Algorithm for finding sub-sequences?

[hopesfall]

I'm trying to work through some problems in this textbook in my spare time and I came across this very interesting problem that I'm unable to find a solution for. Can anyone suggest an efficient algorithm for this problem? Here's a link to the problem:

http://i.stack.imgur.com/PmEKD.jpg

[LB]

I don't understand how 011 is a subsequence of 0101?

[JLBorges]

http://en.wikipedia.org/wiki/Shortest_common_supersequence

[Duthomhas]

@LB
In this particular problem, the word subsequence is with its mathematical meaning. A subsequence cares about order, not adjacency.

So, given {a b c d},

{a c d} is a subsequence, but

{c a b} is not.

[keskiverto]

The scs link refers to lcs, which in turn describes a dynamic programming algorithm.

Given a=0110 and b=0101, we get an alignment:

  a = 01-10
  b = 0101-

lcs = 01 1
scs = 01010

The '-' denotes a "gap", a deletion -- this sequence lacks (has lost) what the other has at this position.
Alternatively, an insertion has occurred in the other sequence, i.e. it has an additional position.
(Bioinformatics' terminology; genes, mutation, evolution, common ancestor.)