Optimal Tour Length

Some articles on lengths, length, optimal:

Travelling Salesman Problem - Computing A Solution - Special Cases - Metric TSP
... from A to B is never longer than the route via intermediate C The edge lengths then form a metric on the set of vertices ... The length of the minimum spanning tree of the network is a natural lower bound for the length of the optimal route, because deleting any edge of the optimal route yields a Hamiltonian path, which is a spanning tree in ... the minimum spanning tree and design an algorithm that has a provable upper bound on the length of the route ...

Famous quotes containing the words length, optimal and/or tour:

    What though the traveler tell us of the ruins of Egypt, are we so sick or idle that we must sacrifice our America and today to some man’s ill-remembered and indolent story? Carnac and Luxor are but names, or if their skeletons remain, still more desert sand and at length a wave of the Mediterranean Sea are needed to wash away the filth that attaches to their grandeur. Carnac! Carnac! here is Carnac for me. I behold the columns of a larger
    and purer temple.
    Henry David Thoreau (1817–1862)

    In the most desirable conditions, the child learns to manage anxiety by being exposed to just the right amounts of it, not much more and not much less. This optimal amount of anxiety varies with the child’s age and temperament. It may also vary with cultural values.... There is no mathematical formula for calculating exact amounts of optimal anxiety. This is why child rearing is an art and not a science.
    Alicia F. Lieberman (20th century)

    Left Washington, September 6, on a tour through Ohio, Kentucky, Tennessee, Georgia, and Virginia.... Absent nineteen days. Received every where heartily. The country is again one and united! I am very happy to be able to feel that the course taken has turned out so well.
    Rutherford Birchard Hayes (1822–1893)