Open Access
An approximation algorithm for a generalized assignment problem with small resource requirements
Frederik Spieksma,J. Aerts,Jan Korst +2 more
- 01 Jan 2003
TL;DR: A generalized assignment problem where the resource requirements are either 1 or 2 is investigated, and it is derived that the LP-relaxation of a special case of the problem is half-integral, and a weak persistency property is derived.
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Abstract: We investigate a generalized assignment problem where the resource requirements are either 1 or 2. This problem is motivated by a question that arises when data blocks are to be retrieved from parallel disks as efficiently as possible. The resulting problem is to assign jobs to ma chines with a given capacity, where each job takes either one or two units of machine capacity, and must satisfy certain assignment restric tions, such that total weight of the assigned jobs is maximized. We derive a ~-approximation result for this problem based on relaxing a formulation of the problem so that the resulting constraint matrix is totally unimod ular. Further, we prove that the LP-relaxation of a special case of the problem is half-integral, and we derive a weak persistency property.
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Citations
An efficient approximation for the generalized assignment problem
TL;DR: Not only does this technique comprise a general interesting framework for the GAP problem; it also matches the best combinatorial approximation for this problem, with a much simpler algorithm and a better running time.
293
A Survey of Algorithms for Paper-reviewer Assignment Problem
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TL;DR: Two hybrid methods that efficiently combine the most common algorithms like genetic algorithm, ant colony optimization and tabu-search are proposed: the ACO-GA and GA-TS algorithms.
46
Extremal Optimisation Applied to Constrained Combinatorial Multi-Objective Optimisation Problems
Pedro Gómez-Meneses
- 01 Jan 2012
TL;DR: Constrained problems, either single or multi-objective, are difficult tasks to be modelled and solved by conventional mathematical techniques and an important area of research is in the domain of novel meta-heuristics that can efficiently solve such problems.
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Construction and Application of a Memetic Algorithm Assigning Catchment Areas to Retailers for Consumer Parcel Flow
Philip Moll
- 07 Jun 2017
TL;DR: The constructed stand-alone solution method involves problem size reduction, LP-Relaxations, a Memetic Algorithm and iterated clustering, which all have been benchmarked against licenced optimisation software (Gurobi) and show that the method is capable of feasibly mapping catchment areas while minimising travelling distance in acceptable computation time.
References
An approximation algorithm for the generalized assignment problem
David B. Shmoys,Éva Tardos +1 more
TL;DR: The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs; each job is to be processed by exactly one machine; processing jobj on machinei requires timepij and incurs a cost ofcij; each machinei is available forTi time units, and the objective is to minimize the total cost incurred.
External memory algorithms and data structures: dealing with massive data
TL;DR: The state of the art in the design and analysis of external memory algorithms and data structures, where the goal is to exploit locality in order to reduce the I/O costs is surveyed.
789
A Branch-and-Price Algorithm for the Generalized Assignment Problem
TL;DR: A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.
473
Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions
TL;DR: This work studies the multiple knapsack problem with assignment restrictions (MKAR) and shows that simple greedy approaches yield 1/3-approximation algorithms for the objective of maximizing assigned weight, and gives an (1/3,2)-approximating algorithm for the bicriteria problem of minimizing utilized capacity.
173
Fast concurrent access to parallel disks
Peter Sanders,Sebastian Egner,Jan Korst +2 more
- 01 Feb 2000
TL;DR: In this paper, it was shown that a shared buffer of O(D) blocks suffices to support efficient writing in an external memory machine with D parallel, independent disks, and the redundancy can be reduced from 2 to 1+1/r for any integer r without a big impact on reading efficiency.
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