Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. SIAM J. Comput., 29(1):180--200, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....i ball makes its choice at time i. Power of multiple choices Now, consider the following scheme. Ball i, chooses d bins uniformly at random, and places itself into the least loaded bin of these. This apparent minor change results in a maximum load of (1) with high probability. Theorem 7. 2 [ABKU99] Suppose that m balls are sequentially placed into n boxes. Each ball is placed in the least full box, at the time of the placement, among d boxes, d 2, chosen independently and uniformly at random (where ties are broken arbitrarily) Then after all the balls are placed, with high probability, ....

Azar, Y. Broder, A. Z. Karlin A. R. Upfal E. Balanced Allocations, Siam J. Comput. (1999) Vol. 29, No. 1: 180-200.

....server to allocate a request. Many studies have focused on the strategy of using a subset of the load information available. This involves first randomly choosing a small number, k, of homogeneous servers and then choosing the least loaded server from within that set [Mit96] ELZ86] VDK96] ABKU94] KLH92] In particular, for homogeneous systems, Mitzenmacher [Mit96] studies the tradeoffs of various choices of k and various degrees of staleness of load information reported. As the degree of staleness increases, smaller values of k are preferable. Genova et al. GC00] propose an ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced Allocations. In Twenty-sixth ACM Symposium on Theory of Computing, 1994.

....optimization technique that has been investigated thoroughly in the fields of telecommunication, distributed systems, and theoretical computer science. The fundamental idea behind MCA is quite simple and intuitive and can be explained best using the well established bins andballs model [2, 18] (cf. Fig. 1) multiple choice d =3 multiple choice d =3 multiple choice d =3 multiple choice d =3 randomchoice randomchoice randomchoice randomchoice Figure 1: Bins and balls model. Top: random ball insertion; Bottom: multiple choice ball insertion. Consider we have n balls to be uniformly ....

....each ball into an independently selected bin, the idea of MCA is to choose a small random subset of d bins and then put the ball into that bin with the least number of balls already in it [18] cf. Fig. 1 Bottom) By this MCA strategy, we can guarantee that the maximum load is ln(d) O(1) see [2] for detailed proof) which is an exponential improvement compared to the pure random approach. After their discovery, MCA have been used as an optimization tool in many different applications. For example, Karp et al. [9] used them for efficient hashing in the context of shared memory computer ....

[Article contains additional citation context not shown here]

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced Allocations", SIAM Journal on Computing, 29(1):180-200, 1999.

....through the DAAD. To motivate this paper, we rst provide the relevant history. It is well known that when n balls are thrown into n bins, the maximum load, or balls in a bin, is ln n ln ln n (1 o(1) with high probability. Azar, Broder, Karlin, and Upfal suggested the following variation [1]. Suppose that n balls are sequentially placed into n bins in the following manner: for each ball, d 2 bins are chosen independently and uniformly at random from the n bins, and the ball is placed in the bin with the fewest balls, ties being broken arbitrarily. Then in this case the maximum load ....

....using two hash functions and place the item in the least loaded bucket, then we can dramatically reduce the maximum load (and hence the maximum search time) for an item. Of course the average search time may increase, since a search requires examining multiple buckets. We note that the paper [1] also examined several related problems, including a closed dynamic model where at each step a random ball is deleted and re inserted into the system. This result was generalized to natural queueing theoretic models independently by Vvedenskaya, Dobrushin, and Karpelevich [14] and Mitzenmacher ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced Allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593-602.

....at one for service. To motivate this paper, we first provide the relevant history. It is well known that when n balls are thrown into n bins, the maximum load, or balls in a bin, is ln n ln ln n (1 o(1) with high probability. Azar, Broder, Karlin, and Upfal suggested the following variation [1]. Suppose that n balls are sequentially placed into n bins in the following manner: for each ball, d 2 bins are chosen independently and uniformly at random from the n bins, and the ball is placed in the bin with the fewest balls, ties being broken arbitrarily. Then in this case the maximum load ....

