Fast and simple approximation schemes for generalized flow

Fleischer, Lisa; Wayne, Kevin

doi:10.1007/s101070100238

Cited by 49 publications

(64 citation statements)

References 35 publications

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“…Fleischer [13]). Although the flow problems studied in this paper also have this property, the requirement that flow pass through all operators (if not eliminated along the way) does not arise in generalized maximum flow problems.…”

Section: Related Workmentioning

confidence: 99%

Algorithms for distributional and adversarial pipelined filter ordering problems

Condon

Deshpande

Hellerstein

et al. 2009

ACM Trans. Algorithms

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Pipelined filter ordering is a central problem in database query optimization. The problem is to determine the optimal order in which to apply a given set of commutative filters (predicates) to a set of elements (the tuples of a relation), so as to find, as efficiently as possible, the tuples that satisfy all of the filters. Optimization of pipelined filter ordering has recently received renewed attention in the context of environments such as the web, continuous high-speed data streams, and sensor networks. Pipelined filter ordering problems are also studied in areas such as fault detection and machine learning under names such as learning with attribute costs, minimumsum set cover, and satisficing search. We present algorithms for two natural extensions of the classical pipelined filter ordering problem: (1) a distributional type problem where the filters run in parallel and the goal is to maximize throughput, and (2) an adversarial type problem where the goal is to minimize the expected value of multiplicative regret. We present two related algorithms for solving (1), both running in time O(n 2 ), which improve on the O(n 3 log n) algorithm of Kodialam. We use techniques from our algorithms for (1) to obtain an algorithm for (2).

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Section: Related Workmentioning

confidence: 99%

Algorithms for distributional and adversarial pipelined filter ordering problems

Condon

Deshpande

Hellerstein

et al. 2009

ACM Trans. Algorithms

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show abstract

“…They have been improved and adapted to different models in a series of papers [12,13,17,20,22,25,27,32]. While all this research was built on the idea of rerouting existing flows, the idea of augmenting flow has led to a couple of new algorithms with improved running times [7,8,10,16,34]. Several publications also report about the usability of approximation algorithms for multicommodity flow problems in practice [1,11,13,28,29].…”

Section: The Fptasmentioning

confidence: 99%

Multicommodity Flow Approximation Used for Exact Graph Partitioning

Sellmann

Sensen

Timajev

2003

Algorithms - ESA 2003

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Abstract. We present a fully polynomial-time approximation scheme for a multicommodity flow problem that yields lower bounds of the graph bisection problem. We compare the approximation algorithm with Lagrangian relaxation based cost-decomposition approaches and linear programming software when embedded in an exact branch&bound approach for graph bisection. It is shown that the approximation algorithm is clearly superior in this context. Furthermore, we present a new practical addition to the approximation algorithm which improves its performance distinctly. Finally, we prove the performance of the graph bisection algorithm using multicommodity flow approximation by computing formerly unknown bisection widths of some DeBruijn-and Shuffle-Exchange-Graphs.

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“…There exist fast fully polynomial-time approximation schemes for computing a fractional solution [4,12,20,21,25]. Using the rounding technique from [23], this leads to a (2 + ε)-approximation for the discrete problem.…”

Section: Introductionmentioning

confidence: 99%

“…Using the rounding technique from [23], this leads to a (2 + ε)-approximation for the discrete problem. The approximation schemes can be divided into those that approximate generalized maximum flows [4,21,25] and those that directly address the scheduling problem [12,20].…”

Section: Introductionmentioning

confidence: 99%

A Faster Combinatorial Approximation Algorithm for Scheduling Unrelated Parallel Machines

Gairing

Monien

Woclaw

2005

Automata, Languages and Programming

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Abstract.We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time pij on machine j, and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. The best known approximation algorithms for this problem compute an optimum fractional solution and then use rounding techniques to get an integral 2-approximation.In this paper we present a combinatorial approximation algorithm that matches this approximation quality. It is much simpler than the previously known algorithms and its running time is better. This is the first time that a combinatorial algorithm always beats the interior point approach for this problem. Our algorithm is a generic minimum cost flow algorithm, without any complex enhancements, tailored to handle unsplittable flow. It pushes unsplittable jobs through a two-layered bipartite generalized network defined by the scheduling problem. In our analysis, we take advantage from addressing the approximation problem directly. In particular, we replace the classical technique of solving the LP-relaxation and rounding afterwards by a completely integral approach. We feel that this approach will be helpful also for other applications.

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Fast and simple approximation schemes for generalized flow

Cited by 49 publications

References 35 publications

Algorithms for distributional and adversarial pipelined filter ordering problems

Algorithms for distributional and adversarial pipelined filter ordering problems

Multicommodity Flow Approximation Used for Exact Graph Partitioning

A Faster Combinatorial Approximation Algorithm for Scheduling Unrelated Parallel Machines

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