Constant time per edge is optimal on rooted tree networks

Mitzenmacher, Michael

doi:10.1007/s004460050036

Cited by 4 publications

(3 citation statements)

References 19 publications

(25 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(See, for example, [13,25,26,29,31]. ) Generally, such results are achieved using stochastic comparison techniques.…”

Section: 1mentioning

confidence: 99%

On the analysis of randomized load balancing schemes

Mitzenmacher¹

1997

Proceedings of the Ninth Annual ACM Symposium on Parallel Algorithms and Architectures - SPAA '97

Self Cite

View full text Add to dashboard Cite

It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems.In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Unlike previous analyses, we do not assume that in equilibrium each server is stoehastically independent from other servers.Our work extends a previous analysis of the supermarket model, a model that abstracts a simple, efficient load balancing scheme in the setting where jobs arrive at a large system of parallel processors.In this model, customers arrive at a system of n servers as a Poisson stream of rate An, J < 1, with service requirements exponentially distributed with mean 1. Each customer chooses d servers independently and uniformly at random from the n servers, and is served at the choice with the fewest customers according to the First In First Out (FIFO) protocol.We wish to understand how the system behaves in equilibrium.Here we examine several variations, including constant service times and threshold models, where a customer makes up to d successive choices until finding one below a set threshold.Our approach involves studying limiting, deterministic models representing the behavior of these systems as the number of servers n goes to infinity. Important results of our work include useful general theorems for showing that these deterministic systems are stable or converge exponentially to fixed points.We also demonstrate that allowing customers two choices instead of just one leads to exponential improvements in the expected time a customer spends in the system in several of the related models we study. Permission (0 make digllallhard cofrIes olall m IXII1 ot'LIIIs malCI-I;Il Iiw personfil or closwoom use is granted without tic pro!lried 11141 (IIC qNcs art not made or distributed f'hr prolit 01-comn]crci:]i

show abstract

“…(See, for example, [13,25,26,29,31]. ) Generally, such results are achieved using stochastic comparison techniques.…”

Section: 1mentioning

confidence: 99%

On the analysis of randomized load balancing schemes

Mitzenmacher¹

1997

Proceedings of the Ninth Annual ACM Symposium on Parallel Algorithms and Architectures - SPAA '97

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, in many cases in queueing theory, results are proven for models where service times are exponentially distributed (as these results are often easier to obtain), and it is assumed that the behavior when service times are constant (with the same mean) is similar. In some cases there are even provable relationships between the two models (see, for example, 11,16]). In this case, however, changing the distribution of the random variable X causes a dramatic change in behavior.…”

Section: Simulationsmentioning

confidence: 99%

How useful is old information (extended abstract)?

Mitzenmacher¹

1997

Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing - PODC '97

Self Cite

View full text Add to dashboard Cite

We consider the problem of load balancing in dynamic distributed systems in cases where new incoming tasks can make use of old information. For example, consider a multiprocessor system where incoming tasks with exponentially distributed service requirements arrive a s a P oisson process, the tasks must choose a processor for service, and a task knows when making this choice the processor loads from T seconds ago. What is a good strategy for choosing a processor, in order for tasks to minimize their expected time in the system? Such models can also be used to describe settings where there is a transfer delay b e t ween the time a task enters a system and the time it reaches a processor for service.Our models are based on considering the behavior of limiting systems where the number of processors goes to in nity. The limiting systems can be shown to accurately describe the behavior of su ciently large systems, and simulations demonstrate that they are reasonably accurate even for systems with a small number of processors. Our studies of speci c models demonstrate the importance of using randomness to break symmetry in these systems and yield important rules of thumb for system design. The most signi cant result is that only small amounts of load information can be extremely useful in these settings for example, having incoming tasks choose the least loaded of two randomly chosen processors is extremely e ective o ver a large range of possible system parameters. In contrast, using global information can actually degrade performance unless used correctly for example, unlike most settings where the load information is current, having tasks go to the least loaded server can signi cantly hurt performance.

show abstract

“…Trees are important because many real-life networks are built upon them (for example, hierarchical infrastructures), which explains the interest that this type of routing problem has generated in the literature (see, for example, [2,3,20,25,27,29,34]). Furthermore, as articulated by Leighton [20], a spanning tree can be used to route packets in an arbitrary network.…”

Section: Introductionmentioning

confidence: 99%

Near-Optimal Hot-Potato Routing on Trees

Busch

Magdon‐Ismail

Mavronicolas

et al. 2004

Lecture Notes in Computer Science

View full text Add to dashboard Cite

In hot-potato (deflection) routing, nodes in the network have no buffers for packets in transit, so that some conflicting packets must be deflected away from their destinations. In this work, we study one-tomany batch routing problems on arbitrary tree topologies with n nodes. The routing time of a routing algorithm is the time for the last packet to reach its destination. Denote by rt * the optimal routing time for a given routing problem.We construct the first hot-potato routing algorithms whose routing times are asymptotically nearoptimal; that is, the incurred routing times are within polylogarithmic factors from optimal. More specifically, we present: A deterministic algorithm whose routing time is O(δ · rt* · lg n), where δ is the maximum node degree; thus, for bounded-degree trees, the routing time becomes O(rt * · lg n).2. A randomized algorithm whose routing time is O(rt * · lg 2 n) with high probability; randomization is used for adjusting packet priorities.Both algorithms are local, hence distributed, and greedy; so, routing decisions are made locally, and packets are advanced towards their destinations whenever possible, respectively.

show abstract

Constant time per edge is optimal on rooted tree networks

Cited by 4 publications

References 19 publications

On the analysis of randomized load balancing schemes

On the analysis of randomized load balancing schemes

How useful is old information (extended abstract)?

Near-Optimal Hot-Potato Routing on Trees

Contact Info

Product

Resources

About