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### lec17

Course: CS 17, Fall 2008
School: Berkeley
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Word Count: 1824

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CS174 Lecture 17 &lt;a href=&quot;/keyword/minimum-spanning-tree/&quot; &gt;&lt;a href=&quot;/keyword/minimum-spanning/&quot; &gt;minimum spanning&lt;/a&gt; tree&lt;/a&gt; s Remember the &lt;a href=&quot;/keyword/minimum-spanning-tree/&quot; &gt;&lt;a href=&quot;/keyword/minimum-spanning/&quot; &gt;minimum spanning&lt;/a&gt;...

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CS174 Lecture 17 <a href="/keyword/minimum-spanning-tree/" ><a href="/keyword/minimum-spanning/" >minimum spanning</a> tree</a> s Remember the <a href="/keyword/minimum-spanning-tree/" ><a href="/keyword/minimum-spanning/" >minimum spanning</a> tree</a> problem from CS170 you are given a graph G with weighted edges (real values on each edge) and the goal is to find a spanning tree T whose total weight is minimal. The <a href="/keyword/minimum-spanning-tree/" ><a href="/keyword/minimum-spanning/" >minimum spanning</a> tree</a> is the least expensive way to connect up all the nodes. In the graph below, the <a href="/keyword/minimum-spanning-tree/" ><a href="/keyword/minimum-spanning/" >minimum spanning</a> tree</a> is shown with heavy shaded edges. 5 12 17 10 8 4 8 13 11 6 14 <a href="/keyword/minimum-spanning-tree/" ><a href="/keyword/minimum-spanning/" >minimum spanning</a> tree</a> s are useful for designing networks: computer networks, communication networks, and distribution networks...
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Berkeley - CS - 174
CS174 Lecture 17Minimum Spanning TreesRemember the minimum spanning tree problem from CS170 you are given a graph G with weighted edges (real values on each edge) and the goal is to find a spanning tree T whose total weight is minimal. The minimum
Berkeley - CS - 174
CS174Lecture 25John CannySecret Sharing and Threshold DecryptionThe goal of secret-sharing is to divide a secret S into n pieces S1 , . . . , Sn such that any m + 1 pieces are sufcient to reconstruct S, but any m pieces give no information abo
Berkeley - CS - 25
CS174Lecture 25John CannySecret Sharing and Threshold DecryptionThe goal of secret-sharing is to divide a secret S into n pieces S1 , . . . , Sn such that any m + 1 pieces are sufcient to reconstruct S, but any m pieces give no information abo
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CS174Lecture 24John CannyZero-Knowledge Proofs for discrete logsSuppose you want to prove your identity to someone, in order to cash a check or pick up a package. Most forms of ID can be copied or forged, but there is a zero-knowledge method t
Berkeley - CS - 24
CS174Lecture 24John CannyZero-Knowledge Proofs for discrete logsSuppose you want to prove your identity to someone, in order to cash a check or pick up a package. Most forms of ID can be copied or forged, but there is a zero-knowledge method t
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CS174Monte-Carlo vs. Las VegasLecture 2John CannyA random algorithm is Las Vegas if it always produces the correct answer. The running time depends on the random choices made in the algorithm. Random Quicksort (where pivot elements are chosen
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CS174Lecture 8John CannyMore on Coupon CollectingRecall that coupon collecting is equivalent to placing m balls in n bins so that no bin is empty. Last time we derived an upper bound for the probability that some bin is empty which is Pr[some
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CS174Lecture 22John CannySecure Hash AlgorithmsAnother basic tool for cryptography is a secure hash algorithm. Unlike encryption, given a variablelength message x, a secure hash algorithm computes a function h(x) which has a xed and often smal
Berkeley - CS - 22
CS174Lecture 22John CannySecure Hash AlgorithmsAnother basic tool for cryptography is a secure hash algorithm. Unlike encryption, given a variablelength message x, a secure hash algorithm computes a function h(x) which has a xed and often smal
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CS174 Sp2001Homework 12 Solutionsout: May 3, 20011. Each secret share si of a secret s is a pair xi ; yi where yi1= pxi andpx = rtxt + + r x + smod p is a polynomial whose coefcients r ; : : : ; rt are chosen independently and uniformly
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CS174 Sp2001Homework 12 Solutionsout: May 3, 20011. Each secret share si of a secret s is a pair xi ; yi where yi1= pxi andpx = rtxt + + r x + smod p is a polynomial whose coefcients r ; : : : ; rt are chosen independently and uniformly
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CS174Tail BoundsLecture 6John CannyLast time we looked at occupancy problems and derived some results on the distribution of some random variables. We derived bounds on the probability of a bin containing more than k balls, and the expected nu
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CS174Tail BoundsLecture 6John CannyLast time we looked at occupancy problems and derived some results on the distribution of some random variables. We derived bounds on the probability of a bin containing more than k balls, and the expected nu
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CS174 J. CannyMidterm 1Spring 2000 Feb 29This is a closed-book exam with 4 questions. You have 80 minutes. All questions are worth equal points, so be sure to budget 20 minutes per question. You are allowed to use the formula sheet that will be
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CS174 J. CannyMidterm 2Spring 2000 April 6This is a closed-book exam with 4 questions. You are allowed to use the 4 sides of notes that you brought with you. The marks for each question are shown in parentheses, and the total is 80 points. Make
