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Handbook of semidefinite programming
"... Semidefinite programming (or SDP) has been one of the most exciting and active research areas in optimization during the 1990s. It has attracted researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, con ..."
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Cited by 89 (3 self)
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Semidefinite programming (or SDP) has been one of the most exciting and active research areas in optimization during the 1990s. It has attracted researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity was spurred by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interiorpoint algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. This book includes nineteen chapters on the theory, algorithms, and applications of semidefinite programming. Written by the leading experts on the subject, it offers an advanced and broad overview of the current state of the field. The coverage is somewhat less comprehensive, and the overall level more advanced, than we had planned at the start of the project. In order to finish the book in a timely fashion, we have had to abandon hopes for separate chapters on some important topics (such as a discussion of SDP algorithms in the
Stability of Adaptive and NonAdaptive Packet Routing Policies in Adversarial Queueing Networks
 In Proc. of the 31st STOC
, 2000
"... We investigate stability of packet routing policies in adversarial queueing networks. We provide a simple classification of networks which are stable under any greedy scheduling policy  network is stable if and only if the underlying undirected connected graph contains at most two edges. We also ..."
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Cited by 46 (4 self)
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We investigate stability of packet routing policies in adversarial queueing networks. We provide a simple classification of networks which are stable under any greedy scheduling policy  network is stable if and only if the underlying undirected connected graph contains at most two edges. We also propose a simple and distributed policy which is stable in an arbitrary adversarial queueing network even for the critical value of the arrival rate r = 1. Finally, a simple and checkable network flow type load condition is formulated for adaptive adversarial queueing networks and a policy is proposed which achieves stability under this new load condition. This load condition is a relaxation of the integral network flow type condition considered previously in the literature.
SteadyState Scheduling on Heterogeneous Clusters: Why and How?
, 2004
"... In this paper, we consider steadystate scheduling techniques for heterogeneous systems, such as clusters and grids. We advocate the use of steadystate scheduling to solve a variety of important problems, which would be too difficult to tackle with the objective of makespan minimization. We give a ..."
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Cited by 41 (20 self)
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In this paper, we consider steadystate scheduling techniques for heterogeneous systems, such as clusters and grids. We advocate the use of steadystate scheduling to solve a variety of important problems, which would be too difficult to tackle with the objective of makespan minimization. We give a few successful examples before discussing the main limitations of the approach.
Pipelining broadcasts on heterogeneous platforms
, 2005
"... In this paper, we consider the communications involved by the execution of a complex application, deployed on a heterogeneous platform. Such applications extensively use macrocommunication schemes, for example, to broadcast data items. Rather than aiming at minimizing the execution time of a single ..."
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Cited by 36 (15 self)
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In this paper, we consider the communications involved by the execution of a complex application, deployed on a heterogeneous platform. Such applications extensively use macrocommunication schemes, for example, to broadcast data items. Rather than aiming at minimizing the execution time of a single broadcast, we focus on the steadystate operation. We assume that there is a large number of messages to be broadcast in pipeline fashion, and we aim at maximizing the throughput, i.e., the (rational) number of messages which can be broadcast every timestep. We target heterogeneous platforms, modeled by a graph where resources have different communication and computation speeds. Achieving the best throughput may well require that the target platform is used in totality: We show that neither spanning trees nor DAGs are as powerful as general graphs. We show how to compute the best throughput using linear programming, and how to exhibit a periodic schedule, first when restricting to a DAG, and then when using a general graph. The polynomial compactness of the description comes from the decomposition of the schedule into several broadcast trees that are used concurrently to reach the best throughput. It is important to point out that a concrete scheduling algorithm based upon the steadystate operation is asymptotically optimal, in the class of all possible schedules (not only periodic solutions).
A simplex based algorithm to solve separated continuous linear programs
 Mathematical Programming
, 2008
"... We consider the separated continuous linear programming problem with linear data. We characterize the form of its optimal solution, and present an algorithm which solves it in a finite number of steps, using simplex pivot iterations. 1 ..."
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Cited by 30 (5 self)
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We consider the separated continuous linear programming problem with linear data. We characterize the form of its optimal solution, and present an algorithm which solves it in a finite number of steps, using simplex pivot iterations. 1
A realistic network/application model for scheduling divisible loads on largescale platforms
, 2004
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A Fluid Heuristic for Minimizing Makespan in JobShops
 Oper. Res
, 2001
"... We describe a simple online heuristic for scheduling jobshops. We assume there is a fixed set of routes for the jobs, and many jobs, say N , on each route. The heuristic uses safety stocks and keeps the bottleneck machine busy at almost all times, while the other machines are paced by the bottlene ..."