....balls, ties being broken arbitrarily. Then in this case the maximum load is only ln d Sigma Theta(1) with high probability. This implies that two choices yields an exponential improvement over one choice, but three choices is just a small factor better than two. We note that the paper [1] also examined several related problems, including a closed dynamic model where at each step a random ball is deleted and re inserted into the system. This result was generalized to natural queueing theoretic models independently by by Vvedenskaya, Dobrushin, and Karpelevich [14] and Mitzenmacher ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced Allocations", Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593--602.

....parallelize and could therefore even be used for very large systems with thousands of disks. A well known technique, shortest queue, maintains a FIFO queue of committed requests. A newly arrived request fi; jg that could be served on two disks i and j is committed to the disk with shortest queue [6, 31, 23]. We show that executing the requests locally in FIFO order is indeed optimal. However, immediately committing a request when it arrives is unnecessary. Perhaps the simplest more flexible strategy, lazy, puts a request fi; jg in the queues of both disks i and j. When a disk i finishes a request, ....

....like Q(1=e) i.e. they can become rather large as e approaches zero. Nonredundant random placement has been proposed for the parallel file system RAMA [22] Combining random placement and redundancy has first been considered in parallel computing for PRAM emulation [17] and online load balancing [6]. For scheduling disk accesses, these techniques have been used for multimedia applications [29, 30, 19, 24, 8, 28] These papers use shortest queue, do not specify the scheduling algorithm, or schedule large batches in a synchronous fashion. Some RAID arrays use load balancing techniques to ....

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In 26th ACM Symposium on the Theory of Computing, pages 593--602, 1994.

....l max = Theta(log(n) log log n) whp can be proven. Now consider the slightly more adaptive approach called balanced random allocation. Jobs are considered one after the other. Two random possible target PEs are chosen for each job and the job is allocated on the PE with lower load. Azar et al. [1] have shown that l max = O(m=n) 1 o(1) log ln n whp for m = n. Interestingly, this bound shows that balanced random allocation is exponentially better than plain random allocation. However, for large m their methods of analysis yield even weaker bounds than that for plain random ....

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In 26th ACM Symposium on the Theory of Computing, pages 593--602, 1994.

....problem. Our results are also interesting from a more abstract point of view independent of the external memory model. Load balancing when two randomly chosen locations of load units are available has been studied using several models usually for the case N = D or N = Theta(D) Azar et al. [4] show that an optimal online strategy commits each arriving request to the least loaded unit. This strategy achieves a maximum load of O(log log D) whp. They also state that load O(1) can be achieved using offline scheduling. In Section 4.2 we review how such offline algorithms can be used to get ....

....is almost trivial to see why Dinic algorithm can solve the problem in time O D log and a revision of the analysis of preflow push algorithms shows that those even work in time O(D log D) 4.2 Linear Time Approximation. In their forthcoming full paper on balanced allocation, Azar et al. [4] give a construction that achieves maximum load 10 for N = D. This is mainly of theoretical interest but they attribute a method that achieves maximum load 2 for N 1:6D to Frieze. A similar result is described in more detail by Czumaj and Stemann in the full paper [8, Section 7] using a result by ....

Azar, Y., Broder, A. Z., Karlin, A. R., and Upfal, E. Balanced allocations. In 26th ACM Symposium on the Theory of Computing (1994), pp. 593--602. Full version to appear in SIAM J. Computing.

....positive integer. When each ball arrives, it picks d bins at random, and chooses to go to the one among these d that is least loaded at that point, breaking ties arbitrarily. The case d = 1 corresponds to ordinary dart throwing; so we just consider the case d 2 now. A remarkable fact shown in [7] is that the expected value of the maximum number of balls in any bin here, is just O( ln ln n) ln d) Theta(1) Note the significant improvement over ordinary dart throwing, even for the case of d = 2. Such a result may naturally be expected to be algorithmically significant: applications to ....

