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The p-Center Problem. Given a set of n points and the distance dij between any two...
Problem 2 (22+ poits). Consider some unknown vi, ., V/n E Rd with d < n and you are given the cor...
Problem 2 (22+ poits). Consider some unknown vi, ., V/n E Rd with d < n and you are given the corresponding distance matrix Dij = llui-villa (a) Prove that D is not a positive semi-definite matrix unless Dij 0 for all i,j. (b) Show that we cannot recover v\, ...,Vn exactly given D. (c) Design a polynomial time algorithm to recover points x1, ,x,e Rd such that Dij la-x112.
Problem 2 (22+ poits). Consider some unknown vi, ., V/n...
s points) Given the two points P2,4) and Qu,-5) (a) Find the distance between P and...
s points) Given the two points P2,4) and Qu,-5) (a) Find the distance between P and Q (b) Find the midpoint of the segment joining P and Q. (c) Find the slope of the line through P and Q. (d) Determine an equation of the line through P and Q (e) Find an equation of a line perpendicular to the line in part (d) through (5,7). (f) Find the equation of a horizontal line through P.
c Programming Levenshtein Distance Problem; The problem requires a matrix and that is where I'm getting...
c Programming Levenshtein Distance Problem; The problem requires a matrix and that is where I'm getting hung up, I'm not real sure on what to use to be able to execute the program properly. The program is supposed to tell the distance between two words when they are entered. This is in c -declare two strings of maximum size WORD_LEN -declare an integer square matrix dist with WORD_LEN+1 rows and WORD_LEN+1 columns -read the two words to compare if the...
Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl...
I do not need the two metrics to be proved (that they are a
metric).
Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl0, 11 define - max f(x) - g(z) and di(f,g)-If(x) - g(x)d. a) Prove that for any n 2 1, one can find n points in C[O, 1 such that, in daup metric, the distance between any two points is equai to 1....
Two points P and Q are given. P(2, 1, 0), Q(−1, 2, −3) (a) Find the distance between P and Q.
Two points P and Q are given. P(2, 1, 0), Q(−1, 2, −3) (a) Find the distance between P and Q.
Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl...
Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl0, 11 define - max f(x) - g(z) and di(f,g)-If(x) - g(x)d. a) Prove that for any n 2 1, one can find n points in C[O, 1 such that, in daup metric, the distance between any two points is equai to 1. b) Can one find 100 points in C[0, 1] such that, in di metric, the...
Suppose that trade volume between any pair of countries i and j, Tij, is given by...
Suppose that trade volume between any pair of countries i and j, Tij, is given by the following gravity model: Tij = 2 * Yi * Yj/Dij Country GDP (Y) Distance from A Distance from B 12000 100 | 14000 100 21000 150 a) Suppose Z=0.005. What is the distance between A and C if the trading volume between A and B is the same as the trading volume between A and C? Show your working. b) Briefly explain why...
Problem 1 (5+15 points) Consider the set P of n points and suppose we are given...
Problem 1 (5+15 points) Consider the set P of n points and suppose we are given the points of P one point at a time. After receiving each point, we compute the convex hull of the points seen so far. (a) As a naive approach, we could run Graham’s scan once for each point, with a total running time of O(n2 log n). Write down the pesuedocode for this algorithm. (b) Develop an O(n2) algorithm to solve the problem. Write...
4. A particle P travels along a straight line so that it's distance s m, from...
4. A particle P travels along a straight line so that it's distance s m, from a fixed point O on the line is given by s-3i where t is the time in seconds after passing O. i Find the velocity and speed of the particle P after 4 seconds. i) Find out the distance of turning points from the point O i) Find the acceleration after 3 seconds. (iv) Calculate the total distance traveled during first 5 seconds. (10...
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set...
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set 1, 2,...,n} uniformly at random, with replacement. Say that the picks i and j with i < j are a match if a -aj. What is the expected total number of matches? Hint: Use indicators. Wİ
Problem 2 (22+ poits). Consider some unknown vi, ., V/n E Rd with d < n and you are given the corresponding distance matrix Dij = llui-villa (a) Prove that D is not a positive semi-definite matrix unless Dij 0 for all i,j. (b) Show that we cannot recover v\, ...,Vn exactly given D. (c) Design a polynomial time algorithm to recover points x1, ,x,e Rd such that Dij la-x112.
Problem 2 (22+ poits). Consider some unknown vi, ., V/n...
s points) Given the two points P2,4) and Qu,-5) (a) Find the distance between P and Q (b) Find the midpoint of the segment joining P and Q. (c) Find the slope of the line through P and Q. (d) Determine an equation of the line through P and Q (e) Find an equation of a line perpendicular to the line in part (d) through (5,7). (f) Find the equation of a horizontal line through P.
I do not need the two metrics to be proved (that they are a
metric).
Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl0, 11 define - max f(x) - g(z) and di(f,g)-If(x) - g(x)d. a) Prove that for any n 2 1, one can find n points in C[O, 1 such that, in daup metric, the distance between any two points is equai to 1....
Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl0, 11 define - max f(x) - g(z) and di(f,g)-If(x) - g(x)d. a) Prove that for any n 2 1, one can find n points in C[O, 1 such that, in daup metric, the distance between any two points is equai to 1. b) Can one find 100 points in C[0, 1] such that, in di metric, the...
Suppose that trade volume between any pair of countries i and j, Tij, is given by the following gravity model: Tij = 2 * Yi * Yj/Dij Country GDP (Y) Distance from A Distance from B 12000 100 | 14000 100 21000 150 a) Suppose Z=0.005. What is the distance between A and C if the trading volume between A and B is the same as the trading volume between A and C? Show your working. b) Briefly explain why...
4. A particle P travels along a straight line so that it's distance s m, from a fixed point O on the line is given by s-3i where t is the time in seconds after passing O. i Find the velocity and speed of the particle P after 4 seconds. i) Find out the distance of turning points from the point O i) Find the acceleration after 3 seconds. (iv) Calculate the total distance traveled during first 5 seconds. (10...
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set 1, 2,...,n} uniformly at random, with replacement. Say that the picks i and j with i < j are a match if a -aj. What is the expected total number of matches? Hint: Use indicators. Wİ
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