Your company has just bought a new Intel Core i5 dual-core processor, and you have been tasked with optimizing your software for thisprocessor. You will run two applications on this dual core, but the resourcerequirements are not equal. The first application requires 80% of the resources,and the other only 20% of the resources. Assume that when you parallelize a por-tion of the program, the speedup for that portion is 2.a. [10] <1.10> Given that 40% of the first application is parallelizable, howmuch speedup would you achieve with that application if run in isolation?b. [10] <1.10> Given that 99% of the second application is parallelizable, howmuch speedup would this application observe if run in isolation?c. [20] <1.10> Given that 40% of the first application is parallelizable, howmuch overall system speedup would you observe if you parallelized it?d. [20] <1.10> Given that 99% of the second application is parallelizable, howmuch overall system speedup would you observe if you parallelized it?1.18 [10/20/20/20/25] <1.10> When parallelizing an application, the ideal speedup isspeeding up by the number of processors. This is limited by two things: percent-age of the application that can be parallelized and the cost of communication.Amdahl’s law takes into account the former but not the latter.a. [10] <1.10> What is the speedup with N processors if 80% of the applicationis parallelizable, ignoring the cost of communication?b. [20] <1.10> What is the speedup with 8 processors if, for every processoradded, the communication overhead is 0.5% of the original execution time.c. [20] <1.10> What is the speedup with 8 processors if, for every time the num-ber of processors is doubled, the communication overhead is increased by0.5% of the original execution time?d. [20] <1.10> What is the speedup with N processors if, for every time thenumber of processors is doubled, the communication overhead is increasedby 0.5% of the original execution time?e. [25] <1.10> Write the general equation that solves this question: What is thenumber of processors with the highest speedup in an application in which P%of the original execution time is parallelizable, and, for every time the num-ber of processors is doubled, the communication is increased by 0.5% of theoriginal execution time? For a universe of items U, there are a total of 2|U| – 1 distinct subsets, excluding theempty set. All 25 subsets for a universe of 5 items are illustrated in Fig. 4.1. Therefore,one possibility would be to generate all these candidate itemsets, and count their supportagainst the transaction database T . In the frequent itemset mining literature, the termcandidate itemsets is commonly used to refer to itemsets that might possibly be frequent (orcandidates for being frequent). These candidates need to be verified against the transactiondatabase by support counting. To count the support of an itemset, we would need to checkwhether a given itemset I is a subset of each transaction Ti ? T . Such an exhaustiveapproach is likely to be impractical, when the universe of items U is large. Consider thecase where d = |U| = 1000. In that case, there are a total of 21000 > 10300 candidates.To put this number in perspective, if the fastest computer available today were somehowable to process one candidate in one elementary machine cycle, then the time required toprocess all candidates would be hundreds of orders of magnitude greater than the age ofthe universe. Therefore, this is not a practical solution.Of course, one can make the brute-force approach faster by observing that no (k + 1)-patterns are frequent if no k-patterns are frequent. This observation follows directly fromthe downward closure property. Therefore, one can enumerate and count the support ofall the patterns with increasing length. In other words, one can enumerate and count thesupport of all patterns containing one item, two items, and so on, until for a certain length l,none of the candidates of length l turn out to be frequent. For sparse transaction databases,the value of l is typically very small compared to |U|. At this point, one can terminate. Thisis a significant improvement over the previous approach because it requires the enumerationof li=1 |U|i 2|U| candidates. Because the longest frequent itemset is of much smallerlength than |U| in sparse transaction databases, this approach is orders of magnitude faster.However, the resulting computational complexity is still not satisfactory for large values ofU. For example, when |U| = 1000 and l = 10, the value of 10i=1 |U|iis of the order of 1023.This value is still quite large and outside reasonable computational capabilities availabletoday.One observation is that even a very minor and rather blunt application of the downwardclosure property made the algorithm hundreds of orders of magnitude faster. Many of thefast algorithms for itemset generation use the downward closure property in a more refinedway, both to generate the candidates and to prune them before counting. Algorithms for frequent pattern mining search the lattice of possibilities (or candidates) for frequent pat-terns (see Fig. 4.1) and use the transaction database to count the support of candidates inthis lattice. Better efficiencies can be achieved in a frequent pattern mining algorithm byusing one or more of the following approaches:1. Reducing the size of the explored search space (lattice of Fig. 4.1) by pruning candidateitemsets (lattice nodes) using tricks, such as the downward closure property.2. Counting the support of each candidate more efficiently by pruning transactions thatare known to be irrelevant for counting a candidate itemset.3. Using compact data structures to represent either candidates or transaction databasesthat support efficient counting.The first algorithm that used an effective pruning of the search space with the use of thedownward closure property was the Apriori algorithm.Image transcription text24. If the supply of loanable funds is given by Q. =99 . r – 6.9, and the demand for loanable funds isgiven by Qa = 13 – 100 * r, what is the e… Show more… Show moreImage transcription text7. Suppose X1….. X10,one areindependent, Poisson randomvariables of mean 1, As us… Show more… Show moreImage transcription textQuestion 5. Suppose we have threerandom variables as follows: (X] ~ N(0,V3′) X2 ~ Unif(-3,3) X3~ fx… Show more… Show moreEngineering & TechnologyComputer ScienceCIS 101
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