....of balls in any bin here, is just O( ln ln n) ln d) Theta(1) Note the significant improvement over ordinary dart throwing, even for the case of d = 2. Such a result may naturally be expected to be algorithmically significant: applications to dynamic load balancing and hashing are shown in [7]. Also see [37, 52] for related resource allocation and hashing processes. In light of this, a natural question may be whether there is a variant of random initial delays that leads to an improvement in the approximation bound for job shop scheduling. However, by a random construction, it has ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proc. ACM Symposium on Theory of Computing, pages 593--602, 1994.

....point given finite initial conditions. Mitzenmacher also develops a new approach to analyzing M M n systems based on density dependent jump Markov processes which we will elaborate on in Section 1.3.1 and use extensively later. Mitzenmacher s d choice technique is based on the work of Azar et al. [3], which examines d choices in the static context of the bin packing problem. That is, given n balls and n bins, how can you place the balls to minimize the maximum number of balls in any given bin Azar et al. show that by placing each successive ball in the least loaded of d bins chosen uniformly ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994.

....In this paper we aim at comparing symmetric and asymmetric multiple choice allocation schemes. We focus on sequential, online balls and bins games in which balls are inserted one after the other. B. V ocking: Multiple Choice Algorithms 3 2. 1 Symmetric allocation Azar, Broder, Karlin and Upfal [2, 3] investigate multiple choice allocation for on line load balancing and hashing. Algorithm sym[d] for d 2, inserts one ball after the other and chooses d alternative bins independently and uniformly at random for each ball and assigns the ball to one of its d alternatives with minimal number of ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proc. of the 26th ACM Symp. on Theory of Computing (STOC), pages 593--602, 1994.

....une loi de Rayleigh. 5 Occupation maximale d une urne Dans le mod ele classique, lorsqu on place s equentiellement n boules parmi m = n urnes, le nombre de boules dans l urne la plus remplie est de l ordre de log n= log log n : cf. Gonnet [14] pour une analyse d etaill ee de ceci. Azar et al. [4] montrent qu une variante simple suffit a obtenir un remplissage maximal d ordre, en moyenne, log log n : il suffit de choisir deux urnes pour chaque boule, et de mettre la boule dans l urne la moins remplie. Le r esultat exact est donn e lorsqu on choisit la moins remplie de d urnes, et est le ....

Y. AZAR, A.Z. BRODER, A.R. KARLIN, and E. UPFAL. Balanced allocations. In Symposium on Theory Of Computing, 1994.

....For instance, while the k server problem has been used to model the behavior of multiple heads on a disk, the cnn problem can be used to model retrieving information which resides on multiple disks. This, for example, happens when we replicate data to achieve higher performance or fault tolerance [1, 4, 16, 20, 21]. Each disk may have information in completely different locations, leading to independent costs for information retrieval. We wish to minimize time spent looking for data, but do not actually care which disk the information comes from. In contrast, writing must be performed to all disks; this is ....

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In Proc. 26th Annual ACM Symposium on the Theory of Computing, (STOC '94), pages 593--602, 1994.

....to physical blocks on the disks. The developed hash function is very flexible and allows to add and to remove some disks with a minimum number of virtual blocks that have to be replaced. Scheduling. We have implemented several strategies which are motivated by so called balls into bins games (see [5], 17] 8] These strategies are able to exploit the redundancy generated by our placement strategies. Simple minimum game: The requests are fulfilled from the k of the least loaded k 1 disks storing the requested data. The scheduler sends a load request to each of the k 1 disks holding a ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocation. In Proceedings of the 26th Symposium on Theory of Computing (Stoc), pages 593--602, 1994.

....for replicated blocks to the least loaded disk is easily mapped to a problem that has been well studied in the computer science literature for load balancing in distributed systems [10] which is often referred to as random probing . Analytical models addressing this problem are studied in [1] and [20] Random data allocation for multimedia servers has also been considered in [3] 28] 4] 19] Tewari et al..l [28] analyze the performance of a clustered video server with random allocation of data blocks, using both an analytical model and simulation. However, they do not consider data ....

