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The programmer' s primary weapon in the never-ending battle against slow systems is to change the intramodular structure . Our first response should be to reorganize the module' s data structures . Brooks [ 1 975 , Chapter 9] accurately describes the importance of data structures: "representation is the essence of programming" . By changing the representation of data, we can often drastically reduce the time required to operate on it. Courses in data structures are now well established in computer science curri t ula.

3 We can now use the fact that integer arithmetic is faster than real arithmetic on many machines, and convert the arithmetic from r ea l to i n t e ge r . The reader should complain that the cost difference is there for a good reason: r eal arithmetic solves a different problem. Henceforth we can advertise this program as finding only an ap­ proximation to a Nearest Neighbor tour, but we should remember that we al�eady accepted the fact that a nearest neighbor tour gives only an approximation to the true tour.

2 . Every computing system has been designed at all of the levels described there: the overall system structure, intramodular structure, efficient code , translation to machine code, underlying system software, and un­ derlying hardware . If a system is inefficient, then we should try to gain ef­ ficiency at the proper level . Sometimes that level is the overall system design: we should build a new system based on a new design (Brooks [ 1 975 , Chapter 1 1 ] advises us to "plan to throw one away; you will, anyhow") .

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Algorithms for Comm. Systs and Their Applns by N. Benvenuto, et al.,

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