Thanks for that clarification, but you still haven't answered Corion's equally good objection++ above, namely:

The rule is each array contains a sorted (ascending) sequence of non-contiguous, unique integers, but my @a3 = ( 205, 206, 315 ); contains the two contiguous numbers 205 and 206.

Should we be reasoning based on your descripition of the problem, or on your supplied dataset?

use strict;
use warnings;

my @a1 = ( 100, 204, 208, 312 );
my @a2 = ( 102, 313, 409 );
my @a3 = ( 205, 206, 315 );
my @a4 = ( 207, 210, 314 );

my $a = [\@a1,\@a2,\@a3,\@a4];
my @ai = (0, 0, 0, 0);
my ($a1a2, $a3a4) = (getLess(0), getLess(2));
my @circle = (getNext(),getNext(),getNext());
my $ci = 3;
while (defined($circle[$ci] = getNext())) {
    if ($circle[$ci][2]-3 == $circle[($ci+1)%4][2]) {
    for (my $i = 1; $i < 5; $i++) {
        print $circle[($ci+$i)%4][2].
          ' ['.$circle[($ci+$i)%4][0].','.$circle[($ci+$i)%4][1].'] ';
    }
    print "\n";
    }
    $ci = ($ci+1)%4;    
}


sub getLess {
    my $offset = shift;
    my $ret;
    if (defined $$a[$offset][$ai[$offset]]) {
    if (defined $$a[$offset+1][$ai[$offset+1]]) {
        $offset++ if $$a[$offset][$ai[$offset]] > $$a[$offset+1][$ai[$
+offset+1]];
    }
    $ret = [$offset, $ai[$offset], $$a[$offset][$ai[$offset]]];
    $ai[$offset]++;
    } else {
    $offset++;
    if (defined $$a[$offset][$ai[$offset]]) {
        $ret = [$offset, $ai[$offset], $$a[$offset][$ai[$offset]]];
        $ai[$offset]++;
    }    
    }
    return $ret;
}

sub getNext {
    my $ret;
    if (defined $a1a2) {
    if (defined $a3a4) {
        if ($$a1a2[2] < $$a3a4[2]) {
        $ret = $a1a2;
        $a1a2 = getLess(0);
        } else {
        $ret = $a3a4;
        $a3a4 = getLess(2);
        }
    } else {
        $ret = $a1a2;
        $a1a2 = getLess(0);
    }
    } else {
    if (defined $a3a4) {
        $ret = $a3a4;
        $a3a4 = getLess(2);
    }    
    }
    return $ret;
}
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204 [0,1] 205 [2,0] 206 [2,1] 207 [3,0]
205 [2,0] 206 [2,1] 207 [3,0] 208 [0,2]
312 [0,3] 313 [1,1] 314 [3,2] 315 [2,2]
[download]