Approximate Max-Min Resource Sharing for Structured Concave Optimization

Grigoriadis, Michael D.; Khachiyan, Leonid; Porkolab, Lorant; Villavicencio, Jorge

doi:10.1137/s1052623499358689

Cited by 61 publications

(67 citation statements)

References 9 publications

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“…Given set of weights v i , is there a feasible configuration with total weight of items more than 1. From the well-known connection between separation and optimization [14,24,15], solving the dual separation problem to within a (1 + ) accuracy suffices to solve the configuration LP within 1 + accuracy. Note that the configurations in (2.1) are defined based on the original item sizes (without any rounding).…”

Section: Introductionmentioning

confidence: 99%

Improved Approximation Algorithm for Two-Dimensional Bin Packing

Bansal¹,

Khan²

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study the two-dimensional bin packing problem with and without rotations. Here we are given a set of two-dimensional rectangular items I and the goal is to pack these into a minimum number of unit square bins. We consider the orthogonal packing case where the edges of the items must be aligned parallel to the edges of the bin. Our main result is a 1.405-approximation for two-dimensional bin packing with and without rotation, which improves upon a recent 1.5 approximation due to Jansen and Prädel. We also show that a wide class of rounding based algorithms cannot improve upon the factor of 1.5.

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Section: Introductionmentioning

confidence: 99%

Improved Approximation Algorithm for Two-Dimensional Bin Packing

Bansal¹,

Khan²

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…It is indeed a fractional covering problem where the columns of A represent configurations: a configuration assigns item slots to one bin (for Bin Packing) or to one shelf of the strip (for Strip Packing) such that the slots fit into the bin or the strip. The primal LP is then approximately solved with a method by Grigoriadis et al [7] (see also [9]). The columns (i.e.…”

Section: Theorem 1 There Is An Fptas For Ukp With a Running Time Inmentioning

confidence: 99%

A faster FPTAS for the Unbounded Knapsack Problem

Jansen

Kraft

2018

European Journal of Combinatorics

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The Unbounded Knapsack Problem (UKP) is a well-known variant of the famous 0-1 Knapsack Problem (0-1 KP). In contrast to 0-1 KP, an arbitrary number of copies of every item can be taken in UKP. Since UKP is NP-hard, fully polynomial time approximation schemes (FPTAS) are of great interest. Such algorithms find a solution arbitrarily close to the optimum OPT(I), i.e. of value at least (1 − ε)OPT(I) for ε > 0, and have a running time polynomial in the input length and

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“…This can be done by solving a linear program approximately similar to [15]. The approximation scheme is based on a general technique for max-min resource sharing and fractional covering problems [12]. The main new idea is an algorithm to convert the approximate preemptive schedule into an approximate non-preemptive schedule (via computing a unique allotment for almost all tasks).…”

Section: The Running Time Of a Is Polynomial In N And 1/ε With A Prepmentioning

confidence: 99%

“…Let the n covering constraints be represented by Ax ≥ λ. We can compute a (1 − ρ)-approximate solution for (2) by O(n(ρ −2 + ln n)) iterations (coordination steps) [12]. Starting with an initial solution, we compute in each iteration for the current vectorx ∈ B a price vector y = y(x) ∈ IR + n .…”

Section: 2mentioning

confidence: 99%

“…We show how to use preemptive schedules (with migration) for P|fctn j , pmtn|C max and a new rounding technique in order to generalize the result by Kenyon and Remila to malleable tasks for the PRAM, linear array and hypercube model. By combining ideas from [12], [15], [18], [21], we get the following main result: THEOREM 1.1. There is an algorithm A which, given an instance I with n tasks, m processors and execution times p j ( ) ≤ 1 depending on the numbers ∈ D ⊂ {1, .…”

Section: Introductionmentioning

confidence: 97%

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Scheduling Malleable Parallel Tasks: An Asymptotic Fully Polynomial Time Approximation Scheme

Jansen

2004

Algorithmica

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A malleable parallel task is one whose execution time is a function of the number of (identical) processors allotted to it. We study the problem of scheduling a set of n independent malleable tasks on an arbitrary number m of parallel processors and propose an asymptotic fully polynomial time approximation scheme. For any fixed ε > 0, the algorithm computes a non-preemptive schedule of length at most (1 + ε) times the optimum (plus an additive term) and has running time polynomial in n, m and 1/ε.

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Approximate Max-Min Resource Sharing for Structured Concave Optimization

Cited by 61 publications

References 9 publications

Improved Approximation Algorithm for Two-Dimensional Bin Packing

Improved Approximation Algorithm for Two-Dimensional Bin Packing

A faster FPTAS for the Unbounded Knapsack Problem

Scheduling Malleable Parallel Tasks: An Asymptotic Fully Polynomial Time Approximation Scheme

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