Some Open Questions Related to Cuckoo Hashing

Mitzenmacher, Michael

doi:10.1007/978-3-642-04128-0_1

Cited by 29 publications

(23 citation statements)

References 37 publications

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“…We review cuckoo hashing and its connection to random hypergraphs; for more background, see [19]. In standard cuckoo hashing [23], keys are placed into a hash table with each bucket containing one item, and each key has two choices of bucket locations determined by random hash values.…”

Section: Cuckoo Hashingmentioning

confidence: 99%

Peeling arguments and double hashing

Mitzenmacher

Thaler

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-The analysis of several algorithms and data structures can be reduced to the analysis of the following greedy "peeling" process: start with a random hypergraph; find a vertex of degree at most k, and remove it and all of its adjacent hyperedges from the graph; repeat until there is no suitable vertex. This specific process finds the k-core of a hypergraph, and variations on this theme have proven useful in analyzing for example decoding from low-density parity-check codes, several hash-based data structures such as cuckoo hashing, and algorithms for satisfiability of random formulae. This approach can be analyzed several ways, with two common approaches being via a corresponding branching process or a fluid limit family of differential equations.In this paper, we make note of an interesting aspect of these types of processes: the results are generally the same when the randomness is structured in the manner of double hashing. This phenomenon allows us to use less randomness and simplify the implementation for several hash-based data structures and algorithms. We explore this approach from both an empirical and theoretical perspective, examining theoretical justifications as well as simulation results for specific problems.

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Section: Cuckoo Hashingmentioning

confidence: 99%

Peeling arguments and double hashing

Mitzenmacher

Thaler

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…Though cuckoo hashing has been mostly studied as a technique for software hash tables, hardware variants have been proposed to implement lookup tables in IP routers [16]. For additional references, Mitzenmacher has a survey on recent research in cuckoo hashing [32].…”

Section: Related Workmentioning

confidence: 99%

The ZCache: Decoupling Ways and Associativity

Sánchez

Kozyrakis

2010

2010 43rd Annual IEEE/ACM International Symposium on Microarchitecture

166

110

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Abstract-The ever-increasing importance of main memory latency and bandwidth is pushing CMPs towards caches with higher capacity and associativity. Associativity is typically improved by increasing the number of ways. This reduces conflict misses, but increases hit latency and energy, placing a stringent trade-off on cache design. We present the zcache, a cache design that allows much higher associativity than the number of physical ways (e.g. a 64-associative cache with 4 ways). The zcache draws on previous research on skew-associative caches and cuckoo hashing. Hits, the common case, require a single lookup, incurring the latency and energy costs of a cache with a very low number of ways. On a miss, additional tag lookups happen off the critical path, yielding an arbitrarily large number of replacement candidates for the incoming block.Unlike conventional designs, the zcache provides associativity by increasing the number of replacement candidates, but not the number of cache ways. To understand the implications of this approach, we develop a general analysis framework that allows to compare associativity across different cache designs (e.g. a set-associative cache and a zcache) by representing associativity as a probability distribution. We use this framework to show that for zcaches, associativity depends only on the number of replacement candidates, and is independent of other factors (such as the number of cache ways or the workload). We also show that, for the same number of replacement candidates, the associativity of a zcache is superior than that of a set-associative cache for most workloads. Finally, we perform detailed simulations of multithreaded and multiprogrammed workloads on a large-scale CMP with zcache as the last-level cache. We show that zcaches provide higher performance and better energy efficiency than conventional caches without incurring the overheads of designs with a large number of ways.

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“…Together with (13), this proves (12). It follows from (12) that to finish the proof, all we need to show is that if > 0 is an arbitrary positive constant then we have…”

Section: Proof Of Lemmamentioning

confidence: 56%

“…They showed that given ε , their bounds hold for any d large enough to give the existence of a matching w.h.p. Mitzenmacher gives a survey on Cuckoo Hashing and Problem 1 of the survey asks for the expected insertion time.…”

Section: Introductionmentioning

confidence: 99%

On the insertion time of random walk cuckoo hashing

Frieze

Johansson

2018

Random Struct Algorithms

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Cuckoo Hashing is a hashing scheme invented by pervious study of Pagh and Rodler. It uses d ≥ 2 distinct hash functions to insert n items into the hash table of size m = (1 + ε)n. In their original paper they treated d = 2 and m = (2 + ε)n. It has been an open question for some time as to the expected time for Random Walk Insertion to add items when d > 2. We show that if the number of hash functions d ≥ dε = O(1) then the expected insertion time is O(1) per item.

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Some Open Questions Related to Cuckoo Hashing

Abstract: Abstract. The purpose of this brief note is to describe recent work in the area of cuckoo hashing, including a clear description of several open problems, with the hope of spurring further research.

Cited by 29 publications

References 37 publications

Peeling arguments and double hashing

Peeling arguments and double hashing

The ZCache: Decoupling Ways and Associativity

On the insertion time of random walk cuckoo hashing

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