Results 1  10
of
42
BALANCED ALLOCATIONS: THE HEAVILY LOADED CASE
, 2006
"... We investigate ballsintobins processes allocating m balls into n bins based on the multiplechoice paradigm. In the classical singlechoice variant each ball is placed into a bin selected uniformly at random. In a multiplechoice process each ball can be placed into one out of d ≥ 2 randomly selec ..."
Abstract

Cited by 58 (7 self)
 Add to MetaCart
We investigate ballsintobins processes allocating m balls into n bins based on the multiplechoice paradigm. In the classical singlechoice variant each ball is placed into a bin selected uniformly at random. In a multiplechoice process each ball can be placed into one out of d ≥ 2 randomly selected bins. It is known that in many scenarios having more than one choice for each ball can improve the load balance significantly. Formal analyses of this phenomenon prior to this work considered mostly the lightly loaded case, that is, when m ≈ n. In this paper we present the first tight analysis in the heavily loaded case, that is, when m ≫ n rather than m ≈ n. The best previously known results for the multiplechoice processes in the heavily loaded case were obtained using majorization by the singlechoice process. This yields an upper bound of the maximum load of bins of m/n + O ( √ m ln n/n) with high probability. We show, however, that the multiplechoice processes are fundamentally different from the singlechoice variant in that they have “short memory. ” The great consequence of this property is that the deviation of the multiplechoice processes from the optimal allocation (that is, the allocation in which each bin has either ⌊m/n ⌋ or ⌈m/n ⌉ balls) does not increase with the number of balls as in the case of the singlechoice process. In particular, we investigate the allocation obtained by two different multiplechoice allocation schemes,
Space Efficient Hash Tables With Worst Case Constant Access Time
 In STACS
, 2003
"... We generalize Cuckoo Hashing [23] to dary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ffl) n memory cells, for any constant ffl ? 0. Assuming uniform hashing, accessing or deleting table entries takes at most d = O(ln ffl ) probes ..."
Abstract

Cited by 47 (4 self)
 Add to MetaCart
We generalize Cuckoo Hashing [23] to dary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ffl) n memory cells, for any constant ffl ? 0. Assuming uniform hashing, accessing or deleting table entries takes at most d = O(ln ffl ) probes and the expected amortized insertion time is constant. This is the first dictionary that has worst case constant access time and expected constant update time, works with (1 + ffl) n space, and supports satellite information. Experiments indicate that d = 4 choices suffice for ffl 0:03. We also describe variants of the data structure that allow the use of hash functions that can be evaluted in constant time.
Distributed selfish load balancing
 In Proc. 17th Ann. ACM–SIAM Symp. on Discrete Algorithms (SODA
, 2006
"... Abstract. Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A gametheoretic mechanism to find a suitable allocation is to associate each task with a “selfish agent”, and require each agent to select a resource, with the cost of a resource being the n ..."
Abstract

Cited by 31 (3 self)
 Add to MetaCart
Abstract. Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A gametheoretic mechanism to find a suitable allocation is to associate each task with a “selfish agent”, and require each agent to select a resource, with the cost of a resource being the number of agents to select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced. Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For m ≫ n, the system becomes approximately balanced (an ǫNash equilibrium) in expected time O(log log m). We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time O(log log m + n 4). We also give a lower bound of Ω(max{log log m, n}) for the convergence time. 1. Introduction. Suppose
Asynchronous Parallel Disk Sorting
 IN 15TH ACM SYMPOSIUM ON PARALLELISM IN ALGORITHMS AND ARCHITECTURES
, 2003
"... We develop an algorithm for parallel disk sorting, whose I/O cost approaches the lower bound and that guarantees almost perfect overlap between I/O and computation. Previous algorithms have either suboptimal I/O volume or cannot guarantee that I/O and computations can always be overlapped. We give a ..."
Abstract

