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Selfish Load Balancing and Atomic Congestion Games
, 2007
"... We revisit a classical load balancing problem in the modern context of decentralized systems and selfinterested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unitlength job and selfishly wants to minimize its own late ..."
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Cited by 72 (3 self)
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We revisit a classical load balancing problem in the modern context of decentralized systems and selfinterested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unitlength job and selfishly wants to minimize its own latency (job completion time). A server’s latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. This interaction is naturally modeled as an atomic congestion game, which we call selfish load balancing. We analyze the Nash equilibria of this game and prove nearly tight bounds on the price of anarchy (worstcase ratio between a Nash solution and the social optimum). In particular, for linear latency functions, we show that if the server speeds are relatively bounded and the number of clients is large compared with the number of servers, then every Nash assignment approaches social optimum. Without any assumptions on the number of clients, servers, and server speeds, the price of anarchy is at most 2.5. If all servers have the same speed, then the price of anarchy further improves to 1 + 2 / √ 3 ≈ 2.15. We also exhibit a lower bound of 2.01. Our proof techniques can also be adapted for the coordinated load balancing problem under L2 norm, where it slightly improves the best previously known upper bound on the competitive ratio of a simple greedy scheme.
Tight bounds for selfish and greedy load balancing
 ICALP 2006. LNCS
, 2006
"... Abstract. 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 ..."
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Cited by 43 (6 self)
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Abstract. 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 selects to run its job to the server among its permissible servers 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 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 and price of stability 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. 1
Online scheduling
 ONLINE ALGORITHMS, LECTURE NOTES IN COMPUTER SCIENCE 1442
, 1998
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OnLine Scheduling  A Survey
, 1997
"... Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequ ..."
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Cited by 38 (0 self)
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Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequence of jobs that have to be processed on the machines available to us. In the most basic problem, each job is characterized by its running time and has to be scheduled for that time on one of the machines. In other variants there may be additional restrictions or relaxations specifying which schedules are allowed. We want to schedule the jobs as efficiently as possible, which most often means that the total length of the schedule (the makespan) should be as small as possible, but other objective functions are also considered. The notion of an online algorithm is intended to formalize the realistic scenario, where the algorithm does not have the access to the whole inp...
Approximation schemes for scheduling on parallel machines
 Journal of Scheduling
, 1998
"... We discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The goal is to optimize objective functions that solely depend on the machine completion times. As a main result, we identify some conditions on the objective function, under which ..."
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Cited by 37 (6 self)
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We discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The goal is to optimize objective functions that solely depend on the machine completion times. As a main result, we identify some conditions on the objective function, under which the resulting scheduling problems possess a polynomial time approximation scheme. Our result contains, generalizes, improves, simplifies, and unifies many other results in this area in a natural way.
Server Scheduling in the L_p Norm: A Rising Tide Lifts All Boat (Extended Abstract)
, 2003
"... Often server systems do not implement the best known algorithms for optimizing average Quality of Service (QoS) out of concern of that these algorithms may be insu#ciently fair to individual jobs. The standard method for balancing average QoS and fairness is optimize the Lp metric, 1 <p<#. T ..."
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Cited by 24 (5 self)
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Often server systems do not implement the best known algorithms for optimizing average Quality of Service (QoS) out of concern of that these algorithms may be insu#ciently fair to individual jobs. The standard method for balancing average QoS and fairness is optimize the Lp metric, 1 <p<#. Thus we consider server scheduling strategies to optimize the Lp norms of the standard QoS measures, flow and stretch. We first show that there is no n competitive online algorithm for the Lp norms of either flow or stretch. We then show that the standard clairvoyant algorithms for optimizing average QoS, SJF and SRPT, are O(1+#)speed O(1/# ) competitive for the Lp norms of flow and stretch. And that the standard nonclairvoyant algorithm for optimizing average QoS, SETF,isO(1+#)speed O(1/# )competitive for the Lp norms of flow. These results argue that these standard algorithms will not starve jobs until the system is near peak capacity. In contrast, we show that the Round Robin, or Processor Sharing algorithm, which is sometimes adopted because of its seeming fairness properties, is not O(1 + #)speed n competitive for sufficiently small #.
Convex Combinatorial Optimization
, 2004
"... We introduce the convex combinatorial optimization problem, a farreaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edgeguaranteed family, and discuss several applications. ..."
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Cited by 18 (7 self)
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We introduce the convex combinatorial optimization problem, a farreaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edgeguaranteed family, and discuss several applications.
Better Bounds for Online Load Balancing on Unrelated Machines
"... We study the problem of scheduling permanent jobs on unrelated machines when the objective is to minimize the Lp norm of the machine loads. The problem is known as load balancing under the Lp norm. We present an improved upper bound for the greedy algorithm through simple analysis; this bound is als ..."
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Cited by 14 (1 self)
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We study the problem of scheduling permanent jobs on unrelated machines when the objective is to minimize the Lp norm of the machine loads. The problem is known as load balancing under the Lp norm. We present an improved upper bound for the greedy algorithm through simple analysis; this bound is also shown to be best possible within the class of deterministic online algorithms for the problem. We also address the question whether randomization helps online load balancing under Lp norms on unrelated machines; this is a challenging question which is open for more than a decade even for the L2 norm. We provide a positive answer to this question by presenting the first randomized online algorithms which outperform deterministic ones under any (integral) Lp norm for p = 2,..., 137. Our algorithms essentially compute in an online manner a fractional solution to the problem and use the fractional values to make random choices. The local optimization criterion used at each step is novel and rather counterintuitive: the values of the fractional variables for each job correspond to flows at an approximate Wardrop equilibrium for an appropriately defined nonatomic congestion game. As corollaries of our analysis and by exploiting the relation between the Lp norm and the makespan of machine loads, we obtain new competitive algorithms for online makespan minimization, making progress in another longstanding open problem.
An Efficient Polynomial Time Approximation Scheme for the Constrained Minimum Spanning Tree Using Matroid Intersection
, 2003
"... Given an undirected graph G = (V, E) with V = n and E = m, nonnegative integers c_e and d_e for each edge e ∈ E, and a bound D, the constrained minimum spanning tree problem (CST) is to find a spanning tree T = (V, E_T) such that d e D and c e is minimized. We present an efficient pol ..."
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Cited by 13 (1 self)
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Given an undirected graph G = (V, E) with V = n and E = m, nonnegative integers c_e and d_e for each edge e &isin; E, and a bound D, the constrained minimum spanning tree problem (CST) is to find a spanning tree T = (V, E_T) such that d e D and c e is minimized. We present an efficient polynomial time approximation scheme (EPTAS) for this problem. Specifically, for every &epsilon; > 0 we present an (1 + &epsilon;)approximation algorithm with time complexity O(...). Our method is based on Lagrangean relaxation and matroid intersection.