We generalize Cuckoo Hashing [23] to d-ary 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.

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.

Abstract. We investigate randomized processes underlying load balancing based on the multiple-choice 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.

We survey a set of algorithmic techniques that make it possible to build a high performance storage server from a network of cheap components. Such a storage server oers a very simple programming model. To the clients it looks like a single very large disk that can handle many requests in parallel with minimal interference between the requests.

this paper we use randomization and data redundancy to enable good load balancing. We focus on duplicate storage strategies, i.e., each data block is stored twice. This means that a request for a block can be serviced by two disks. A consequence of such a storage strategy is that we have to decide for each block which disk to use for its retrieval. This results in a so-called retrieval selection problem. We describe a graph model for duplicate storage strategies and derive polynomial time optimization algorithms for the retrieval selection problems of several storage strategies. Our model unifies and generalizes chained declustering and random duplicate assignment strategies. Simulation results and a probabilistic analysis complete this paper

An important cost issue in multimedia servers is disk load balancing, such that the available hard disks are used as efficiently as possible. Disk load balancing is often done on a block basis, but can also be done on a time basis, by taking into account the actual transfer times of the blocks. In the latter approach we can also embed the disk switch times. In this paper we revisit blockbased load balancing and introduce time-based load balancing. For each approach we present a mathematical model and analyze the complexity of the corresponding retrieval problem. We give algorithms with a performance bound for the NP-hard time-based retrieval problem and use simulation to compare the results of these algorithms with a maximum flow algorithm for the blockbased retrieval problem. 1

Experimental algorithmics yields large amounts of data that depends on many parameters. This paper collects a number of rules for presenting this data in concise, meaningful, understandable diagrams that have sufficiently high quality to be printed in scientific journals. The focus