Y. Azar, A. Broder, A. Karlin, and E.Upfal. Balanced allocations. In Proc. 26th Annual ACM Symposium on the Theory of Computing (STOC 94), pages 593--602, 1994.

....the attempt is to minimize the length of time during whichatask is denied service, then S2istheschedule of choice, since it is, in an intuitive sense, fairer. Temporal fairness. This issue of fairness in resource allocation and scheduling has recently been attracting considerable attention [1, 2,3,4]. Motivated no doubt in part by applications, suchasmultimedia, which are characterized by fairly regular resource requirements over extended intervals, attempts have been made to formalize and characterize notions of temporal fairness. This research addresses the issue of designing fair ....

....a problem instance Phi, ensures that Algorithm WM will schedule Phi in a pfair manner. 2 Pfairness: Definitions, and related work We start with some conventions: ffl We adopt the standard notation of having [a# b) denote the contiguous natural numbers a# a 1#: #b; 1. slots: 0] 1] [2] [t ; 1] t] instants: 0 1 2 3 t ; 1 t t 1 Figure 1: Notation: Time instants and time slots ffl Scheduling decisions are made at integral values of time, numbered from 0. The real interval between time t and time t 1 (including t, excluding t 1) will be referred to as slot t, t 2 N (see ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the Twenty-sixth Annual ACM Symposium on Theory of Computing,May1994.

....through the DAAD. 1 To motivate this paper, we first provide the relevant history. It is well known that when n balls are thrown into n bins, the maximum load, or balls in a bin, is ln n ln ln n (1 o(1) with high probability. Azar, Broder, Karlin, and Upfal suggested the following variation [1]. Suppose that n balls are sequentially placed into n bins in the following manner: for each ball, d 2 bins are chosen independently and uniformly at random from the n bins, and the ball is placed in the bin with the fewest balls, ties being broken arbitrarily. Then in this case the maximum load ....

....using two hash functions and place the item in the least loaded bucket, then we can dramatically reduce the maximum load (and hence the maximum search time) for an item. Of course the average search time may increase, since a search requires examining multiple buckets. We note that the paper [1] also examined several related problems, including a closed dynamic model where at each step a random ball is deleted and re inserted into the system. This result was generalized to natural queueing theoretic models independently by Vvedenskaya, Dobrushin, and Karpelevich [14] and Mitzenmacher ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced Allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593--602.

....into n bins so that for each ball, d 2 bins are chosen independently and uniformly at random from the n bins, and the ball is placed in the bin with the fewest balls, ties being broken arbitrarily. Then in this case the maximum load is only ln ln n ln d Sigma Theta(1) with high probability [1]. This result was generalized to natural queueing models independently in [6] and [2, 3] Suppose that tasks arrive at a bank of n First In First Out processors as a Poisson process of rate n, where 1; tasks require an exponentially distributed amount of service with mean 1. If each task queues ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced Allocations. In Proc. of the 26th ACM Symp. on the Theory of Computing, 1994, pp. 593--602.

....on the disks, the higher the probability that the server can find a disk to schedule the requests for that movie. ffl Balancing workload among disks: Placing the first chunks of the movies on randomly selected disks makes it highly probable that the requests are uniformly distributed on the disks Azar et al. 1994; Barve et al. 1997. We discuss the details in Section 4.1. 3.2 REQUEST SCHEDULING To service four requests in T , scheme 2DB uses the disk scheduling policy Fixed Stretch, which divides the period into four equally separated service slots, each lasting time Delta (T = 4 Theta Delta) ....

....hot movies are similar to those shown in Figure 1.3 for two copies. We use a similar problem, placing balls in runs, to explain this surprising result. Suppose that we sequentially place n balls into m urns by putting each ball into a randomly chosen urn. It has been shown by many studies (e.g. Azar et al. 1994; Barve et al. 1997; Berson et al. 1994; Papoulis, 1984) that there is a high probability the balls can be distributed among the urns quite unevenly. However, if for each ball we randomly select two locations and each ball is placed in the least full urn between these two possible locations, the ....

