We consider the traveling salesman problem when the cities are points in &##x211D;<sup><i>d</i></sup> for some fixed <i>d</i> and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding a tour of <i>maximum</i> length can be solved in polynomial time. Ifâ€¦ (More)

We consider the traveling salesman problem when the cities are points in R for some fixed d and distances are computed according to a polyhedral norm. We show that for any such norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(nfâˆ’2 logâ€¦ (More)

It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohenâ€“Macaulay order complex in exactly the same conditions. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and ofâ€¦ (More)

We consider the traveling salesman problem when the cities are points in R d for some xed d and distances are computed according to a polyhedral norm. We show that for any such norm, the problem of nding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(n f?2 logâ€¦ (More)