Approximating the Traffic Grooming Problem with Respect to ADMs and OADMs

Flammini, Michele; Monaco, Gianpiero; Moscardelli, Luca; Shalom, Mordechai; Zaks, Shmuel

doi:10.1007/978-3-540-85451-7_99

Cited by 14 publications

(15 citation statements)

References 14 publications

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“…In the Appendix we give a 2-approximation algorithm for instances where any two intervals intersect. While an algorithm with the same approximation ratio was given in [7], the present algorithm as well as the analysis are different. We believe it may find uses in solving our problem for other subclasses of instances.…”

Section: Our Contributionmentioning

confidence: 99%

Minimizing total busy time in parallel scheduling with application to optical networks

Flammini

Monaco

Moscardelli

et al. 2009

2009 IEEE International Symposium on Parallel &Amp; Distributed Processing

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We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = {J 1 , . . . , J n }. Each job, J j , is associated with an interval [s j , c j ] along which it should be processed. Also given is the parallelism parameter g ≥ 1, which is the maximal number of jobs that can be processed simultaneously by a single machine. Each machine operates along a contiguous time interval, called its busy interval, which contains all the intervals corresponding to the jobs it processes. The goal is to assign the jobs to machines such that the total busy time of the machines is minimized.The problem is known to be NP-hard already for g = 2. We present a 4-approximation algorithm for general instances, and approximation algorithms with improved ratios for instances with bounded lengths, for instances where any two intervals intersect, and for instances where no interval is properly contained in another. Our study has important application in optimizing the switching costs of optical networks.

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Section: Our Contributionmentioning

confidence: 99%

Minimizing total busy time in parallel scheduling with application to optical networks

Flammini

Monaco

Moscardelli

et al. 2009

2009 IEEE International Symposium on Parallel &Amp; Distributed Processing

Self Cite

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“…6 In their paper, the problem is called real-time scheduling. 7 The bound of four for these algorithms is tight, as shown in the Appendix B.…”

Section: Definition 14mentioning

confidence: 99%

LP rounding and combinatorial algorithms for minimizing active and busy time

Chang

Khuller

Mukherjee

2017

J Sched

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Abstract. We consider fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at most g jobs are active at any given time. The duration for which a machine is active (i.e., "on") is referred to as its active time. The goal is to find a feasible schedule for all jobs, minimizing the total active time. When preemption is allowed at integer time points, we show that a minimal feasible schedule already yields a 3-approximation (and this bound is tight) and we further improve this to a 2-approximation via LP rounding techniques. Our second contribution is for the non-preemptive version of this problem. However, since even asking if a feasible schedule on one machine exists is NP-hard, we allow for an unbounded number of virtual machines, each having capacity of g. This problem is known as the busy time problem in the literature and a 4-approximation is known for this problem. We develop a new combinatorial algorithm that gives a 3-approximation. Furthermore, we consider the preemptive busy time problem, giving a simple and exact greedy algorithm when unbounded parallelism is allowed, i.e., g is unbounded. For arbitrary g, this yields an algorithm that is 2-approximate.

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“…For this version of the problem the paper gives a 4-approximation algorithm for general inputs and better bounds for some subclasses of inputs. In particular, the paper presents a 2-approximation algorithm for instances where no interval is properly contained in another (i.e., the input forms a proper interval graph), and a (2 + ε)-approximation for bounded lengths instances, i.e., the length (or, processing time) of any job is bounded by some fixed integer d. ‡ A 2-approximation algorithm was given in [9] for instances where any two intervals intersect, i.e., the input forms a clique (see also in [10]). In this paper we improve and extend the results of [9].…”

Section: Related Workmentioning

confidence: 99%

Real-time scheduling to minimize machine busy times

Khandekar

Schieber

Shachnai

et al. 2014

J Sched

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ABSTRACT.We consider the following fundamental scheduling problem. The input consists of n jobs to be scheduled on a set of machines of bounded capacities. Each job is associated with a release time, a due date, a processing time and demand for machine capacity. The goal is to schedule all of the jobs non-preemptively in their release-time-deadline windows, subject to machine capacity constraints, such that the total busy time of the machines is minimized. Our problem has important applications in power-aware scheduling, optical network design and customer service systems. Scheduling to minimize busy times is APX-hard already in the special case where all jobs have the same (unit) processing times and can be scheduled in a fixed time interval. Our main result is a 5-approximation algorithm for general instances. We extend this result to obtain an algorithm with the same approximation ratio for the problem of scheduling moldable jobs, that requires also to determine, for each job, one of several processing-time vs. demand configurations. Better bounds and exact algorithms are derived for several special cases, including proper interval graphs, intervals forming a clique and laminar families of intervals. * Work partially supported by funding for DIMACS visitors.

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Approximating the Traffic Grooming Problem with Respect to ADMs and OADMs

Cited by 14 publications

References 14 publications

Minimizing total busy time in parallel scheduling with application to optical networks

Minimizing total busy time in parallel scheduling with application to optical networks

LP rounding and combinatorial algorithms for minimizing active and busy time

Real-time scheduling to minimize machine busy times

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