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Algorithm Design

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8O4<br />

Epilogue: <strong>Algorithm</strong>s That Run Forever<br />

(E.i~) By moving avo stable matchings in each time step, according, to the<br />

preferences just defined, the switch is able to simulate the behavior of pare<br />

output qaeaeing.<br />

Overall, the algorithm makes for a surprising last-minute appearance by<br />

the topic with which we began the book--and rather than matching men with<br />

women or applicants with employers, we find ourselves matching input finks<br />

to output links in a high-speed Internet router.<br />

This has been one glimpse into the issue of algorithms that run forever,<br />

keeping up with an infinite stream of new events. It is an intriguing topic, full<br />

of open directions and unresolved issues. But that is for another time, and<br />

another book; and, as for us, we are done.<br />

References<br />

E. Aarts and J. K. Lenstra (eds.). Local Search in Combinatorial Optimization.<br />

Wiley, 1997.<br />

R. K. Ahu)a, T. L. Magnanti, and J. B. Or]in. Network Flows: Theory, <strong>Algorithm</strong>s,<br />

and Applications. Prentice Hall, 1993.<br />

N. Alon and J. Spencer. The Probabilistic Method (2nd edition). Wiley, 2000.<br />

M. Anderberg. Cluster Analysis for Applications. Academic Press, 1973.<br />

E. Anshelevich, A. Dasgupta, J. Kleinberg, 1~. Tardos, T. Wexier, and T. Roughgarden.<br />

The price of stability for network design with fair cost allocation. Proc. 4Sth<br />

IEEE Symposium on Foundations of Computer Science, pp. 295-304, 2004.<br />

K. Appel and W. Haken. The solution of the four-color-map problem. Scientific<br />

American, 237:4(1977), 108-121.<br />

S. Arora and C. Lund. Hardness of approximations. In Approximation <strong>Algorithm</strong>s<br />

for N-P-Hard Problems, edited by D. S. Hochbaum. PWS Publishing, 1996.<br />

B. Awerbuch, Y Azar, and S. Plotldn. Tkroughput-compefitive online routing,<br />

Proc. 34th IEEE Symposium on Foundations of Computer Science, pp. 32-40, 1993.<br />

R. Bar-Yehuda and S. Even. A linear-time approximation algorithm for the weighted<br />

vertex cover problem. J. <strong>Algorithm</strong>s 2 (1981), 198-203.<br />

A.-L. Barabasi. Linked: The New Science of Networks. Perseus, 2002.<br />

M. Beckmann, C. B. McGuire, and C. B. Winsten. Studies in the Economics of<br />

Transportation. Yale University Press, 1956.<br />

L. Belady. A study of replacement algorithms for virtual storage computers. !BM<br />

Systems Journal 5 (1966), 78-101.<br />

T. C. Bell, J. G. Cleary, and I. H. Witten. Text Compression. Prentice Hall, 1990.<br />

R. E. Bellman. Dynamic Programming. Princeton University Press, 1957.

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