Resource Allocation in Bounded Degree Trees

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

doi:10.1007/s00453-007-9121-7

Cited by 14 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…UFP and its variations are motivated by several applications in bandwidth allocation [8,17,24], caching…”

Section: Introductionmentioning

confidence: 99%

“…UFP and its variations are motivated by several applications in bandwidth allocation [8,17,24], caching [18], scheduling [4], multi-commodity demand ow [16], and resource allocation [7,11,19,25]. For example, one can interpret edges as time-slots, and their capacity as the amount of a given resource whose supply varies over time.…”

Section: Introductionmentioning

confidence: 99%

“…Each task i ∈ T is specied by a subpath P (i) between the start (i. e., leftmost) vertex s(i) ∈ V and the end (i. e., rightmost) vertex t(i) ∈ V , a demand d(i) ∈ N, and a prot (or weight) w(i) ≥ 0. Our goal is to select a subset T ⊆ T of tasks of maximum total prot such that for each edge e the total demand of the selected tasks using e does not exceed u(e).UFP and its variations are motivated by several applications in bandwidth allocation [8,17,24], caching[18], scheduling [4], multi-commodity demand ow [16], and resource allocation [7,11,19,25] In terms of polynomial-time approximation, the rst non-trivial result was an O(log n)-approximation by Bansal et al [6]. To achieve that, Bansal et al reduced…”

mentioning

confidence: 99%

See 2 more Smart Citations

To Augment or Not to Augment: Solving Unsplittable Flow on a Path by Creating Slack

Grandoni¹,

Mömke²,

Wiese³

et al. 2017

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

View full text Add to dashboard Cite

In the Unsplittable Flow on a Path problem (UFP) we are given a path with non-negative edge capacities and a set of tasks, each one characterized by a subpath, a demand, and a prot. Our goal is to select a subset of tasks of maximum total prot so that the total demand of the selected tasks on each edge does not exceed the respective edge capacity.UFP tasks in the optimal solution (with a small loss of prot) in order to create a sucient amount of slack capacity on each edge. This slack turns out to be large enough to substitute the additional capacity we would gain from resource augmentation.Crucial for our approach is that we obtain slack from tasks with relatively small and relatively large demand simultaneously. In all prior polynomial time approximation algorithms the sacriced tasks came from only one of these two groups. IntroductionIn the Unsplittable Flow on a Path problem (UFP) we are given an undirected path G = (V, E), with edge capacities u(e) ∈ N for e ∈ E. Furthermore, we are given a set T of n tasks. Each task i ∈ T is specied by a subpath P (i) between the start (i. e., leftmost) vertex s(i) ∈ V and the end (i. e., rightmost) vertex t(i) ∈ V , a demand d(i) ∈ N, and a prot (or weight) w(i) ≥ 0. Our goal is to select a subset T ⊆ T of tasks of maximum total prot such that for each edge e the total demand of the selected tasks using e does not exceed u(e).UFP and its variations are motivated by several applications in bandwidth allocation [8,17,24], caching[18], scheduling [4], multi-commodity demand ow [16], and resource allocation [7,11,19,25] In terms of polynomial-time approximation, the rst non-trivial result was an O(log n)-approximation by Bansal et al. [6]. To achieve that, Bansal et al. reduced

show abstract

“…UFP and its variations are motivated by several applications in bandwidth allocation [8,17,24], caching…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

To Augment or Not to Augment: Solving Unsplittable Flow on a Path by Creating Slack

Grandoni¹,

Mömke²,

Wiese³

et al. 2017

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

View full text Add to dashboard Cite

show abstract

“…UFP and variations of it are motivated by several applications in settings such as bandwidth allocation [8,15,20], caching [16], multicommodity demand flow [14], scheduling [2], or resource allocation [6,10,17,21]. For example, edge capacities might model a given resource whose supply varies over a time horizon.…”

Section: Introductionmentioning

confidence: 99%

A Mazing 2+∊ Approximation for Unsplittable Flow on a Path

Anagnostopoulos

Grandoni

Leonardi

et al. 2013

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

View full text Add to dashboard Cite

We study the unsplittable flow on a path problem (UFP), which arises naturally in many applications such as bandwidth allocation, job scheduling, and caching. Here we are given a path with nonnegative edge capacities and a set of tasks, which are characterized by a subpath, a demand, and a profit. The goal is to find the most profitable subset of tasks whose total demand does not violate the edge capacities. Not surprisingly, this problem has received a lot of attention in the research community.If the demand of each task is at most a small enough fraction δ of the capacity along its subpath (δ-small tasks), then it has been known for a long time [Chekuri et al., ICALP 2003] how to compute a solution of value arbitrarily close to the optimum via LP rounding. However, much remains unknown for the complementary case, that is, when the demand of each task is at least some fraction δ > 0 of the smallest capacity of its subpath (δ-large tasks). For this setting a constant factor approximation, improving on an earlier logarithmic approximation, was found only recently [Bonsma et al., FOCS 2011].In this paper we present a PTAS for δ-large tasks, for any constant δ > 0. Key to this result is a complex geometrically inspired dynamic program. Each task is represented as a segment underneath the capacity curve, and we identify a proper maze-like structure so that each corridor of the maze is crossed by only O(1) tasks in the optimal solution. The maze has a tree topology, which guides our dynamic program. Our result implies a 2 + ε approximation for UFP, for any constant ε > 0, improving on the previously best 7 + ε approximation by Bonsma et al. We remark that our improved approximation algorithm matches the best * Sapienza

show abstract