TY - GEN

T1 - A constant factor approximation algorithm for the storage allocation problem

AU - Bar-Yehuda, Reuven

AU - Beder, Michael

AU - Rawitz, Dror

PY - 2013

Y1 - 2013

N2 - We study the storage allocation problem (sap) which is a variant of the unsplittable flow problem on paths (ufpp). a sap instance consists of a path P = (V, E) and a set J of tasks. Each edge e ⋯ E has a capacity c e and each task j ⋯ J is associated with a path Ij in P, a demand dj and a weight Wj. The goal is to find a maximum weight subset S ⊆ J of tasks and a height function h : S → ℝ+ such that (i) h(j)+dj ≤ ce, for every e ⋯ IJ; and (ii) if j, i ⋯ S such that I j ∩ Ii ≠ and h (j) ≥ h(i), then h(J) ≥ h(i) + di. SAP can be seen as a rectangle packing problem in which rectangles can be moved vertically, but not horizontally. We present a polynomial time (9 + e)-approximation algorithm for SAP. Our algorithm is based on a variation of the framework for approximating UFPP by Bonsma et al. [FOCS 2011] and on a (4 + ε)-approximation algorithm for δ-small SAP instances (in which dj ≤ δ · ce, for every e ⋯ Ij, for a sufficiently small constant δ > 0). In our algorithm for δ-small instances, tasks are packed carefully in strips in a UFPP manner, and then a (1 + ε) factor is incurred by a reduction from SAP to UFPP in strips. The strips are stacked to form a SAP solution. Finally, we show that SAP is strongly NP-hard, even with uniform weights and even if assuming the no bottleneck assumption.

AB - We study the storage allocation problem (sap) which is a variant of the unsplittable flow problem on paths (ufpp). a sap instance consists of a path P = (V, E) and a set J of tasks. Each edge e ⋯ E has a capacity c e and each task j ⋯ J is associated with a path Ij in P, a demand dj and a weight Wj. The goal is to find a maximum weight subset S ⊆ J of tasks and a height function h : S → ℝ+ such that (i) h(j)+dj ≤ ce, for every e ⋯ IJ; and (ii) if j, i ⋯ S such that I j ∩ Ii ≠ and h (j) ≥ h(i), then h(J) ≥ h(i) + di. SAP can be seen as a rectangle packing problem in which rectangles can be moved vertically, but not horizontally. We present a polynomial time (9 + e)-approximation algorithm for SAP. Our algorithm is based on a variation of the framework for approximating UFPP by Bonsma et al. [FOCS 2011] and on a (4 + ε)-approximation algorithm for δ-small SAP instances (in which dj ≤ δ · ce, for every e ⋯ Ij, for a sufficiently small constant δ > 0). In our algorithm for δ-small instances, tasks are packed carefully in strips in a UFPP manner, and then a (1 + ε) factor is incurred by a reduction from SAP to UFPP in strips. The strips are stacked to form a SAP solution. Finally, we show that SAP is strongly NP-hard, even with uniform weights and even if assuming the no bottleneck assumption.

KW - Approximation algorithms

KW - Bandwidth allocation

KW - Rectangle packing

KW - Storage allocation

KW - Unsplittable flow

UR - http://www.scopus.com/inward/record.url?scp=84883519642&partnerID=8YFLogxK

U2 - 10.1145/2486159.2486177

DO - 10.1145/2486159.2486177

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AN - SCOPUS:84883519642

SN - 9781450315722

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 204

EP - 213

BT - SPAA 2013 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures

PB - Association for Computing Machinery

T2 - 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013

Y2 - 23 July 2013 through 25 July 2013

ER -