Russell Woodroofe

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We consider the traveling salesman problem when the cities are points in &&num;&num;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. If(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(nf−2 log(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 Cohen–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 of(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 log(More)
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