Application To Traffic Control
Robbins (1939) introduces the problem of strong orientation with a story about a town, whose streets and intersections are represented by the given graph G. According to Robbins' story, the people of the town want to be able to repair any segment of road during the weekdays, while still allowing any part of the town to be reached from any other part using the remaining roads as two-way streets. On the weekends, all roads are open, but because of heavy traffic volume, they wish to convert all roads to one-way streets and again allow any part of town to be reached from any other part. Robbins' theorem states that a system of roads is suitable for weekday repairs if and only if it is suitable for conversion to a one-way system on weekends. For this reason, his result is sometimes known as the one-way street theorem.
Subsequently to the work of Robbins, a series of papers by Roberts and Xu modeled more carefully the problem of turning a grid of two-way city streets into one-way streets, and examined the effect of this conversion on the distances between pairs of points within the grid. As they showed, the traditional one-way layout in which parallel streets alternate in direction is not optimal in keeping the pairwise distances as small as possible. However, the improved orientations that they found include points where the traffic from two one-way blocks meets itself head-on, which may be viewed as a flaw in their solutions.
Read more about this topic: Strong Orientation
Famous quotes containing the words application to, application, traffic and/or control:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one other—only in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.”
—Talcott Parsons (1902–1979)
“There was a girl who was running the traffic desk, and there was a woman who was on the overnight for radio as a producer, and my desk assistant was a woman. So when the world came to an end, we took over.”
—Marya McLaughlin, U.S. television newswoman. As quoted in Women in Television News, ch. 3, by Judith S. Gelfman (1976)
“All industries are brought under the control of such people [film producers] by Capitalism. If the capitalists let themselves be seduced from their pursuit of profits to the enchantments of art, they would be bankrupt before they knew where they were. You cannot combine the pursuit of money with the pursuit of art.”
—George Bernard Shaw (1856–1950)