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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
A Parallel Hybrid Approach to Hard Optimization Problems
, 1997
"... This paper presents a software platform for the distributed solution of complex optimization problems. For such problems there are often no outstanding approaches which always perform well. That is why we propose to use different solution methods simultaneously. They can communicate and thus profita ..."
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Cited by 9 (0 self)
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Introduction There is a large number of important hard optimization problems as for example satisfiability, integer programming, covering and scheduling problems. It is not known whether such problem can be solved deterministically in polynomial time. Therefore efficient heuristcs or exponential time
The Dynamics of a Genetic Algorithm on a Model Hard Optimization Problem
 Complex Systems
, 1997
"... this paper we analyze a previously published model of a hard optimization problem [14] which addresses the last two instances. The problem is known as the 'Basin with a Barrier' fitness landscape and is a function of unitation. It has some of the features of a hard optimization problem but ..."
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Cited by 9 (7 self)
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this paper we analyze a previously published model of a hard optimization problem [14] which addresses the last two instances. The problem is known as the 'Basin with a Barrier' fitness landscape and is a function of unitation. It has some of the features of a hard optimization problem
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
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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to solve a particular computational problem. The most studied resource is computer time and here “time ” is used to mean the number of elementary operations getting a theory that is independent of technology. Clearly it is more difficult to solve large instances of a problem and thus one studies
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
SIMULATED ELECTRICAL NETWORK APPROACH (SENA) TO HARD OPTIMIZATION PROBLEMS
, 2008
"... A novel method is proposed for hard optimization type of problem wherein an exact optimal solution is increasingly difficult in terms of run time and memory requirements. Especially for the cases when search graph has higher number of nodes and more number of paths, which increase as factorial of no ..."
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A novel method is proposed for hard optimization type of problem wherein an exact optimal solution is increasingly difficult in terms of run time and memory requirements. Especially for the cases when search graph has higher number of nodes and more number of paths, which increase as factorial
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