minimizing the final completion time we close this section by considering very similar problem suppose we are only concerned with when the last job finishes in our two examples abovethese completion times are and respectively figure shows that the minimum final completion time is and this clearly cannot be improvedbecause every processor is always busy although this schedule does not have minimum mean completion timeit has merit in that the completion time of the entire sequence is earlier if the same user owns all these jobsthen this is the preferable method of scheduling although these problems are very similarthis new problem turns out to be np-completeit is just another way of phrasing the knapsack or bin packing problemswhich we will encounter later in this section thusminimizing the final completion time is apparently much harder than minimizing the mean completion time huffman codes in this sectionwe consider second application of greedy algorithmsknown as file compression the normal ascii character set consists of roughly "printablecharacters in order to distinguish these characterslog bits are required seven bits allow the representation of charactersso the ascii character set adds some other "nonprintablecharacters an eighth bit is added as parity check the important pointhoweveris that if the size of the character set is cthen log cbits are needed in standard encoding suppose we have file that contains only the characters aeistplus blank spaces and newlines suppose furtherthat the file has ten 'sfifteen 'stwelve 'sthree 'sfour 'sthirteen blanksand one newline as the table in figure showsthis file requires bits to representsince there are characters and each character requires three bits in real lifefiles can be quite large many of the very large files are output of some program and there is usually big disparity between the most frequent and least frequent characters for instancemany large data files have an inordinately large amount of digitsblanksand newlinesbut few ' and ' we might be interested in reducing the file size in figure minimizing the final completion time