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Now examine the two terms in (5.71). By assumption, since L (p ) is the optimal length for p , we have L(p ) L (p ) 0. Similarly, the length of the extension of the optimal code for p has to have an average length at least as large as the optimal code for p [i.e., L(p) L (p) 0]. But the sum of two nonnegative terms can only be 0 if both of them are 0, which implies that L(p) = L (p) (i.e., the extension of the optimal code for p is optimal for p). Consequently, if we start with an optimal code for p with m 1 symbols and construct a code for m symbols by extending the codeword corresponding to pm 1 + pm , the new code is also optimal. Starting with a code for two elements, in which case the optimal code is obvious, we can by induction extend this result to prove the following theorem. Theorem 5.8.1 Huffman coding is optimal; that is, if C is a Huffman code and C is any other uniquely decodable code, L(C ) L(C ). Although we have proved the theorem for a binary alphabet, the proof can be extended to establishing optimality of the Huffman coding algorithm for a D-ary alphabet as well. Incidentally, we should remark that Huffman coding is a greedy algorithm in that it coalesces the two least likely symbols at each stage. The proof above shows that this local optimality ensures global optimality of the nal code. 5.9 SHANNON FANO ELIAS CODING

Room Availability Personnel Assignment Analysis Housekeeper s Report Equipment/Supplies Inventory Maintenance Requests

s front of ce manager of The Times Hotel, you want to project the number of additional rooms you will need to book to achieve 100 percent occupancy for the night of April 15. Use the following historical data to determine the number of additional room reservations needed to achieve 100 percent occupancy: 500 rooms available, 100 con rmed reservations with a 5 percent no-show history, 200 guaranteed rooms with a 2 percent no-show history, 15 stayovers, 10 understays, and 45 walk-ins.

To follow along with this exercise, copy to your hard drive the simpleChaserBegin.fla file. Use your operating system s utility to disable the file s read-only attribute.

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I had come to feel over the years that there was an acute need for a discipline that was determined to study not the individual organism or the social heritage, but the interpersonal situations through which persons manifest mental health or mental disorder. (Sullivan, 1953b, p. 18) Personality is the relatively enduring pattern of recurrent interpersonal situations which characterize a human life. (Sullivan, 1953b, pp. 110 111)

20. K. Ballinger et al., Web Services Inspection Language (WS Inspection) 1.0; http:// www.106.ibm.com/developerworks/webservices/library/ws-wsilspec.html. 21. Liberty Alliance; http://www.projectliberty.org/. 22. Open Mobile Alliance; http://www.openmobilealliance.org/. 23. Java Community Process, JSR 172; http://www.jcp.org/en/jsr/detail id 172. 24. J. Ibbotson, ed., SOAP Version 1.2 Usage Scenarios, W3C Working Draft; http:// www.w3.org/TR/2002/WD-xmlp-scenarios-20020626/. Copyright Notice: http:// www.w3.org/Consortium/Legal/2002/copyright-documents-20021231. 25. N. Mendelsohn, M. Nottingham, and H. Ruellan, eds., XML-binary Optimized Packaging, W3C Working Draft, http://www.w3.org/TR/2004/WD-xop10-20040608/. 26. E. Levinson, The MIME Multipart/Related Content-type, RFC 2387, IETF, August 1998, http://www.ietf.org/rfc/rfc2387.txt. 27. N. Mendelsohn, M. Nottingham, and H. Ruellan, eds., SOAP Message Transmission Optimization Mechanism, W3C Working Draft, http://www.w3.org/TR/2004/WDsoap12-mtom-20040608/.

1. Abril J., Comellas F., Cortes A., Ozon J., and Vaquer M., A Multiagent system for frequency assignment in cellular radio networks, IEEE Transactions on Vehicular Technology, 49, 5, 1558 1565, 2000. 2. Al-Khaled F. S., Optimal radio channel assignment through the new binary dynamic simulated annealing algorithm, International Journal of Communication Systems, 11, 327 336, 1998. 3. Anderson L. G., A Simulation study of some dynamic channel assignment algorithms in a high capacity mobile telecommunications system, IEEE Transactions on Communications, 21, 1294 1301, 1973. 4. Bouju A., Boyce J. F., Dimitropoulos C. H. D., Vom Scheidt G., Taylor J. G., Likas A., Papageorgiou G., and Stafylopatis A., Intellegent search for the radio links frequency assignment problem, International Conference for Digital Signal Processing (DSP 95), Limassol, Cyprus, 1995. 5. Box F., A Heuristic technique for assigning frequencies to mobile radio nets, IEEE Transactions on Vehicular Technology, 27, 57 74, 1978. 6. Capone A. and Trubian M., Channel Assignment problem in cellular systems: A new model and a tabu search algorithm, IEEE Transactions on Vehicular Technology, 48, 4, July 1999.

Most antivirus programs also scan for worms, so install a trusted, respected brand of antivirus software and keep it updated constantly. Download the most recent Windows patches, updates, and service packs. Turn on the Automatic Update feature of Windows to ensure that it automatically downloads and installs the latest Windows security xes as soon as they are available. Do not open e-mail attachments that have le extensions such as .exe, .scr, and .vbs or have double le extensions such as .txt.vbs (see Figure 5-3).

salt due to their initial lower pH and excessive moisture (Arnau et al. 1995). The quality of hams (texture, appearance, color, and avor) is monitored and evaluated by experts. There is a traditional snif ng test, still in use, for the rapid evaluation of the avor quality of the ham and/or the detection of any spoilage inside the ham. This technique consists of the insertion of a small

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