Cited by 22 (8 self)
 Add to MetaCart
We develop an algorithm for parallel disk sorting, whose I/O cost approaches the lower bound and that guarantees almost perfect overlap between I/O and computation. Previous algorithms have either suboptimal I/O volume or cannot guarantee that I/O and computations can always be overlapped. We give an efficient implementation that can (at least) compete with the best practical implementations but gives additional performance guarantees. For the experiments we have configured a state of the art machine that can sustain full bandwidth I/O with eight disks and is very cost effective.
Perfectly balanced allocation
 in Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, Princeton, NJ, 2003, Lecture Notes in Comput. Sci. 2764
, 2003
"... Abstract. We investigate randomized processes underlying load balancing based on the multiplechoice paradigm: m balls have to be placed in n bins, and each ball can be placed into one out of 2 randomly selected bins. The aim is to distribute the balls as evenly as possible among the bins. Previousl ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
Abstract. We investigate randomized processes underlying load balancing based on the multiplechoice paradigm: m balls have to be placed in n bins, and each ball can be placed into one out of 2 randomly selected bins. The aim is to distribute the balls as evenly as possible among the bins. Previously, it was known that a simple process that places the balls one by one in the least loaded bin can achieve a maximum load of m/n + Θ(log log n) with high probability. Furthermore, it was known that it is possible to achieve (with high probability) a maximum load of at most ⌈m/n ⌉ +1using maximum flow computations. In this paper, we extend these results in several aspects. First of all, we show that if m ≥ cn log n for some sufficiently large c, thenaperfect distribution of balls among the bins can be achieved (i.e., the maximum load is ⌈m/n⌉) with high probability. The bound for m is essentially optimal, because it is known that if m ≤ c ′ n log n for some sufficiently small constant c ′ , the best possible maximum load that can be achieved is ⌈m/n ⌉ +1with high probability. Next, we analyze a simple, randomized load balancing process based on a local search paradigm. Our first result here is that this process always converges to a best possible load distribution. Then, we study the convergence speed of the process. We show that if m is sufficiently large compared to n,thenno matter with which ball distribution the system starts, if the imbalance is ∆, then the process needs only ∆·n O(1) steps to reach a perfect distribution, with high probability. We also prove a similar result for m ≈ n, and show that if m = O(n log n / log log n), then an optimal load distribution (which has the maximum load of ⌈m/n ⌉ +1) is reached by the random process after a polynomial number of steps, with high probability.
Duality between prefetching and queued writing with applications to external sorting
 IN EUROPEAN SYMPOSIUM ON ALGORITHMS, VOLUME 2161 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... Parallel disks promise to be a cost effective means for achieving high bandwidth in applications involving massive data sets, but algorithms for parallel disks can be difficult to devise. To combat this problem, we define a useful and natural duality between writing to parallel disks and the seeming ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
Parallel disks promise to be a cost effective means for achieving high bandwidth in applications involving massive data sets, but algorithms for parallel disks can be difficult to devise. To combat this problem, we define a useful and natural duality between writing to parallel disks and the seemingly more difficult problem of prefetching. We first explore this duality for applications involving readonce accesses using parallel disks. We get a simple linear time algorithm for computing optimal prefetch schedules and analyze the efficiency of the resulting schedules for randomly placed data and for arbitrary interleaved accesses to striped sequences. Duality also provides an optimal schedule for the integrated caching and prefetching problem, in which blocks can be accessed multiple times. Another application of this duality gives us the rst parallel disk sorting algorithms that are provably optimal up to lower order terms. One of these algorithms is a simple and practical variant of multiway merge sort, addressing a question that has been open for some time.
Reconciling Simplicity and Realism in Parallel Disk Models
 Parallel Computing
, 2001
"... For the design and analysis of algorithms that process huge data sets, a machine model is needed that handles parallel disks. There seems to be a dilemma between simple and flexible use of such a model and accurate modelling of details of the hardware. This paper explains how many aspects of this pr ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
For the design and analysis of algorithms that process huge data sets, a machine model is needed that handles parallel disks. There seems to be a dilemma between simple and flexible use of such a model and accurate modelling of details of the hardware. This paper explains how many aspects of this problem can be resolved. The programming model implements one large logical disk allowing concurrent access to arbitrary sets of variable size blocks. This model can be implemented efficienctly on multiple independent disks even if zones with different speed, communication bottlenecks and failed disks are allowed. These results not only provide useful algorithmic tools but also imply a theoretical justification for studying external memory algorithms using simple abstract models.
Asynchronous scheduling of redundant disk arrays
, 2000
"... Random redundant allocation of data to parallel disk arrays can be exploited to achieve low access delays. New algorithms are proposed which improve the previously known shortest queue algorithm by systematically exploiting that scheduling decisions can be deferred until a block access is actually s ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
Random redundant allocation of data to parallel disk arrays can be exploited to achieve low access delays. New algorithms are proposed which improve the previously known shortest queue algorithm by systematically exploiting that scheduling decisions can be deferred until a block access is actually started on a disk. These algorithms are also generalized for coding schemes with low redundancy. Using extensive experiments, practically important quantities are measured which have so far eluded an analytical treatment: The delay distribution when a stream of requests approaches the limit of the sytem capacity, the system efficiency for parallel disk applications with bounded prefetching buffers, and the combination of both for mixed traffic. A further step towards practice is taken by outlining the system design for α: automatically loadbalanced parallel harddisk array. 1
Distribution Sort with Randomized Cycling
 In Proceedings of the Twelfth Annual ACMSIAM Symposium on Discrete Algorithms (SODA01
, 2001
"... Paxallel independent disks can enhance the performance of external memory (EM) algorithms, but the programming task is often difficult. In this paper we develop randomized vaxiants of distribution sort for use with paxallel independent disks. We propose a simple vaxiant called randomized cycling dis ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
Paxallel independent disks can enhance the performance of external memory (EM) algorithms, but the programming task is often difficult. In this paper we develop randomized vaxiants of distribution sort for use with paxallel independent disks. We propose a simple vaxiant called randomized cycling distribution sort (RCD) and prove that it has optimal expected I/O complexity. The analysis uses a novel reduction to a model with significantly fewer probabilistic interdependencies. Experimental evidence is provided to support its practicality. Other simple vaxiants axe also examined experimentally and appeax to offer similax advantages to RCD. Based upon ideas in RCD we propose general techniques that transpaxently simulate algorithms developed for the unrealistic multihead disk model so that they can be run on the realistic paxallel disk model. The simulation is optimal for two important classes of algorithms: the class of multipass algorithms, which make a complete pass through their data before accessing any element a second time, and the algorithms based upon the wellknown distribution paxadigm of EM computation.