Resource Allocation for Covering Time Varying Demands

Chakaravarthy, Venkatesan T.; Kumar, Amit; Roy, Sambuddha; Sabharwal, Yogish

doi:10.1007/978-3-642-23719-5_46

Cited by 13 publications

(29 citation statements)

References 13 publications

(19 reference statements)

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“…For example, one can think of the tasks as representing time intervals when employees are available, and one aims at providing certain service level that changes over the day. The best known approximation algorithm for UFP cover is a 4-approximation [8,11]. This essentially matches the best known result for GSP without release dates.…”

Section: Introductionsupporting

confidence: 74%

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

Höhn

Mestre

Wiese

2014

Automata, Languages, and Programming

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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 123Algorithmica 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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Section: Introductionsupporting

confidence: 74%

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

Höhn

Mestre

Wiese

2014

Automata, Languages, and Programming

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“…When viewing UFPP as a packing problem, the corresponding covering problem has also been studied [15,16]. In that case, tasks have costs instead of profits, and the objective is to find a minimum cost set of tasks F , such that for each edge, the sum of the demands of all tasks in F that use this edge is at least its capacity.…”

Section: Related Resultsmentioning

confidence: 99%

“…In that case, tasks have costs instead of profits, and the objective is to find a minimum cost set of tasks F , such that for each edge, the sum of the demands of all tasks in F that use this edge is at least its capacity. Recently, Chakaravarthy et al [15] designed a primal-dual 4-approximation algorithm for this problem.…”

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

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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.

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“…The priority interval cover problem is studied by Chakrabarty et al [5] and Chakaravarthy et al [4]. They provide polynomial time optimal algorithms based on the dynamic programming.…”

Section: Introductionmentioning

confidence: 99%

Set Cover Problems with Small Neighborhood Covers

et al. 2018

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In this paper, we study a class of set cover problems that satisfy a special property which we call the small neighborhood cover property. This class encompasses several well-studied problems including vertex cover, interval cover, bag interval cover and tree cover. We design unified distributed and parallel algorithms that can handle any set cover problem falling under the above framework and yield constant factor approximations. These algorithms run in polylogarithmic communication rounds in the distributed setting and are in NC, in the parallel setting.

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Resource Allocation for Covering Time Varying Demands

Cited by 13 publications

References 13 publications

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

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

A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

Set Cover Problems with Small Neighborhood Covers

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