Polynomial-Time Approximation Schemes

Shachnai, Hadas; Tamir, Tami

doi:10.1201/9781420010749.ch9

Cited by 4 publications

(2 citation statements)

References 30 publications

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“…In the context of optimization, some polynomial time approximation schemes have been designed thanks to the guessing technique [1]. This technique can be decomposed in two steps: proving an approximation ratio while assuming that a little part of the optimal solution is known, and finally enumerating the possibilities for this part of the optimal solution.…”

Section: B Related Workmentioning

confidence: 99%

Combining multiple heuristics on discrete resources

Bougeret

Dutot

Goldman

et al. 2009

2009 IEEE International Symposium on Parallel &Amp; Distributed Processing

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Abstract-In this work we study the portfolio problem which is to find a good combination of multiple heuristics to solve given instances on parallel resources in minimum time. The resources are assumed to be discrete, it is not possible to allocate a resource to more than one heuristic. Our goal is to minimize the average completion time of the set of instances, given a set of heuristics on homogeneous discrete resources. This problem has been studied in the continuous case in [18]. We first show that the problem is hard and that there is no constant ratio polynomial approximation in the general case. Then, we design several approximation schemes for a restricted version of the problem where each heuristic must be used at least once. These results are obtained by using oracle with several guesses, leading to various tradeoff between the size of required information and the approximation ratio. Some additional results based on experiments are finally reported using a benchmark of instances on SAT solvers.

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Section: B Related Workmentioning

confidence: 99%

Combining multiple heuristics on discrete resources

Bougeret

Dutot

Goldman

et al. 2009

2009 IEEE International Symposium on Parallel &Amp; Distributed Processing

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“…We proposed an approximation scheme (cf., e.g., [39]), constructing a feasible solution for P2|d j = d|X based on a simplified instance of this problem. We adopted the idea of polynomial time approximation scheme given by Schuurman and Woeginger [40] for the two-machine problem with the makespan criterion, P2||C max , based on structuring problem input, which was originally proposed by Sahni [41].…”

Section: Polynomial Time Approximation Schemementioning

confidence: 99%

Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work

Sterna

Czerniachowska

2017

J Optim Theory Appl

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We study the scheduling problem with a common due date on two parallel identical machines and the total early work criterion. The problem is known to be NPhard. We prove a few dominance properties of optimal solutions of this problem. Their proposal was inspired by the results of some auxiliary computational experiments. Test were performed with the dynamic programming algorithm and list algorithms. Then, we propose the polynomial time approximation scheme, based on structuring problem input. Moreover, we discuss the relationship between the early work criterion and the related late work criterion. We compare the computational complexity and approximability of scheduling problems with both mentioned objective functions.

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Selecting Sources for Query Approximation with Bounded Resources

Guo

Gao

2020

Combinatorial Optimization and Applications

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Polynomial-Time Approximation Schemes

Cited by 4 publications

References 30 publications

Combining multiple heuristics on discrete resources

Combining multiple heuristics on discrete resources

Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work

Selecting Sources for Query Approximation with Bounded Resources

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