Azar, Y., Broader, A., Karlin, A., and Upfal, E. (1994). Balanced allocations. ACM Symposium on Theory of Computing, pages 593--602.

....For instance, while the k server problem has been used to model the behavior of multiple heads on a disk, the cnn problem can be used to model retrieving information which resides on multiple disks. This, for example, happens when we replicate data to achieve higher performance or fault tolerance [1, 4, 16, 20, 21]. Each disk may have information in completely di erent locations, leading to independent costs for information retrieval. We wish to minimize time spent looking for data, but do not actually care which disk the information comes from. In contrast, writing must be performed to all disks; this is ....

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In Proc. 26th Annual ACM Symposium on the Theory of Computing, (STOC '94), pages 593-602, 1994.

....is Theta( ln n lnd1 n m Deltaln ne m=n) w.h.p. 1 We shall refer to this process as the classical allocation process, CAP (see [14, 17] for a general exposition 1 Throughout the paper w.h.p. will denote that a given event holds with of this process and its applications) Azar et al. [6] extended this process and showed that if each ball chooses i.u.r. with replacements d 1 bins and then it is placed into the bin with the smallest load, then the maximum load decreases dramatically to (1 o(1) Delta ln ln n= ln d Theta(m=n) w.h.p. We will refer to the process of Azar et ....

....will refer to the process of Azar et al. as ABKU[d] They also proved that each randomized on line process that does not reallocate the balls and has the maximum allocation time d must have a bin with load (1 o(1) Delta ln ln n= ln d Omega Gamma m=n) w.h.p. In the case m = n, Azar et al. [6] were able to tighten these bounds up to an additive constant term. They showed that the maximum load in ABKU[d] is ln ln n= ln d Theta(1) w.h.p. and that every randomized on line process that has the maximum allocation time d (and does not reallocate the balls) must have a bin with load ln ln ....

[Article contains additional citation context not shown here]

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing, pages 593-- 602, 1994.

....faults and concurrency. Our main technical contribution in this chapter is the derivation of sharp threshold phenomena associated with certain random allocation experiments. Several recent papers have studied similar processes that arise in dynamic resource allocation and parallel load balancing [2, 25, 108]. 60 Chapter 3 Fast Fault Tolerant Concurrent Access to Shared Objects 3.1 Introduction In this chapter, we design and analyze a simple local protocol for providing fast concurrent access to shared objects in a faulty distributed network. We model the network as a faulty O(log n) arbitrary ....

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing, pages 593--602, May 1994.

....When C receives the election messages from the hosts it can choose to use either of the two rounds of drawing, whichever optimizes its operation 2 . In particular, this al 2 This technique is similar in spirit to the one used by Azar et al. for the balanced allocation of balls into bins [ABKU99] 6 10 1 10 2 10 3 10 4 1 1.1 1.2 1.3 1.4 number of users (n) skip reset choice 10 1 10 2 10 3 10 4 6 8 10 12 14 16 number of users (n) expected number of messages, N(n) skip reset choice Fig. 9. Algorithm Skip Reset vs. the choice algorithm: T (n) and N(n) ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocation. SIAM J. Computing, 29:180 -- 200, 1999.

....component in GA = GA (m) m = c 0 n is bounded by (log n) O(1) Note that this says that a choice of two edges reduces the size of the largest component from order n to order polylog n, i.e. by an exponential factor. This is reminiscent of the beautiful result of Azar, Broder, Karlin and Upfal [2] where, in the framework of n balls in n boxes, the choice of one of two random boxes for each ball reduces the number of balls in the box containing the most balls from roughly log n log log n to about log log n. We prove Theorem 1 assuming edges are chosen with replacement. Since we choose ....

