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Limits of Approximation Algorithms: PCPs and Unique Games (DIMACS Tutorial Lecture Notes) 1
, 2009
"... meticulous work. Special thanks to Rebecca Wright and Tami Carpenter at DIMACS but for whose organizational support and help, this workshop would have been impossible. We thank Alantha Newman, a phone conversation with whom sparked the idea of this workshop. We thank the Imdadullah Khan and Aleksand ..."
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and Aleksandar Nikolov for video recording the lectures. The video recordings of the lectures will be posted at the DIMACS tutorial webpage
Modern cryptography, probabilistic proofs and pseudorandomness, volume 17 of Algorithms and Combinatorics
, 1999
"... all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that new copies bear this notice and the full citation on the first page. Abstracting with credit is permitted. IIPreface You can start by put ..."
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Cited by 131 (13 self)
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all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that new copies bear this notice and the full citation on the first page. Abstracting with credit is permitted. IIPreface You can start by putting the do not disturb sign. Cay, in Desert Hearts (1985). The interplay between randomness and computation is one of the most fascinating scientific phenomena uncovered in the last couple of decades. This interplay is at the heart of modern cryptography and plays a fundamental role in complexity theory at large. Specifically, the interplay of randomness and computation is pivotal to several intriguing notions of probabilistic proof systems and is the focal of the computational approach to randomness. This book provides an introduction to these three, somewhat interwoven domains (i.e., cryptography, proofs and randomness). Modern Cryptography. Whereas classical cryptography was confined to
CS880: Approximations Algorithms
"... Today we discuss the background and motivation behind studying approximation algorithms and give a few examples of approximations for classic problems. Approximation algorithms make up a broad topic and are applicable to many areas. In this course a variety of different techniques for crafting appro ..."
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Today we discuss the background and motivation behind studying approximation algorithms and give a few examples of approximations for classic problems. Approximation algorithms make up a broad topic and are applicable to many areas. In this course a variety of different techniques for crafting
Approximation Algorithms for NPHard Problems
 MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH REPORT NO. 28/2004
, 2004
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Approximation Algorithms for NPHard Problems
 MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH REPORT NO. 28/2004
, 2004
"... ..."
Some New Randomized Approximation Algorithms
, 2000
"... The topic of this thesis is approximation algorithms for optimization versions of NPcomplete decision problems. No exact algorithms with subexponential running times are known for these problems, and therefore approximation algorithms with polynomial running times are studied. An approximation alg ..."
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The topic of this thesis is approximation algorithms for optimization versions of NPcomplete decision problems. No exact algorithms with subexponential running times are known for these problems, and therefore approximation algorithms with polynomial running times are studied. An approximation
Efficiency and Computational Limitations of Learning Algorithms
, 2007
"... This thesis presents new positive and negative results concerning the learnability of several wellstudied function classes in the Probably Approximately Correct (PAC) model of learning. Learning Disjunctive Normal Form (DNF) expressions in the PAC model is widely considered to be the main open prob ..."
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This thesis presents new positive and negative results concerning the learnability of several wellstudied function classes in the Probably Approximately Correct (PAC) model of learning. Learning Disjunctive Normal Form (DNF) expressions in the PAC model is widely considered to be the main open
Lecture 1
"... I assume that most students have encountered Turing machines before. (Students who have not may want to look at Sipser’s book [3].) A Turing machine is defined by an integer k ≥ 1, a finite set of states Q, an alphabet Γ, and a transition function δ: Q × Γ k → Q × Γ k−1 × {L, S, R} k where: • k is t ..."
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I assume that most students have encountered Turing machines before. (Students who have not may want to look at Sipser’s book [3].) A Turing machine is defined by an integer k ≥ 1, a finite set of states Q, an alphabet Γ, and a transition function δ: Q × Γ k → Q × Γ k−1 × {L, S, R} k where: • k is the number of (infinite, onedimensional) tapes used by the machine. In the general case we have k ≥ 3 and the first tape is a readonly input tape, the last is a writeonce output tape, and the remaining k −2 tapes are work tapes. For Turing machines with boolean output (which is what we will mostly be concerned with in this course), an output tape is unnecessary since the output can be encoded into the final state of the Turing machine when it halts. • Q is assumed to contain a designated start state qs and a designated halt state qh. (In the case where there is no output tape, there are two halting states qh,0 and qh,1.) • We assume that Γ contains {0, 1}, a “blank symbol”, and a “start symbol”. • There are several possible conventions for what happens when a head on some tape tries to move left when it is already in the leftmost position, and we are agnostic on this point. (Anyway, by our convention, below, that the leftmost cell of each tape is “marked ” there is really no reason for this to ever occur...). The computation of a Turing machine M on input x ∈ {0, 1} ∗ proceeds as follows: All tapes of the Turing machine contain the start symbol followed by blank symbols, with the exception of the input tape which contains the start symbol followed by x (and then the remainder of the input tape is filled with blank symbols). The machine starts in state q = qs with its k heads at the leftmost position of each tape. Then, until q is a halt state, repeat the following: 1. Let the current contents of the cells being scanned by the k heads be γ1,..., γk ∈ Γ.
Results 1  10
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217