Approximation schemes for scheduling on parallel machines

Alon, Noga; Azar, Yossi; Woeginger, Gerhard J.; Yadid, Tal

doi:10.1002/(sici)1099-1425(199806)1:1<55::aid-jos2>3.0.co;2-j

Cited by 194 publications

(307 citation statements)

References 15 publications

Supporting

Mentioning

301

Contrasting

Order By: Relevance

“…From the algorithmic point of view, load balancing has been studied extensively, including papers studying online versions of the problem (e.g., [2,4,5,7,9,13,28,32,33]). In online load balancing, clients appear in online fashion; when a client appears, it has to make an irrevocable decision and assign its job to a server.…”

Section: Greedy Load Balancingmentioning

confidence: 71%

Tight Bounds for Selfish and Greedy Load Balancing

et al. 2010

View full text Add to dashboard Cite

We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it chooses, among its permissible servers, to run its job on the server having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server Algorithmica (2011) 61:606-637 607 that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness.We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions. In addition, we prove a tight upper bound on the price of stability of linear congestion games.

show abstract

Section: Greedy Load Balancingmentioning

confidence: 71%

Tight Bounds for Selfish and Greedy Load Balancing

et al. 2010

View full text Add to dashboard Cite

show abstract

“…Our paper is directly motivated by Alon et al [1], who proved similar general results for scheduling on identical machines. We generalize it to uniformly related machines and a similar set of functions f .…”

mentioning

confidence: 71%

“…For p = 2 and identical machines this problem was studied in [5], and [4], motivated by storage allocation problems. For a general p a PTAS for identical machines was given in [1]. For related machines this problem was not studied before.…”

mentioning

confidence: 99%

“…We generalize it to uniformly related machines and a similar set of functions f . Even for identical machines, our result is stronger than that of [1] since in that case we allow a more general class of functions f . In Section 6 we also disprove a conjecture of [1] concerning the class of functions f allowing PTAS for identical machines.…”

mentioning

confidence: 99%

“…This rounding technique traces back to Hochbaum and Shmoys [12]. We also use an important improvement from [1]: the small jobs are clustered into blocks of jobs of small but non-negligible size. The final ingredient is that of [13], and [2]: the rounding factor is different for each machine, increasing with the weight of the machine (i.e., the total processing time of jobs assigned to it).…”

mentioning

confidence: 99%

See 2 more Smart Citations

Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines

Epstein

Sgall

2004

Algorithmica

View full text Add to dashboard Cite

show abstract

Approximation algorithms for shop scheduling problems with minsum objective

Queyranne

Sviridenko

2002

J. Sched.

View full text Add to dashboard Cite

SUMMARYWe consider a general class of multiprocessor shop scheduling problems, preemptive or non-preemptive, with precedence constraints between operations, with job or operation release dates, and with a class of objective functions including weighted sums of job, operations and stage completion times. We present a general approximation method combining a linear programming relaxation in the operation completion times, with any algorithm for the makespan version of these problems without release dates. If the latter produces a schedule with makespan no larger than times the 'trivial lower bound' consisting of the largest of all stage average loads (or 'congestion') and job lengths (or 'dilation'), then our method produces a feasible schedule with minsum objective no larger than 2e times the optimum where 2e ≈ 5:44. This leads, in particular, to a polynomial time algorithm with polylogarithmic performance guarantee for the minsum multiprocessor dag-shop problem J (P)|r ij ; dag j | S w S C S where S w S C S is a general minsum objective including weighted sum of operation and job completion times, stages makespans and others, whereas the best known earlier performance guarantees were O(m) (where m is the number of stages) for the special cases J C j ; F(P)|r j | w j C j and O C j . We also obtain a O(1) performance guarantee for the acyclic job shop problem J |p ij = 1; acyclic-dag j | S w S C S with unit processing times and weighted sum of operation (or job) completion time objective. Our results extend to a broad class of minsum objective functions including some convex objectives related to load balancing. We then present an improved 5:83-approximation algorithm for the open shop problem O|r j | w j C j with total weighted job completion time objective. We conclude with a very simple method which yields O(m)-approximation algorithms for various job shop problems (preemptive, non-preemptive, and no-wait) with m single-processor stages and total weighted job completion time objective.

show abstract

Approximation schemes for scheduling on parallel machines

Cited by 194 publications

References 15 publications

Tight Bounds for Selfish and Greedy Load Balancing

Tight Bounds for Selfish and Greedy Load Balancing

Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines

Approximation algorithms for shop scheduling problems with minsum objective

Contact Info

Product

Resources

About