Solving Superstring Exactly
I've studied the problem and I found some results.
Shortest Common Superstring (SCS) can be solved in time $2^n$ with only polynomial space(Kohn, Gottlieb, Kohn; Karp; Bax, Franklin).

The best known approximation is $2\frac{11}{30}$ (Paluch).

The best known approximation of compression is $3\over4$ (Paluch).

If SCS can be approximated by a factor $\alpha$ over the binary alphabet, then it can be approximated by a factor $\alpha$ over any alphabet (Vassilevska-Williams).

SCS cannot be approximated with a ratio better than $1.0029$ unless P=NP (Karpinski, Schmied).

Maximal Compression cannot be approximated with a ratio better than $1.0048$ unless P=NP (Karpinski, Schmied).

I would be grateful for any additions and suggestions.