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CS174 Lecture 14Data-Punctuated Token Trees (Berlekamp)Fingerprints provide a fast and communication-efficient way to check whether two strings are identical or not. Rather than sending S and T over a network, you can send the fingerprint f(S) from
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CS174 Lecture 14Data-Punctuated Token Trees (Berlekamp)Fingerprints provide a fast and communication-efficient way to check whether two strings are identical or not. Rather than sending S and T over a network, you can send the fingerprint f(S) from
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CS174 Lecture 11Routing in a Parallel ComputerWe study the problem of moving packets around in a parallel computer. In this lecture we will consider parallel computers with hypercube connection networks. The methods we describe are easy to adapt to
Berkeley - CS - 174
CS174 Lecture 11Routing in a Parallel ComputerWe study the problem of moving packets around in a parallel computer. In this lecture we will consider parallel computers with hypercube connection networks. The methods we describe are easy to adapt to
Berkeley - CS - 174
CS174 J. CannyMidterm 1Spring 99 Mar 2This is a closed-book exam with 4 questions. You have 80 minutes. All questions are worth equal points, so be sure to budget 20 minutes per question. You are allowed to use the formula sheet that will be ha
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CS174 Chernoff BoundsLecture 10John CannyChernoff bounds are another kind of tail bound. Like Markoff and Chebyshev, they bound the total amount of probability of some random variable Y that is in the tail, i.e. far from the mean.Recall that
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CS174 Chernoff BoundsLecture 10John CannyChernoff bounds are another kind of tail bound. Like Markoff and Chebyshev, they bound the total amount of probability of some random variable Y that is in the tail, i.e. far from the mean.Recall that
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CS174 Lecture 19Paging, Online Algorithms and AdversariesYou should be familiar with the paging problem. A computer has a cache memory which can hold k pages. Then there is a much larger slow memory (or disk) which can hold an arbitrary number of p
Berkeley - CS - 19
CS174 Lecture 19Paging, Online Algorithms and AdversariesYou should be familiar with the paging problem. A computer has a cache memory which can hold k pages. Then there is a much larger slow memory (or disk) which can hold an arbitrary number of p
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CS174 Occupancy ProblemsLecture 5John CannyOccupancy problems deal with pairings of objects. The basic occupancy problem is about placing m balls into n bins. This seemingly ordinary problem has a vast number of applications. Let Xi be the rand
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CS174 Occupancy ProblemsLecture 5John CannyOccupancy problems deal with pairings of objects. The basic occupancy problem is about placing m balls into n bins. This seemingly ordinary problem has a vast number of applications. Let Xi be the rand
Berkeley - CS - 174
Solutions for CS174 Homework 6P1. From the lecture notes, E Hij n=2: If the probability of a given packet is delayed more than T n steps is bounded by 2,2n, then we can guarantee that all packets reach their destination in time T n with probabili
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Solutions for CS174 Homework 6P1. From the lecture notes, E Hij n=2: If the probability of a given packet is delayed more than T n steps is bounded by 2,2n, then we can guarantee that all packets reach their destination in time T n with probabili
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CS174Randomized Birthday SearchLecture 1John CannyFrom the table below, copy the number under the month of your birthday onto a piece of paper. Jan 323 Feb 106 Mar Apr May 261 13 75 Jun 137 July 354 Aug 292 Sept 230 Oct 168 Nov 44 Dec 199Now
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CS174 Sp2001 J. CannyHomework 2out: Jan 25, 2001 due: Feb 1, 2001This homework is due by 5pm on Thursday Feb 1st. Please hand it to the CS174 homework box on the second oor of Soda Hall. 1. Suppose you need a biased coin which has probability k
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CS174 Sp2001Quiz 1Feb 8, 2001Please write your name and SID number in the spaces below, and wait for the signal to start:NameSID11. Let X be a random variable which is 1 iff the number on a toss of a fair die is even, 0 otherwise. Let Y
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CS174 Sp2001Homework 5due: Feb 22, 2001This homework is due by 5pm on Thursday Feb 22th. Please hand it to the CS174 homework box on the second oor of Soda Hall. 1. Let G be a random graph with n vertices and m edges generated using the rst ran
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The problemPractical Byzantine Fault ToleranceMiguel Castro and Barbara Liskov MITPresented to cs294-4 by Owen CooperProvide a reliable answer to a computation even in the presence of Byzantine faults. A client would like to Transmit a r
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University of California, Berkeley College of Engineering Computer Science Division EECS Spring 2007 John KubiatowiczMarch 21st, 2007 CS252 Graduate Computer ArchitectureMidterm IYour Name: SID Number:Problem 1 2 3 4 5 TotalPossible 16 21
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CS252 Graduate Computer Architecture Lecture 18 Error CorrectionJohn Kubiatowicz Electrical Engineering and Computer Sciences University of California, Berkeley http:/www.eecs.berkeley.edu/~kubitron/cs252 http:/www-inst.eecs.berkeley.edu/~cs252Rev
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