A constant factor approximation algorithm for the storage allocation problem

Bar-Yehuda, Reuven; Beder, Michael; Rawitz, Dror

doi:10.1145/2486159.2486177

Cited by 5 publications

(10 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…RAP on contiguous machines has been considered under the name storage allocation problem (SAP), in which tasks are axis-aligned rectangles that are only allowed to move vertically. Leonardi et al [32] provide a 12-approximation algorithm for SAP and Bar-Yehuda et al [9] present a (2 + ǫ + 1/(e − 1))-approximation algorithm.…”

Section: Related Resultsmentioning

confidence: 99%

A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

Bonsma

Schulz

Wiese

2011

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science

View full text Add to dashboard Cite

In the unsplittable flow problem on a path, we are given a capacitated path P and n tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge e of P , the total demand of selected tasks that use e does not exceed the capacity of e. This is a well-studied problem that has been studied under alternative names, such as resource allocation, bandwidth allocation, resource constrained scheduling, temporal knapsack and interval packing.We present a polynomial time constant-factor approximation algorithm for this problem. This improves on the previous best known approximation ratio of O(log n). The approximation ratio of our algorithm is 7 + ǫ for any ǫ > 0.We introduce several novel algorithmic techniques, which might be of independent interest: a framework which reduces the problem to instances with a bounded range of capacities, and a new geometrically inspired dynamic program which solves a special case of the maximum weight independent set of rectangles problem to optimality. In the setting of resource augmentation, wherein the capacities can be slightly violated, we give a (2 + ǫ)-approximation algorithm. In addition, we show that the problem is strongly NP-hard even if all edge capacities are equal and all demands are either 1, 2, or 3.

show abstract

Section: Related Resultsmentioning

confidence: 99%

A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

Bonsma

Schulz

Wiese

2011

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science

View full text Add to dashboard Cite

show abstract

“…[20]. Then the claim follows from Bar-Yehuda et al [8,Lemma 9] (based on a result of Buchsbaum et al [12]).…”

Section: Polynomial Time Algorithm For Boxable Solutionsmentioning

confidence: 78%

“…to a (2 + ε)-approximation [7]. Bar-Yehuda et al [8] presented the first constant factor approximation algorithm for SAP for arbitrary capacities, having an approximation ratio of 9 + ε. A related problem is the dynamic storage allocation problem (DSA) where in the input we are given a set of tasks like in SAP and we all need to pack all of them as non-overlapping rectangles, minimizing the maximum height of a packed item.…”

Section: Other Related Workmentioning

confidence: 99%

“…Hence, (T , h ) or (T , h ) satisfies the claim of the lemma. Formally, our candidate solutions are OPT (1) := OPT S , OPT (2) := OPT L ∪ OPT S,bottom,S , OPT (3) := OPT L ∪ OPT S,bottom,L , OPT (4) := OPT L ∪ OPT S,top,S OPT (5) := OPT L ∪ OPT S,top,L , OPT (6) := T box , OPT (7) := T box , OPT (8) := OPT L ∪ OPT S,cross , OPT (7) := OPT L,top ∪ OPT L,bottom ∪ OPT S,mid,top,S , OPT (8) := OPT L,top ∪ OPT L,bottom ∪ OPT S,mid,top,L , OPT (9) := OPT L,top ∪ OPT L,bottom ∪ OPT S,mid,bottom,S , OPT (10) := OPT L,top ∪ OPT L,bottom ∪ OPT S,mid,bottom,L , OPT (11) := T sw , and OPT (12) := T sw .…”

Section: Types Of Points In the Middlementioning

confidence: 99%

“…We have that OPT (1) , OPT (9) , and OPT (10) are pile boxable solutions, OPT (2) , OPT (4) , OPT (7) , and OPT (9) are laminar boxable solutions, OPT (3) , OPT (5) , OPT (8) , and OPT (10) are δ-jammed solutions, and finally OPT (7) and OPT (8) are O δ (1)-boxable solutions.…”

Section: Types Of Points In the Middlementioning

confidence: 99%

See 2 more Smart Citations

Breaking the Barrier of 2 for the Storage Allocation Problem

Mömke,

Wiese

2019

Preprint

View full text Add to dashboard Cite

Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack (2DKP) and Unsplittable Flow on a Path (UFP). For the latter two problems, recently the first polynomial time approximation algorithms with better approximation ratios than 2 were presented [Gálvez et al., FOCS 2017][Grandoni et al., STOC 2018. In this paper we break the barrier of 2 for the Storage Allocation Problem (SAP) which is a natural intermediate problem between 2DKP and UFP. We are given a path with capacitated edges and a set of tasks where each task has a start vertex, an end vertex, a size, and a profit. We seek to select the most profitable set of tasks that we can draw as non-overlapping rectangles underneath the capacity profile of the edges where the height of each rectangle equals the size of the corresponding task. This problem is motivated by settings of allocating resources like memory, bandwidth, etc. where each request needs a contiguous portion of the resource.The best known polynomial time approximation algorithm for SAP has an approximation ratio of 2 + ε [Mömke and Wiese, ICALP 2015] and no better quasi-polynomial time algorithm is known. We present a polynomial time (63/32 + ε) < 1.969-approximation algorithm for the case of uniform edge capacities and a quasi-polynomial time (1.997 + ε)-approximation algorithm for non-uniform quasipolynomially bounded edge capacities. Key to our results are building blocks consisting of stair-blocks, jammed tasks, and boxes that we use to construct profitable solutions and which allow us to compute solutions of these types efficiently. Finally, using our techniques we show that under slight resource augmentation we can obtain even approximation ratios of 3/2 + ε in polynomial time and 1 + ε in quasi-polynomial time, both for arbitrary edge capacities.

show abstract

A $$(2+\epsilon )$$-Approximation Algorithm for the Storage Allocation Problem

Mömke

Wiese

2015

Automata, Languages, and Programming

View full text Add to dashboard Cite

A constant factor approximation algorithm for the storage allocation problem

Cited by 5 publications

References 15 publications

A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

Breaking the Barrier of 2 for the Storage Allocation Problem

A $$(2+\epsilon )$$-Approximation Algorithm for the Storage Allocation Problem

Contact Info

Product

Resources

About