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Cited by 28 (5 self)
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We describe a simple online heuristic for scheduling jobshops. We assume there is a fixed set of routes for the jobs, and many jobs, say N , on each route. The heuristic uses safety stocks and keeps the bottleneck machine busy at almost all times, while the other machines are paced by the bottleneck machine. We perform a probabilistic analysis of the heuristic, under some assumptions on the distributions of the processing times. We show that our heuristic produces makespan which exceeds the optimal makespan by no more than c log N with a probability which exceeds 1  1/N for all N # 1, where c is some constant independent of N . 1 The JobShop Scheduling Problem with Fixed Routes A jobshop consists of machines i = 1, . . . , I, and routes r = 1, . . . , R. Route r consists of steps (r, k) where k = 1, . . . , K r indicate the steps along route r, in their required order of execution, and step (r, k) is carried out by machine #(r, k). We let C i denote the set of steps performed on machine i. In the standard jobshop formulation [23] there is one job on each route, and the objective is to schedule all the jobs so as to minimize the makespan, the earliest time by which all the jobs are completed. In our formulation of the job shop problem we assume that there are many jobs on each of the routes. In practice, in particular in factories, routes may correspond to various production processes, or to various types of products manufactured in the factory. In that case the jobs may correspond to parts or lots and there will indeed be many such jobs for each route. # School of Industrial and Systems Engineering and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 303320205, USA; Research supported in part by NSF grants DMI9457336 and DMI9813345, US...
Assessing the impact and limits of steadystate scheduling for mixed task and data parallelism on heterogeneous platforms
, 2004
"... ..."
Source Routing and Scheduling in Packet Networks
, 2001
"... We study routing and scheduling in packetswitched networks. We assume an adversary that controls the injection time, source, and destination for each packet injected. A set of paths for these packets is admissible if no link in the network is overloaded. We present the first online routing algorit ..."
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Cited by 23 (5 self)
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We study routing and scheduling in packetswitched networks. We assume an adversary that controls the injection time, source, and destination for each packet injected. A set of paths for these packets is admissible if no link in the network is overloaded. We present the first online routing algorithm that finds a set of admissible paths whenever this is feasible. Our algorithm calculates a path for each packet as soon as it is injected at its source using a simple shortest path computation. The length of a link reflects its current congestion. We also show how our algorithm can be implemented under today's Internet routing paradigms.
From fluid relaxations to practical algorithms for job shop scheduling: the makespan objective
 Mathematical Programming
, 2002
"... We design an algorithm for the highmultiplicity jobshop scheduling problem with the objective of minimizing the total holding cost by appropriately rounding an optimal solution to a fluid relaxation in which we replace discrete jobs with the flow of a continuous fluid. The algorithm solves the flu ..."
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Cited by 23 (4 self)
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We design an algorithm for the highmultiplicity jobshop scheduling problem with the objective of minimizing the total holding cost by appropriately rounding an optimal solution to a fluid relaxation in which we replace discrete jobs with the flow of a continuous fluid. The algorithm solves the fluid relaxation optimally and then aims to keep the schedule in the discrete network close to the schedule given by the fluid relaxation. If the number of jobs from each type grow linearly with N,then the algorithm is within an additive factor O�N � from the optimal (which scales as O�N 2�); thus,it is asymptotically optimal. We report computational results on benchmark instances chosen from the OR library comparing the performance of the proposed algorithm and several commonly used heuristic methods. These results suggest that for problems of moderate to high multiplicity,the proposed algorithm outperforms these methods,and for very high multiplicity the overperformance is dramatic. For problems of low to moderate multiplicity,however,the relative errors of the heuristic methods are comparable to those of the proposed algorithm,and the best of these methods performs better overall than the proposed method. Received December 1999; revisions received July 2000,September 2001; accepted September 2002. Subject classifications: Production/scheduling,deterministic: approximation algorithms for deterministic job shops. Queues,optimization: asymptotically optimal solutions to queueing networks. Area of review: Manufacturing,Service,and Supply Chain Operations. 1.