Abstract
Given a subset X of vertices of the n-cube (i.e., the n-dimensional Hamming space), we are interested in the solution of the traveling salesman problem; namely, the minimal length of a cycle passing through all vertices of X. For a given number M, we estimate the maximum of these lengths when X ranges over all possible choices of sets of M vertices. Asymptotically, our estimates show that for a number M of vertices growing exponentially in n, the maximum is attained for a code with maximal possible minimum distance.
Original language | English |
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Pages (from-to) | 1274-1276 |
Number of pages | 3 |
Journal | IEEE Transactions on Information Theory |
Volume | 42 |
Issue number | 4 |
DOIs | |
State | Published - 1996 |
Keywords
- Data compression
- Gray codes
- Minimal cycle
- Traveling salesman