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We present a simple dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738–761, 1994). The space usage is similar to that of binary search trees, i.e., three words per key on average. Besides being conceptually much simpler than previous dynamic dictionaries with worst case constant lookup time, our data structure is interesting in that it does not use perfect hashing, but rather a variant of open addressing where keys can be moved back in their probe sequences. An implementation inspired by our algorithm, but using weaker hash functions, is found to be quite practical. It is competitive with the best known dictionaries having an average case (but no nontrivial worst case) guarantee. Key Words: data structures, dictionaries, information retrieval, searching, hashing, experiments * Partially supported by the Future and Emerging Technologies programme of the EU

This paper presents Ethane, a new network architecture for the enterprise. Ethane allows managers to define a single networkwide fine-grain policy, and then enforces it directly. Ethane couples extremely simple flow-based Ethernet switches with a centralized controller that manages the admittance and routing of flows. While radical, this design is backwards-compatible with existing hosts and switches. We have implemented Ethane in both hardware and software, supporting both wired and wireless hosts. Our operational Ethane network has supported over 300 hosts for the past four months in a large university network, and this deployment experience has significantly affected Ethane’s design. Categories and Subject Descriptors

ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log log n with high probability. Now suppose instead that the balls are placed sequentially, and each ball is placed in the least loaded of d 2 bins chosen independently and uniformly at random. Azar, Broder, Karlin, and Upfal showed that in this case, the maximum load is log log n= log d + (1) with high probability [ABKU99]. The important implication of this result is that even a small amount of choice can lead to drastically different results in load balancing. Indeed, having just two random choices (i.e.,...

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Hashing is fundamental to many algorithms and data structures widely used in practice. For theoretical analysis of hashing, there have been two main approaches. First, one can assume that the hash function is truly random, mapping each data item independently and uniformly to the range. This idealized model is unrealistic because a truly random hash function requires an exponential number of bits to describe. Alternatively, one can provide rigorous bounds on performance when explicit families of hash functions are used, such as 2-universal or O(1)-wise independent families. For such families, performance guarantees are often noticeably weaker than for ideal hashing. In practice, however, it is commonly observed that weak hash functions, including 2-universal hash functions, perform as predicted by the idealized analysis for truly random hash functions. In this paper, we try to explain this phenomenon. We demonstrate that the strong performance of universal hash functions in practice can arise naturally from a combination of the randomness of the hash function and the data. Specifically, following the large body of literature on random sources and randomness extraction, we model the data as coming from a “block source, ” whereby

Many networking applications require fast state lookups in a concurrent state machine, which tracks the state of a large number of flows simultaneously. We consider the question of how to compactly represent such concurrent state machines. To achieve compactness, we consider data structures for Approximate Concurrent State Machines (ACSMs) that can return false positives, false negatives, or a “don’t know” response. We describe three techniques based on Bloom filters and hashing, and evaluate them using both theoretical analysis and simulation. Our analysis leads us to an extremely efficient hashing-based scheme with several parameters that can be chosen to trade off space, computation, and the impact of errors. Our hashing approach also yields a simple alternative structure with the same functionality as a counting Bloom filter that uses much less space. We show how ACSMs can be used for video congestion control. Using an ACSM, a router can implement sophisticated Active Queue Management (AQM) techniques for video traffic (without the need for standards changes to mark packets or change video formats), with a factor of four reduction in memory compared to full-state schemes and with very little error. We also show that ACSMs show promise for real-time detection of P2P traffic.

Abstract. A counting Bloom filter (CBF) generalizes a Bloom filter data structure so as to allow membership queries on a set that can be changing dynamically via insertions and deletions. As with a Bloom filter, a CBF obtains space savings by allowing false positives. We provide a simple hashing-based alternative based on d-left hashing called a d-left CBF (dlCBF). The dlCBF offers the same functionality as a CBF, but uses less space, generally saving a factor of two or more. We describe the construction of dlCBFs, provide an analysis, and demonstrate their effectiveness experimentally. 1

We consider cuckoo hashing as proposed by Pagh and Rodler in 2001. We show that the expected construction time of the hash table is O(n) as long as the two open addressing tables are each of size at least (1 #)n,where#>0andn is the number of data points. Slightly improved bounds are obtained for various probabilities and constraints. The analysis rests on simple properties of branching processes.

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