Consider a binary k-NN classifier where k = 4 and the two labels are “triangle" and "square". Consider classifying a new point x = 1, 1, where two of the x's nearest neighbors are labeled “triangle" and two are labeled “square" as shown below. 2 1 2 Which of the following methods can be used to break ties or avoid ties on this dataset? 1. Assign x the label of its nearest neighbor 2. Flip a coin to randomly assign a label to x (from the labels of its 4 closest points) 3. Use k =3instead 4. Use k =5instead Select one: O 1 only O 2 only O 2, 3, 4 O 2, 4 4 only O 1, 2, 3, 4 None of the above

Consider a binary k-NN classifier where k = 4 and the two labels are “triangle" and "square". Consider classifying a new point x = 1, 1, where two of the x's nearest neighbors are labeled “triangle" and two are labeled “square" as shown below. 2 1 2 Which of the following methods can be used to break ties or avoid ties on this dataset? 1. Assign x the label of its nearest neighbor 2. Flip a coin to randomly assign a label to x (from the labels of its 4 closest points) 3. Use k =3instead 4. Use k =5instead Select one: O 1 only O 2 only O 2, 3, 4 O 2, 4 4 only O 1, 2, 3, 4 None of the above

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Suppose you have a signature scheme S (which is correct and existentially unforgeable), and S can be used to sign any t-bit message. And you have a hash function H which outputs t bits and is collision-resistant. Consider a modified signature scheme S’ which can sign messages of unlimited length, where: S’.Sign(sk, m) = S.sign(sk, H(m)) Prove that this scheme is existentially unforgeable as long as S is existentially unforgeable and H is collision-resistant.
Computing Values of a Hash FunctionInstead of 10,000 students, suppose there are only 6. Define a functionH, from the set of student ID numbers to the set {0, 1, 2, 3, 4, 5, 6,7, 8, 9, 10} as follows:H(n) = n mod 11 for each ID number n.To compute values of H either use a calculator or a computer with abuilt-in mod function or use the formula n mod 11 = n - (n div 11). Inother words, divide n by 11, multiply the integer part of the resultby 11, and subtract that number from n.As an example, since 328343419/11 = 29849401.73.H(328343419) = 328343419 - (11 * 29849401) = 8. To store the link tothe record for the student with ID number n, start by computing H(n).For instance, if the ID numbers are 328343419, 356633102, 223799061,607275830 and 513408716, calculate the hash values and comment in detailwith mathematical justification on the hash function.
Suppose you generate the following RSA key pairs:• p = 37199• q = 49031• N = p · q = 1823904169• (p − 1) · (q − 1) = 1823817940• e = 65537 (for encryption)• d = 1578812933 (for decrption)Assuming a=01, b=02, . . . , z=26, and we group the digits in groups of three. (ii) If you receive strings of digits from a sender: 199770170, 1288754980, 324346846, 1370682962, decrypt the message.
Consider using a linear-probing table to insert the keys A through G and their corresponding hash values into an originally empty table of size 7 (without resizing the table for this issue). Which of the following outcomes from putting these keys in cannot possibly occur? a. E F G A C B Db. C E B G F D Ac. B D F A C E Gd. C G B A D E Fe. F G B D A C Ef. G E C A D B F Describe the smallest and largest number of probes that could be necessary to create a table of size 7 using these keys, along with an insertion sequence that supports your conclusion.
Let s = σ1. . . σk be a binary string of length k > 0. We say that a binary string w = w1 . . . wn contains s as a subsequence if there are k indices 1 ≤ i1 < i2, . . . < ik ≤ n such that wik = sr for every 1 ≤ r ≤ k. For example, if s = 11 then 10001, 1010 and 110 contain s as a subsequence whereas 000 and 1000 do not. Prove that the language of all binary strings containing a fixed binary string s of length k as a subsequence is a regular language.
Let f(n)=2n3 +4n2 +5n+10 and g(n)= n2 +50n+4. Is f(n)=Ω(g(n))? [Bloom Taxonomy: Level 5]
Suppose you are given the following set of keys to insert into a hash table that holds exactly 11 values: 113, 117, 97, 100, 114, 108, 116, 105, 99. Using the hash function= value %table_size. Which of the following best demonstrates the contents of the hash table after all the keys have been inserted using linear probing? a) 100,__,__,113,114,105,116,117,97,108,99 b) 99,100,__,113,114,__,116,117,105,97,108 c) 100,113,117,97,14,108,116,105,99,__,__ d) 117,114,108,116,105,99,__,__,97,100,113
Suppose you generate the following RSA key pairs: • p = 37199• q = 49031• N = p · q = 1823904169• (p − 1) · (q − 1) = 1823817940• e = 65537 (for encryption)• d = 1578812933 (for decrption)Assuming a=01, b=02, . . . , z=26, and we group the digits in groups of three. (i) If someone wants to send the following message: “SELLALL” using your public key, what strings of digits should they send you (i.e., encrypt this message)?
Consider a hash table of size 11 with hash function h(x) = x mod 11. Draw the tablethat results after inserting, in the given order, the following values: 26, 57, 40, 50,13, 33, and 72 for each of the three scenarios below: i. When collisions are handled by separate chaining. ii. When collisions are handled by double hashing using a second hash function ℎ’(?) = (? ??? 7) + 1. Hint, the overall (combined) hash function is ?(?) = ( ℎ(?) + ? × ℎ′(?) ) ??? 11, where i = 0, 1, 2, 3, … iii. When collisions are handled by quadratic probing with a quadratic probe function ℎ′(?,?) = (ℎ(?) + 0.5 ? + 0.5 ?2) ??? 11 where ? = 1, 2, 3,….
Consider a open bucket hash table and closed bucket hash table in which the keys are student identifiers (strings of 6 digits). Assume the following number of buckets and hash function: m = 100; hash(id) = first two digits of id #. Starting with an empty hash table, show the effect of successively adding the following student identifiers: 000014, 990021, 990019, 970036, 000015, 970012, 970023. Use following function as second hash function hash(id) = last digit of id # Show the effect of deleting 000014 from the hash table. (Java Programming DSA)
Given a known set of keys, a perfect hash function is one that translates every key to adifferent bucket index. For example, given the set of keys {'alpha', 'beta', 'gamma', 'delta’},the following is a perfect hash function:m = 4; hash(k) = (initial letter of k - 'a') modulo 4a. Under what circumstances does it make sense to seek a perfect hash function? Explain.b. How can a perfect hash function be exploited in implementing a hash table? Explain.c. Given the following set of keys:{CA, MX, US}find a perfect hash function with m = 3,d. Given the following set of keys:{AT, BE, DE, DK, ES, FI, FR, GR, IE, IT, LU, NL, PT, SE, UK}find a perfect hash function with m < 20.
Consider a binary code to distinguish the elements of a set {a, b, c, d}, with P(a) = 0.7, P(b)=0.15, P(c)=0.1 and P(d)=0.05. On average, how many bits will be used by a sequence of 20 elements confirming to the probability distribution given above. i.e. aaaaaaaaaaaaabbbccd Group of answer choices a. 18 b. 26 c. 2 d. 40