....presented edges Suppose the edges are chosen randomly from the hypercube Q n or another graph. We can also consider the converse problem. Is it possible to create a giant component with ( 1 2 )n edges if we have a choice of two Are there any algorithmic implications, as there are for [2] Can we play this avoidance game for other properties than the existence of a giant component Acknowledgement We thank Dimitris Achlioptas for thinking of this lovely problem and Mike Molloy for some earlier discussions. ....

Y. Azar, A. Z. Broder, A. R. Karlin and E. Upfal, Balanced Allocations, Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, (1994) 593-602.

....generator srand48 leading to almost identical results. Now consider the slightly more adaptive approach called balanced random allocation. Jobs are considered one after the other. Two random possible target PEs are chosen for each job and the job is allocated on the PE with lower load. Azar et al. [1] have shown that l max = O(m=n) 1 o(1) log ln n whp for m = n. Interestingly, this bound shows that balanced random allocation is exponentially better than plain random allocation. However, for large m their methods of analysis yield even weaker bounds than that for plain random allocation. Only ....

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In 26th ACM Symposium on the Theory of Computing, pages 593--602, 1994.

....two choices per task can lead to an exponential improvement over one choice in the maximum load on a processor. In the static setting, this improvement appears to have first been noted by Karp, Luby, and Meyer auf der Heide [7] A more complete analysis was given by Azar, Broder, Karlin, and Upfal [3]. In the dynamic setting, this work was extended in [12, 13] similar results were independently reported in [22] In the queuing theory community, similar previous work includes that of Towsley and Mirchandaney [17] and that of Mirchandaney, Towsley, and Stankovic [9, 10] These authors examine ....

....the queues remain finite over time. However, the strategy of choosing a small number of servers and queueing at the least loaded has been shown to perform significantly better in the case where the load information is up to date [5, 12, 13, 22] It has also proved effective in other similar models [3, 7, 13]. Moreover, the strategy also appears to be practical and have a low overhead in distributed settings, where global information may not be available, but polling a small number of processors may be possible. Going to the server with the smallest load appears natural in more centralized systems ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced Allocations", Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593--602.

....c flDigital Equipment Corporation 1997. All rights reserved Studying Balanced Allocations with Differential Equations # Michael Mitzenmacher y Abstract Using differential equations, we examine the GREEDY algorithm studied by Azar, Broder, Karlin, and Upfal for distributed load balancing [1]. This approach yields accurate estimates of the actual load distribution, provides insight into the exponential improvement GREEDY offers over simple random selection, and allows one to prove tight concentration theorems about the loads in a straightforward manner. 1 Introduction Suppose that n ....

....probability to mean with probability at least 1 O(1 n) where n is the number of balls. Also, log will always mean the natural logarithm, unless otherwise noted. Azar, Broder, Karlin, and Upfal considered how much more evenly distributed the load would be if each ball had two (or more) choices [1]. Suppose that the balls are placed sequentially, and each ball is placed into the less full of two bins chosen independently and uniformly at random with replacement (breaking ties arbitrarily) In this case, they showed that the maximum load drops to log log n log 2 O(1) with high ....

[Article contains additional citation context not shown here]

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced Allocations", Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593--602.

No context found.

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal, Balanced allocations, SIAM J Comput 29(1) (2002), 180--200.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, pages 593--602, 1994.

....rst analyses suggested using multiple tables, with a separate function for each table. Elements that collide in one table percolate to the next. The tables shrunk in size and the hashes could be computed in parallel [3] A seminal result in the area considered the following natural hashing scheme [1], which we here call the d random scheme. Suppose that n items are hashed sequentially into a table with n buckets, in the following manner. Each item is hashed using d hash functions, which we assume yield independent and identically distributed buckets for each item. The item is placed in the ....

