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Online PrimalDual For Nonlinear Optimization with Applications to Speed Scaling
 In: Proceedings of the 10th Workshop on Approximation and Online Algorithms (WAOA
, 2012
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Online Scheduling with General Cost Functions
"... We consider a general online scheduling problem on a single machine with the objective of minimizing j wjg(Fj), where wj is the weight/importance of job Jj, Fj is the flow time of the job in the schedule, and g is an arbitrary nondecreasing cost function. Numerous natural scheduling objectives are ..."
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Cited by 6 (4 self)
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We consider a general online scheduling problem on a single machine with the objective of minimizing j wjg(Fj), where wj is the weight/importance of job Jj, Fj is the flow time of the job in the schedule, and g is an arbitrary nondecreasing cost function. Numerous natural scheduling objectives are special cases of this general objective. We show that the scheduling algorithm Highest Density First (HDF) is (2+ɛ)speed O(1)competitive for all cost functions g simultaneously. We give lower bounds that show the HDF algorithm and this analysis are essentially optimal. Finally, we show scalable algorithms are achievable in some special cases. 1
Energy Efficient Scheduling of Parallelizable Jobs
"... In this paper, we consider scheduling parallelizable jobs in the nonclairvoyant speed scaling setting to minimize the objective of weighted flow time plus energy. Previously, strong lower bounds were shown on this model in the unweighted setting even when the algorithm is given a constant amount of ..."
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In this paper, we consider scheduling parallelizable jobs in the nonclairvoyant speed scaling setting to minimize the objective of weighted flow time plus energy. Previously, strong lower bounds were shown on this model in the unweighted setting even when the algorithm is given a constant amount of resource augmentation over the optimal solution. However, these lower bounds were given only for certain families of algorithms that do not recognize the parallelizability of alive jobs. In this work, we circumvent previous lower bounds shown and give a scalable algorithm under the natural assumption that the algorithm can know the current parallelizability of a job. When a general power function is considered, this is also the first algorithm that has a constant competitive ratio for the problem using any amount of resource augmentation. 1
Competitive algorithms from competitive equilibria: nonclairvoyant scheduling under polyhedral constraints
 In Symposium on Theory of Computing, STOC 2014
"... We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding job ..."
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Cited by 5 (4 self)
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We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding jobs. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling. In this paper, we design nonclairvoyant online algorithms for PSP and its special cases – in this setting, the scheduler is unaware of the sizes of jobs. Our results are summarized as follows. • For minimizing total weighted completion time, we show a O(1)competitive algorithm. Surprisingly, we achieve this result by applying the wellknown Proportional Fairness algorithm (PF) to perform allocations each time instant. Though PF has been extensively studied in the context of maximizing fairness in resource allocation, we present the first analysis in adversarial and gen
SELFISHMIGRATE: A scalable algorithm for nonclairvoyantly scheduling heterogeneous processors
, 2014
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ONLINE SCHEDULING ALGORITHMS FOR AVERAGE FLOW TIME AND ITS VARIANTS
, 2012
"... This dissertation focuses on scheduling problems that are found in a clientserver setting where multiple clients and one server (or multiple servers) are the participating entities. Clients send their requests to the server(s) over time, and the server needs to satisfy the requests using its resour ..."
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This dissertation focuses on scheduling problems that are found in a clientserver setting where multiple clients and one server (or multiple servers) are the participating entities. Clients send their requests to the server(s) over time, and the server needs to satisfy the requests using its resources. This setting is prevalent in many applications including multiuser operating systems, web servers, database servers, and so on. A natural objective for each client is to minimize the flow time (or equivalently response time) of her request, which is defined as its completion time minus its release time. The server, with multiple requests to serve in its queue, has to prioritize the requests for scheduling. Inherently, the server needs a global scheduling objective to optimize. We mainly study the scheduling objective of minimizing `knorms of flow time of all requests, where 1 ≤ k < ∞. These objectives can be used to balance average performance and fairness. A popular performance measure for online scheduling algorithms is competitive
Packet Forwarding Algorithms in a Line Network
"... Abstract. We initiate a competitive analysis of packet forwarding policies for maximum and average flow in a line network. We show that the policies Earliest Arrival and FurthestToGo are scalable, but not constant competitive, for maximum flow. We show that there is no constant competitive algor ..."
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Abstract. We initiate a competitive analysis of packet forwarding policies for maximum and average flow in a line network. We show that the policies Earliest Arrival and FurthestToGo are scalable, but not constant competitive, for maximum flow. We show that there is no constant competitive algorithm for average flow. 1
EnergyEfficient Multiprocessor Scheduling for Flow Time and Makespan
 CoRR
"... Abstract: We consider energyefficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power sα when running at speed s, for α> 1. A scheduling algorithm needs to decide at any time both processor allocations and processor spee ..."
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Abstract: We consider energyefficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power sα when running at speed s, for α> 1. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with timevarying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelismclairvoyant (IPclairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an O(1)competitive algorithm, which significantly improves upon the best known nonclairvoyant algorithm. In the case of makespan plus energy, we present an O(ln1−1/α P)competitive algorithm, where P is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we also study nonclairvoyant scheduling for total flow time plus energy, and present an algorithm that achieves O(lnP)competitive for jobs with arbitrary release time and O(ln1/α P)competitive for jobs with identical release time. Finally, we prove an Ω(ln1/α P) lower bound on the competitive ratio of any nonclairvoyant algorithm.
Temporal Fairness of Round Robin: Competitive Analysis for Lknorms of Flow Time
"... Fairness is an important criterion considered in scheduling together with overall job latency. Round Robin (RR) is a popular scheduling policy that distributes resources to jobs equally at any point in time guaranteeing instantaneous fairness of jobs. In this paper we give the first analysis of RR ..."
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Fairness is an important criterion considered in scheduling together with overall job latency. Round Robin (RR) is a popular scheduling policy that distributes resources to jobs equally at any point in time guaranteeing instantaneous fairness of jobs. In this paper we give the first analysis of RR for the `2norm of flow time and show that it is O(1)speed O(1)competitive on multiple machines. The `2norm is a popular scheduling objective that makes a natural balance between temporal fairness and jobs latency. Prior to our work, RR has not been analyzed for the `2norm even in the single machine setting. Our result establishes that RR is fair not only instantaneously but also temporarily. Categories and Subject Descriptors F.2.2 [Nonnumerical Algorithms and Problem]: Sequencing and scheduling