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On Some Tighter Inapproximability Results
, 1998
"... We prove a number of improved inaproximability results, including the best up to date explicit approximation thresholds for MIS problem of bounded degree, bounded occurrences MAX2SAT, and bounded degree Node Cover. We prove also for the first time inapproximability of the problem of Sorting by Reve ..."
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Cited by 118 (21 self)
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We prove a number of improved inaproximability results, including the best up to date explicit approximation thresholds for MIS problem of bounded degree, bounded occurrences MAX2SAT, and bounded degree Node Cover. We prove also for the first time inapproximability of the problem of Sorting
Improved Inapproximability for TSP
, 2014
"... The Traveling Salesman Problem is one of the most studied problems in the theory of algorithms and its approximability is a longstanding open question. Prior to the present work, the best known inapproximability threshold was 220/219, due to Papadimitriou and Vempala. Here, using an essentially di ..."
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Cited by 9 (1 self)
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The Traveling Salesman Problem is one of the most studied problems in the theory of algorithms and its approximability is a longstanding open question. Prior to the present work, the best known inapproximability threshold was 220/219, due to Papadimitriou and Vempala. Here, using an essentially
Reductions, codes, PCPs, and inapproximability
 Proc. of 36th Annual Symposium of Foundations of Computer Science
, 1995
"... Many recent results show the hardness of approximating NPhard functions. We formalize, in a very simple way, what these results involve: a codelike Levin reduction. Assuming a wellknown complexity assumption, we show that such reductions cannot prove the NPhardness of the following problems, wher ..."
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Cited by 2 (0 self)
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Many recent results show the hardness of approximating NPhard functions. We formalize, in a very simple way, what these results involve: a codelike Levin reduction. Assuming a wellknown complexity assumption, we show that such reductions cannot prove the NPhardness of the following problems, where ffl is any positive fraction: (i) achieving an approximation ratio
Conditional Inapproximability and Limited Independence
, 2008
"... Understanding the theoretical limitations of efficient computation is one of the most fundamental open problems of modern mathematics. This thesis studies the approximability of intractable optimization problems. In particular, we study socalled Max CSP problems. These are problems in which we are ..."
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Understanding the theoretical limitations of efficient computation is one of the most fundamental open problems of modern mathematics. This thesis studies the approximability of intractable optimization problems. In particular, we study socalled Max CSP problems. These are problems in which we are given a set of constraints, each constraint acting on some k variables, and are asked to find an assignment to the variables satisfying as many of the constraints as possible. A predicate P:[q] k →{0, 1} is said to be approximation resistant if it is intractable to approximate the corresponding CSP problem to within a factor which is better than what is expected from a completely random assignment to the variables. We prove that if the Unique Games Conjecture is true, then a sufficient condition for a predicate P: [q] k →{0, 1} to be approximation resistant is that there exists a pairwise independent distribution over [q] k which is supported on the set of satisfying assignments P −1 (1) of P. We also study predicates P: {0, 1} 2 →{0, 1} on two boolean variables. The corresponding CSP problems include fundamental computational problems such as Max Cut
On Some Tighter Inapproximability Results, Further Improvements
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT
, 1998
"... Improved inaproximability results are given, including the best up to date explicit approximation thresholds for bounded occurence satisfiability problems, like MAX2SAT and E2LIN2, and problems in bounded degree graphs, like MIS, Node Cover and MAX CUT. We prove also for the first time inapproxim ..."
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Cited by 16 (2 self)
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inapproximability of the problem of Sorting by Reversals and display an explicit approximation threshold for this problem.
Towards Sharp Inapproximability For Any 2CSP
"... We continue the recent line of work on the connection between semidefinite programmingbased approximation algorithms and the Unique Games Conjecture. Given any boolean 2CSP (or more generally, any nonnegative objective function on two boolean variables), we show how to reduce the search for a good ..."
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Cited by 32 (1 self)
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good inapproximability result to a certain numeric minimization problem. The key objects in our analysis are the vector triples arising when doing clausebyclause analysis of algorithms based on semidefinite programming. Given a weighted set of such triples of a certain restricted type, which
Results 1  10
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1,153