16. Suppose that insertion and deletion costs are 1, and replacement costs are 2 unitsfor the edit distance. Show that the optimal edit distance between two strings can becomputed only with insertion and deletion operations. Under the aforementioned costassumptions, show that the optimal edit distance can be expressed as a function ofthe optimal LCSS distance and the lengths of the two strings. 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 candidateitem sets (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 Apriority algorithm.How can you keep the CPU busy during the delay between sending an answer to a client and then receiving its next?equest without incurring the expense of an operating system-visible thread of control per client? The answer is that?ou can write your server using an asynchronous pattern, where instead of blocking and waiting for data to arrive or?epart from one particular client, the code instead is willing to hear from a whole list of waiting client sockets and?espond whenever one of those clients is ready for more interaction.This pattern is made possible by two features of modern operating system network stacks. The first is that they?ffer a system call that lets a process block waiting on a whole list of client sockets, instead of on only a single client?ocket, which allows a single thread to serve hundreds or thousands of client sockets at a time. The second feature is?hat a socket can be configured as nonblocking, where it promises to never, ever make the calling thread block in a?end() or recv() call but will always return from the send() or recv() system call immediately whether or not further?rogress can be made in the conversation. If progress is delayed, then it is up to the caller to try again later when the?lient looks ready for further interaction.The name asynchronous means that the client code never stops to wait for a particular client and that the?hread of control running the code is not synchronized, or made to wait in lockstep, with the conversation of any one?articular client. Instead, it switches freely among all connected clients to do the work of serving.There are several calls by which operating systems support asynchronous mode. The oldest is the POSIX call?elect(), but it suffers from several inefficiencies that have inspired modern replacements like poll() on Linux and?poll() on BSD. The book UNIX Network Programming by W. Richard Stevens (Prentice Hall, 2003) is the standard?eference on the subject. Here I will focus on poll() and skip the others because the intention of this chapter is?ot really that you implement your own asynchronous control loop. Instead, you are taking a poll()-powered loop?erely as an example so that you understand what happens under the hood of a full asynchronous framework, which?s how you will really want to implement asynchrony in your programs. Several frameworks are illustrated in the?ollowing sections.Image transcription textSuppose that addition andmultiplication have already beendefined for the set of natu… Show more… Show moreImage transcription textRecall from class that we defined thenatural numbers from the empty set 0and the successor functi… Show more… Show moreImage transcription textPart ill | Calculating Unemployment Full-time employed 400,000Not working but looking for work 8,000 Part-time workers 30,000Discouraged workers 1. Labor force = 2. Unemploym… Show more… Show moreImage transcription text4. Packet Transmission on LAN Below is a small LAN that includeswired and wireless computers attached to an Ethernet backbone.Please give all of the MAC addresses (abbreviated as… Show more… Show moreEngineering & TechnologyComputer ScienceCOMPUTER S COS4840
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