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NPhard Optimization Problems
"... F12.24> . Given a set of variables X and a set of equations E each in k of the variables in X , nd an assignment of X . Maximize the number of equations in E that are satised by this assignment of X . Scheduling: Given a set of jobs, a processing time for each job, and a set of processors, assi ..."
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, assign the jobs to the processors. Minimize the time it takes to complete all the jobs assuming a processor can only process one job at a time. In order to prove that these are NPhard optimization problems, we must prove their corresponding decision problems are NPcomplete. For example, to prove vertex
The inapproximability of non NPhard optimization problems
, 1999
"... The inapproximability of non NPhard optimization problems is investigated. Techniques are given to show that problems Log Dominating Set and Log Hypergraph Vertex Cover cannot be approximated to a constant ratio in polynomial time unless the corresponding NPhard versions are also approximable i ..."
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Cited by 4 (2 self)
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The inapproximability of non NPhard optimization problems is investigated. Techniques are given to show that problems Log Dominating Set and Log Hypergraph Vertex Cover cannot be approximated to a constant ratio in polynomial time unless the corresponding NPhard versions are also approximable
Project plan: Approximation of NPhard Optimization Problems
"... This document consists of parts of the description of work of the above grant. It is not a complete document and is intended to give an introduction to the planned research. 1 General research area The goal of complexity theory is to study the amount of computational resources that are needed to sol ..."
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the running time as a function of the input length. A definition that has turned out to be useful is to say that a problem can be solved efficiently if the running time increases polynomially in the size of the input. This class of problems is denoted by P and another central complexity class is NP; problems
Approximation algorithms for NPhard optimization problems
 In Algorithms and Theory of Computation Handbook
, 1999
"... Introduction In this chapter, we discuss approximation algorithms for optimization problems. An optimization problem consists in finding the best (cheapest, heaviest, etc.) element in a large set P , called the feasible region and usually specified implicitly, where the quality of elements of the se ..."
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Cited by 7 (0 self)
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Introduction In this chapter, we discuss approximation algorithms for optimization problems. An optimization problem consists in finding the best (cheapest, heaviest, etc.) element in a large set P , called the feasible region and usually specified implicitly, where the quality of elements
Polynomial Time Approximation Schemes for Some Dense Instances of NPHard Optimization Problems
 Proc. RANDOM 97, LNCS 1269
, 1997
"... We survey recent results on the existence of polynomial time approximation schemes for some dense instances of NPhard combinatorial optimization problems. We indicate further some inherent limits for existence of such schemes for some other dense instances of optimization problems. ..."
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Cited by 23 (10 self)
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We survey recent results on the existence of polynomial time approximation schemes for some dense instances of NPhard combinatorial optimization problems. We indicate further some inherent limits for existence of such schemes for some other dense instances of optimization problems.
Hardness Of Approximations
, 1996
"... This chapter is a selfcontained survey of recent results about the hardness of approximating NPhard optimization problems. ..."
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Cited by 120 (5 self)
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This chapter is a selfcontained survey of recent results about the hardness of approximating NPhard optimization problems.
The hardness of kmeans clustering
, 2008
"... We show that kmeans clustering is an NPhard optimization problem, even if k is fixed to 2. 1 ..."
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Cited by 26 (0 self)
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We show that kmeans clustering is an NPhard optimization problem, even if k is fixed to 2. 1
Polynomial Time Approximation Schemes for Dense Instances of NPHard Problems
, 1995
"... We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3satisfiabi ..."
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Cited by 195 (32 self)
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We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3
The Approximability of Some NPhard Problems
, 2009
"... An αapproximation algorithm is an algorithm guaranteed to output a solution that is within an α ratio of the optimal solution. We are interested in the following question: Given an NPhard optimization problem, what is the best approximation guarantee that any polynomial time algorithm could achiev ..."
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An αapproximation algorithm is an algorithm guaranteed to output a solution that is within an α ratio of the optimal solution. We are interested in the following question: Given an NPhard optimization problem, what is the best approximation guarantee that any polynomial time algorithm could
Results 1  10
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