11s

[ 1:11:24.79] c:\test>845979 2000
Generate fake paragraphs
Sort
Count reversed hash
Solving
1999/2000
[0 1 4 5 6 7 10 12 13 14 15 16 20
[1 3 5 6 7 9 11 13 14 16 17 18 19
[1 3 4 5 6 7 8 9 10 11 13 14 15 1
[1 2 6 7 8 9 10 12 14 19 20 21 22
50s

[ 1:12:25.86] c:\test>845979 4000
Generate fake paragraphs
Sort
Count reversed hash
Solving
3999/4000
[0 1 5 9 10 11 13 14 15 16 18 19 2
[0 1 4 8 9 11 13 14 15 16 18 19 20
[1 4 5 7 8 9 10 11 12 15 16 17 18
[2 3 4 5 6 7 8 9 11 13 17 18 19 21
220s

      [download]

      Each doubling of the number of paras, multiplies the time taken by 4.4. If we double 1000 9 times we get 512,000 (close enough). So, 11 * 4.4^9 gives: 6799340 seconds == 79 days.

      Though you will run out of memory long before then on commodity hardware.

      Using a testcase generator along the lines of yours, my code gives:

      Note Like yours, I don't time the discovery phase. Just the solution phase. 

      [ 1:31:22.89]C:\test>845818 -W=200 -P=1000 > nul
Words: 200
Paras: 1000
Took 0.000000 seconds
All the words are covered by 9 paras:

[ 1:31:38.04]C:\test>845818 -W=200 -P=1000 > nul
Words: 200
Paras: 1000
Took 0.008884907 seconds
All the words are covered by 10 paras:

[ 1:32:07.65]C:\test>845818 -W=200 -P=2000 > nul
Words: 200
Paras: 2000
Took 0.020982027 seconds
All the words are covered by 9 paras:

[ 1:32:30.77]C:\test>845818 -W=200 -P=4000 > nul
Words: 200
Paras: 4000
Took 0.046000004 seconds
All the words are covered by 10 paras:

[ 1:32:53.62]C:\test>845818 -W=200 -P=8000 > nul
Words: 200
Paras: 8000
Took 0.248465061 seconds
All the words are covered by 10 paras:

[ 1:33:32.98]C:\test>845818 -W=200 -P=16000 > nul
Words: 200
Paras: 16000
Took 1.472499847 seconds
All the words are covered by 10 paras:

[ 1:34:44.75]C:\test>845818 -W=200 -P=32000 > nul
Words: 200
Paras: 32000
Took 6.217499971 seconds
All the words are covered by 10 paras:

[ 1:36:55.87]C:\test>845818 -W=200 -P=64000 > nul
Words: 200
Paras: 64000
Took 25.427500010 seconds
All the words are covered by 9 paras:

      [download]

      It requires 4 more doublings to get from 64000 to 512,000. And 25.4 / 6.2 = 4.0. So starting with 25.4 * 4.0^4 = 6502.4 = 1.806 hours.

      To confirm the projection, I'll leave mine running on a 512,000 paras run while I sleep and post the results tomorrow.

      Update: It completed in 27 minutes and used apeek of 500MB::

      [ 1:45:29.21]C:\test>845818 -W=200 -P=512000 > nul
Words: 200
Paras: 512000
Took 1657.894999981 seconds
All the words are covered by 11 paras:

      [download]

      The code incorporating the testcase generator: 

      #! perl -slw
use strict;
use Time::HiRes qw[ time ];

sub uniq{ my %x; @x{@_} = (); keys %x }

$|++;
our $W //= 200;
our $P //= 1000;

my @idx = ( uniq( map int( rand 60000 ), 1 .. 2*$W ) )[ 0 .. $W-1 ];
print STDERR "Words: ", ~~@idx;

my %paras;
for my $p ( 1 .. $P ) {
    local $_ = join ' ', uniq map $idx[ rand @idx ], 0 .. rand( $W/2 )
+;

    $paras{ $p } //= '';
    for my $i ( 0 .. $#idx ) {
        my $word = $idx[ $i ];
        if( m[\b\Q$word]i ) {
            vec( $paras{ $p }, $i, 1 ) = 1;
        }
    }
}
print STDERR "Paras: ", scalar keys %paras;

my $start = time;
my @parasByWordCount = map{
    unpack 'x[N]A*', $_
} sort map {
    pack 'NA*', unpack( '%32b*', $paras{ $_ } ), $_
} keys %paras;

my @set = shift @parasByWordCount;
my $mask = $paras{ $set[ 0 ] };

while( @parasByWordCount ) {
    my $next = shift @parasByWordCount;
    if( ( $mask | $paras{ $next } ) ne $mask ) {
        ## $Next contains new paras, so add to set
        push @set, $next;
        $mask |= $paras{ $next }
    }
    ## otherwise just discard it
}
printf STDERR "Took %.9f seconds\n", time() - $start;

printf  STDERR "All the words are covered by %d paras:\n", scalar @set
+;
printf "%3d : %s\n", $_, unpack 'b*', $paras{ $_ } for sort{ $a<=>$b }
+ @set;
printf "All : %s\n", unpack 'b*', $mask;

__END__
[ 5:17:45.68]C:\test>845818 -W=200 -P=600000 > nul
Words: 200
Paras: 600000
Took 71.555999994 seconds
All the words are covered by 200 paras:

      [download]
      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
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