A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

Bonsma, Paul; Schulz, Jens; Wiese, Andreas

doi:10.1109/focs.2011.10

Cited by 44 publications

(52 citation statements)

References 36 publications

(97 reference statements)

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“…Bansal et al [4] presented a quasi-PTAS for the UF problem under the restriction that all the capacities and demands are quasi-polynomial. Bonsma et al [7] designed a polynomial time (7 + )-approximation algorithm with a "no-bottleneck assumption". Chekuri et al [14] have proposed a (2 + )-approximation algorithm.…”

Section: Related Workmentioning

confidence: 99%

Resource allocation problem under single resource assignment

Mondal¹

2018

RAIRO-Oper. Res.

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We consider a NP-hard resource allocation problem of allocating a set of resources to meet demands over a time period at the minimum cost. Each resource has a start time, finish time, availability and cost. The objective of the problem is to assign resources to meet the demands so that the overall cost is minimum. It is necessary that only one resource contributes to the demand of a slot. This constraint will be referred to as single resource assignment (SRA) constraint. We would refer to the problem as the S_RA problem. So far, only 16-approximation to this problem is known. In this paper, we propose an algorithm with approximation ratio of 12.

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Section: Related Workmentioning

confidence: 99%

Resource allocation problem under single resource assignment

Mondal¹

2018

RAIRO-Oper. Res.

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“…This LP has exactly the same structure as sLP (1) - (7) and hence, we obtain an analogous result to Lemma 4. This means that given a fractional solution (x, y) to the above LP, we can construct an integral solution (x ′ , y ′ ) which is not more costly than (x, y), and which fulfills all constraints (9) -(14) with (11) being replaced by the relaxed constraint j∈Ji p j · y t,j ≤ |D i,t (P i(t) )| + ε · |I t | ∀ t ∈ {i · K, . .…”

Section: Lemma 8 At 1 + ε Speedup We Can Assume Thatmentioning

confidence: 99%

“…This case is still strongly NPhard [20] and the currently best know approximation algorithm for it is a (4 + ε)approximation algorithm [18,23] 4 . As observed by Bansal and Verschae [8], this problem is a generalization of the covering-version of the well-studied Unsplittable Flow on a Path problem (UFP) [2,3,5,11,14,17]. The input of this problem consists of a path, each edge e having a demand u e , and a set of tasks T .…”

Section: Introductionmentioning

confidence: 99%

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How Unsplittable-Flow-Covering Helps Scheduling with Job-Dependent Cost Functions

2017

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Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time (1 + ε)-approximation algorithm that yields an (e + ε)-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with optimal cost at 1 + ε speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most log n many classes. This algorithm allows the jobs even to have up to log n many distinct release dates. All proposed quasi-polynomial time algorithms require the input data to be quasi-polynomially bounded.

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“…For the case where there is only one line-network and there are no windows, improved approximations are known[4,7]. The UFP problem on line-networks (where the bandwidth offered varies over the timeline) has also been well studied (see[3,2,8,10,11]) and a constant factor approximation algorithm is known[6].…”

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confidence: 99%

Distributed algorithms for scheduling on line and tree networks

Chakaravarthy

Roy

Sabharwal

2012

Proceedings of the 2012 ACM Symposium on Principles of Distributed Computing

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We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices u, v , along with a profit; the processor wishes to send data between u and v. Towards that goal, the processor needs to select a graph network accessible to it and a path connecting u and v within the selected network. The processor requires exclusive access to the chosen path, in order to route the data. Thus, the processors are competing for routes/channels. A feasible solution selects a subset of demands and schedules each selected demand on a graph network accessible to the processor owning the demand; the solution also specifies the paths to use for this purpose. The requirement is that for any two demands scheduled on the same graph network, their chosen paths must be edge disjoint. The goal is to output a solution having the maximum aggregate profit. Prior work has addressed the above problem in a distibuted setting for the special case where all the graph networks are simply paths (i.e, line-networks). Distributed constant factor approximation algorithms are known for this case.The main contributions of this paper are twofold. First we design a distributed constant factor approximation algorithm for the more general case of tree-networks. The core component of our algorithm is a tree-decomposition technique, which may be of independent interest. Secondly, for the case of line-networks, we improve the known approximation guarantees by a factor of 5. Our algorithms can also handle the capacitated scenario, wherein the demands and edges have bandwidth requirements and capacities, respectively.

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A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

Cited by 44 publications

References 36 publications

Resource allocation problem under single resource assignment

Resource allocation problem under single resource assignment

How Unsplittable-Flow-Covering Helps Scheduling with Job-Dependent Cost Functions

Distributed algorithms for scheduling on line and tree networks

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