By Richard Bellman, Kenneth L. Cooke
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Extra info for Algorithms, Graphs, and Computers, Vol. 62
1941. Oxford Univ. Press, New York, A . F. Veinott, Jr. and H. M. Wagner, “Optimal Capacity Scheduling,” RM-3021-PR, 1962, The R A N D Corp. J . M. Hamrnersley, “On Steiner’s Network Problem,” Mathematika 8 (1961) 131-132. 6. A variation of Steiner’s problem occurs in printed circuit technology. Suppose that n electrical junctions are to be connected with the shortest possible length of wire and moreover that the wires must run in the horizontal and vertical directions. Solve this problem for n = 3 and n = 4.
Or 10,000! evaluations in a straightforward fashion. It is clear that without the aid of mathematical techniques there is no hope of obtaining the desired numerical results. Brute force must be combined with bright force. 16. Graphs Our discussion of logical trees and maps has now led us to a point where it is natural to introduce the general concept of a graph. By a graph we mean a figure consisting of a finite number of points in the plane (or in a three-dimensional space), and certain line segments joining pairs of points.
1) of these paths. This number is a convenient measure of combinatorial problems, namely lo! = 3,628,800 (2) This represents a considerable amount of hand calculation. Nevertheless, it is feasible to think in terms of 3,628,800 evaluations and comparisons with a computer that can, for example, perform an addition in a microsecond. Enumeration appears feasible. Suppose, however, that there are 22 points. This is certainly not a large map. Then there are at least 20! different paths and clearly * Recall that a microsecond is a millionth of a second.
Algorithms, Graphs, and Computers, Vol. 62 by Richard Bellman, Kenneth L. Cooke
Categories: Differential Equations