....which we assume yield independent and identically distributed buckets for each item. The item is placed in the least loaded bucket (that is, the bucket with the fewest items) ties are broken arbitrarily. A search for an item now requires examining the d possible buckets; however, as shown in [1] the maximum load in a bucket (with high probability) is log d O(1) This compares quite favorably to the situation where just one hash function is used, in which case the maximum load is log n log log n O(1) The key point of this result is that using two hash functions leads to a ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced Allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593-602. 21

....balls. Karp, Luby, and Meyer auf der Heide [18] were the first to notice a dramatic improvement when switching from one hash function to two in the context of PRAM simulations. In fact, it is possible to use a result from [18] to derive a weaker form of our static upper bound. For details see [7]. A preliminary version of this paper has appeared in [7] Subsequently, Adler et al. 1] analyzed parallel implementation of the balanced allocation mechanism and obtained interesting communication vs. load tradeo#s. A related question was considered by Broder et al. 10] In their model the set ....

....first to notice a dramatic improvement when switching from one hash function to two in the context of PRAM simulations. In fact, it is possible to use a result from [18] to derive a weaker form of our static upper bound. For details see [7] A preliminary version of this paper has appeared in [7]. Subsequently, Adler et al. 1] analyzed parallel implementation of the balanced allocation mechanism and obtained interesting communication vs. load tradeo#s. A related question was considered by Broder et al. 10] In their model the set of choices is such that there is a placement that results ....

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal, Balanced allocations, in Proc. 26th Annual ACM Symposium on the Theory of Computing, Montreal, Quebec, Canada, 1994, pp. 593--602.

....analyses suggested using multiple tables, with a separate function for each table. Elements that collide in one table percolate to the next. The tables shrunk in size and the hashes could be computed in parallel [3] A seminal result in the area considered the following natural hashing scheme [1], which we here call the d random scheme. Suppose that n items are hashed sequentially into a table with n buckets, in the following manner. Each item is hashed using d hash functions, which we assume yield independent and identically distributed buckets for each item. The item is placed in the ....

....which we assume yield independent and identically distributed buckets for each item. The item is placed in the least loaded bucket (that is, the bucket with the fewest items) ties are broken arbitrarily. A search for an item now requires examining the d possible buckets; however, as shown in [1] the maximum load in a bucket (with high probability) is log log n log d O(1) This compares quite favorably to the situation where just one hash function is used, in which case the maximum load is log n log log n (1 o(1) with high probability) The key point of this result is that ....

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced Allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593--602.

No context found.

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. SIAM J. Comput., 29(1):180--200, 1999.

No context found.

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal, "Balanced allocations," in Proc. of ACM STOC, Montreal, Canada, May 1994.

No context found.

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. SIAM J. Comput., 29(1):180--200, 1999.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced allocations," in Proceedings 26th ACM STOC, 1994, pp. 593--602.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced Allocations," SIAM J. on Computing, vol. 29, no. 1, 1999.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocation. SIAM J. Computing, 29:180 -- 200, 1999.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced Allocations," SIAM Journal on Computing, vol. 29, July 1999.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal, "Balanced Allocations," SIAM J. on Computing, vol. 29, no. 1, 1999.

No context found.

Y. Azar, A. Broder, and A. Karlin, E. Upfal. Balanced allocations. In Proc. of the 26th Ann. ACM Symp. on Theory of Computing, pages 593--602, May 1994.

No context found.

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In 26th ACM Symposium on the Theory of Computing, pages 593-602, 1994.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings 26th ACM STOC, pages 593--602, 1994.

No context found.

Y. Azar, A. Broder, and A. Karlin, E. Upfal. Balanced allocations. In Proc. of the 26th Ann. ACM Symp. on Theory of Computing, pages 593--602, May 1994.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, pages 593--602, 1994.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. Journal version, preprint.

No context found.

Y. Azar, A.Z. Broder, A.R. Karlin, E. Upfal, Balanced allocations, SIAM J. Comput. 29 (1999) 180--200.

No context found.

Y. Azar, A.Z. Broder, A.R. Karlin, E. Upfal, Balanced allocations (extended abstract), in: Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 593--602.

No context found.

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th ACM Symposium on Theory of Computing, pages 593--602, 1994.

No context found.

Y. Azar, A. Z. Broder, A. R. Karlin and E. Upfal, Balanced Allocations, Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, (1994) 593-602.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC