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19
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.
Stability of load balancing algorithms in dynamic adversarial systems
 In Proc. of the 34th ACM Symp. on Theory of Computing (STOC
, 2002
"... Abstract. In the dynamic load balancing problem, we seek to keep the job load roughly evenly distributed among the processors of a given network. The arrival and departure of jobs is modeled by an adversary restricted in its power. Muthukrishnan and Rajaraman (1998) gave a clean characterization of ..."
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Cited by 23 (2 self)
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Abstract. In the dynamic load balancing problem, we seek to keep the job load roughly evenly distributed among the processors of a given network. The arrival and departure of jobs is modeled by an adversary restricted in its power. Muthukrishnan and Rajaraman (1998) gave a clean characterization of a restriction on the adversary that can be considered the natural analogue of a cut condition. They proved that a simple local balancing algorithm proposed by Aiello et. al. (1993) is stable against such an adversary if the insertion rate is restricted to a (1 − ε) fraction of the cut size. They left as an open question whether the algorithm is stable at rate 1. In this paper, we resolve this question positively, by proving stability of the local algorithm at rate 1. Our proof techniques are very different from the ones used by Muthukrishnan and Rajaraman, and yield a simpler proof and tighter bounds on the difference in loads. In addition, we introduce a multicommodity version of this load balancing model, and show how to extend the result to the case of balancing two different kinds of loads at once (obtaining as a corollary a new proof of the 2commodity MaxFlow MinCut Theorem). We also show how to apply the proof techniques to the problem of routing packets in adversarial systems. Awerbuch et. al. (2001) showed that the same load balancing algorithm is stable against an adversary inserting
Load Balancing in Arbitrary Network Topologies with Stochastic Adversarial Input
 SIAM Journal on Computing
, 2005
"... We study the longterm (steady state) performance of a simple, randomized, local load balancing technique under a broad range of input conditions. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversa ..."
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Cited by 11 (2 self)
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We study the longterm (steady state) performance of a simple, randomized, local load balancing technique under a broad range of input conditions. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversary. The adversary knows the current and past load distribution in the network and can use this information to place the new tasks in the processors. A node can execute one job per step, and can also participate in one load balancing operation in which it can move tasks to a direct neighbor in the network. In the protocol we analyze here, a node equalizes its load with a random neighbor in the graph.
Approximation Algorithms for Average Stretch Scheduling
 J. of Scheduling
, 2003
"... We study the basic problem of preemptive scheduling of a stream of jobs on a single processor. ..."
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Cited by 11 (0 self)
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We study the basic problem of preemptive scheduling of a stream of jobs on a single processor.
Stability and Efficiency of a Random Local Load Balancing Protocol
 In Proceedings FOCS
, 2003
"... We study the long term (steady state) performance of a simple, randomized, local load balancing technique. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversary. The adversary knows the current and ..."
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Cited by 7 (2 self)
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We study the long term (steady state) performance of a simple, randomized, local load balancing technique. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversary. The adversary knows the current and past load distribution in the network and can use this information to place the new tasks in the processors. The adversary can put a number of new jobs in each processor, in each step, as long as the (expected) total number of new jobs arriving at a given step is bounded by #n. A node can execute one job per step, and also participate in one load balancing operation in which it can move tasks to a direct neighbor in the network. In the protocol we analyze here, a node equalizes its load with a random neighbor in the graph.
Stability of the MaxWeight Routing and Scheduling Protocol in Dynamic Networks and at Critical Loads
, 2007
"... We study the stability of the MaxWeight protocol for combined routing and scheduling in communication networks. Previous work has shown that this protocol is stable for adversarial multicommodity traffic in subcritically loaded static networks and for singlecommodity traffic in critically loaded d ..."
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Cited by 6 (2 self)
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We study the stability of the MaxWeight protocol for combined routing and scheduling in communication networks. Previous work has shown that this protocol is stable for adversarial multicommodity traffic in subcritically loaded static networks and for singlecommodity traffic in critically loaded dynamic networks. We show: • The MaxWeight protocol is stable for adversarial multicommodity traffic in adversarial dynamic networks whenever the network is subcritically loaded. • The MaxWeight protocol is stable for fixed multicommodity traffic in fixed networks even if the network is critically loaded. The latter result has implications for the running time of the MaxWeight protocol when it is used to solve multicommodity flow problems. In particular, for a fixed problem instance we show that if the value of the optimum solution is known, the MaxWeight protocol finds a flow that is within a (1 − ε)factor of optimal in time O(1/ε) (improving the previous bound of O(1/ε 2)). If the value of the optimum solution is not known, we show how to apply the MaxWeight algorithm in a binary search procedure that runs in O(1/ε) time.
Secondorder methods for distributed approximate single and multicommodity flow
 In 2nd Int. Workshop on Randomization and Approximation Techniques in Computer Science
, 1998
"... 3This work was done while the author was at Bell Labs. Abstract. We study localcontrol algorithms for maximum flow and multicommodity flow problems in distributed networks. We propose a secondorder method for accelerating the convergence of the “firstorder ” distributed algorithms recently propos ..."
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Cited by 5 (3 self)
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3This work was done while the author was at Bell Labs. Abstract. We study localcontrol algorithms for maximum flow and multicommodity flow problems in distributed networks. We propose a secondorder method for accelerating the convergence of the “firstorder ” distributed algorithms recently proposed by Awerbuch and Leighton. Our experimental study shows that secondorder methods are significantly faster than the firstorder methods for approximate single and multicommodity flow problems. Furthermore, our experimental study gives valuable insights into the diffusive processes that underly these localcontrol algorithms; this leads us to identify many open technical problems for theoretical study. 1
Dynamic Load Balancing Issues In The Earth Runtime System
, 1999
"... Multithreading is a promising approach to address the problems inherent in multiprocessor systems, such as network and synchronization latencies. Moreover, the benefits of multithreading are not limited to loopbased algorithms but apply also to irregular parallelism. EARTH  Efficient Architecture ..."
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Cited by 4 (0 self)
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Multithreading is a promising approach to address the problems inherent in multiprocessor systems, such as network and synchronization latencies. Moreover, the benefits of multithreading are not limited to loopbased algorithms but apply also to irregular parallelism. EARTH  Efficient Architecture for Running THreads, is a multithreaded model supporting finegrain, nonpreemptive threads. This model is supported by a Cbased runtime system which provides the multithreaded environment for the execution of concurrent programs. This thesis describes the design and implementation of a set of dynamic load balancing algorithms, and an indepth study of their behavior with divideandconquer, regular, and irregular classes of applications. The results described in this thesis are based on EARTHSP2, an implementation of the EARTH program execution model on the IBM SP2, a distributed memory multiprocessor system. The main results of this study are as follows: ffl A randomizing load balance...
NETWORK DESIGN AND MANAGEMENT WITH STRATEGIC AGENTS
, 2005
"... Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions (the Nash equilibria) may look quite different from the ..."
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Cited by 2 (0 self)
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Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions (the Nash equilibria) may look quite different from the centrally enforced optimum. We study the price of stability, i.e., the quality of the best Nash equilibrium compared to the optimum network cost. The best Nash equilibrium solution has a natural meaning of stability in this context: it is the optimal solution that can be proposed from which no user will “deviate”. We consider two versions of this game: one where agents may divide the cost of the edges they use in any manner they desire, and one where the cost of each such edge is divided equally between the agents whose connections make use of it. We also study the price of stability of a related game where agents are attempting to route their traffic while incurring minimal latency, instead of trying to construct a network of minimal cost. Since “selfinterest ” could have various meanings, the notion of strategic agents enfolds many types of agents including malicious, altruistic, and obedient agents under a common terminology. For example, we can think of a decentralized algorithm with local knowledge as a set of “selfinterested”
LargeScale Secure Computation: Multiparty Computation for (Parallel) RAM Programs
"... Abstract. We present the first efficient (i.e., polylogarithmic overhead) method for securely and privately processing large data sets over multiple parties with parallel, distributed algorithms. More specifically, we demonstrate loadbalanced, statistically secure computation protocols for computi ..."
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Cited by 2 (2 self)
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Abstract. We present the first efficient (i.e., polylogarithmic overhead) method for securely and privately processing large data sets over multiple parties with parallel, distributed algorithms. More specifically, we demonstrate loadbalanced, statistically secure computation protocols for computing Parallel RAM (PRAM) programs, handling (1/3−) fraction malicious players, while preserving up to polylogarithmic factors the computation and memory complexities of the PRAM program, aside from a onetime execution of a broadcast protocol per party. Additionally, our protocol has polylog communication locality—that is, each of the n parties speaks only with polylog(n) other parties. 1