By Richard Bellman, Kenneth L. Cooke
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Extra resources for Algorithms, Graphs, and Computers, Vol. 62
Consequently, we shall have to replace Table 8 by a new table which includes a time for every link. T h e enlarged array is given in Table 10. Notice that the time required to go from i t o j is not in every case the same as the time to go from j to i, i. e. that t , , # t , , for some i a n d j . A n extreme example of this lack of symmetry occurs in routing problems where there are some one-way streets. For future reference we give in Table 11 a n enlarged array of times for the map in Fig. 11.
A) Find the chromatic number of each of the graphs in Fig. 19. (b) Find the chromatic number of the graph in Fig. 21. (c) What can be said about the chromatic number of a tree? Systems and States 8. 39 In a certain town, the blocks are rectangular, with the streets (of zero width) running East-West, the avenues North-South. A man wishes to go from one corner to another m blocks East and n blocks North. The shortest path can be achieved in many ways. How many? What is the relation between this problem and Pascal’s triangle?
N) in the obvious fashion, we see . . , n) = min(a, min ( b ,c, . ,n)) (6) This is an essential structural property. I t is important for both analytic and computational purposes to appreciate what (6) implies as far as a feasible algorithm for computing rnin (a, b, c, . , n) is concerned. It means that we can use a simple sequential procedure of the following type: Compare a and b, choose the minimum of the two; compare c with this minimum value and choose the minimum of these; and so on.
Algorithms, Graphs, and Computers, Vol. 62 by Richard Bellman, Kenneth L. Cooke