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assign2 - Algorithms in the Real World(15-853 Fall 09...

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Algorithms in the Real World (15-853), Fall 09 Assignment #2 Due: October 1 Complete all problems. You are not permitted to look at solutions of previous year assignments. You can work together in groups, but all solutions have to be written up individually. Problem 1: PPM, LPZ and BW (20pt) The string bcabccabc is encoded using PPM. The (partial) dictionary constructed during encoding is given below. For the following questions, assume that escape count is given by the number of different characters for each context, and exclusion is not used, unless specified. Assume that the alphabet has 26 characters, and use k = 2. (a) Fill in the empty spaces in the dictionary below. Context Counts Context Counts Context Counts empty a = 2 a b = 2 ab c = 2 b = 3 c = 4 b c Figure 1: Dictionary (b) Suppose the next letter in the string is b . Compute the number of bits required to encode b , and also list the changes made to the dictionary. (You do not have to compute the exact number of bits, simply write it as an expression containing logs). The answer
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