Consider a logic circuit with two-bit gates only. The *length* of each gate is the number of bit lines that the gate crosses. How hard is to compute the maximum length for a given circuit? Notice that two circuits are, say, *isomorphic*, if they differ only up to a permutation of the bit lines. Notice that there are clearly $n!$ ways to arrange $n$ bit lines. 



A combinatorial problem concerned with logic circuits
If I understand your question correctly, you're trying to find a permutation of the bit lines so the maximum gate "length" is as small as possible. This is called the [bandwidth problem](http://en.wikipedia.org/wiki/Graph_bandwidth):


Given a graph $G = (V,E)$ find a permutation $\pi : V \rightarrow [1 \ldots n]$ such that $$\max\_{(i,j) \in E} |\pi(i) - \pi(j)|$$ is minimized.


The wikipedia article has more information on the complexity (it's NP-hard and APX-hard) and algorithms. The bandwidth problem is interesting also because it was used to introduce the idea of volume-respecting embeddings.


