*Example.* Consider the following problem (with no attempted biological
motivation.)
*Given:* A set of *n* positive numbers.
*Desired output:* Divide the numbers into two sets, where the
difference between the sums of the sets is as small as possible.
(Given a set of blocks of different heights, put them into two piles that are
as close as possible to the same height.)
Devise a greedy method that attempts to find a solution, and find an instance
where it gives a sub-optimal solution.

*Observation:* The dissussion in Chapter 5 concerns *the unsigned version*
of the Sorting By Reversals Problem. For some ways of identifying genes (for instance,
when the entire genome is sequenced), we also know each gene's orientation (i.e.,
transcription direction). This leads naturally to the *signed* version of the
problem. Here, we are given a permutation of *N* integers, but each now has a sign
(plus or minus). A reversal operation also flips signs in the reversed interval.
Surprisingly, the problem of sorting signed permutations by reversals can be
optimally solved in polynomial time. (Incidentally, this was first shown, about 10
years ago, by a Penn State graduate student, Sridhar Hannenhalli.)
This is discussed in the book's on-line class notes for Chapter 5.