Wear Minimization for Cuckoo Hashing: How Not to Throw a Lot of Eggs into One Basket

Eppstein, David; Goodrich, Michael T.; Mitzenmacher, Michael; Pszona, Paweł

doi:10.1007/978-3-319-07959-2_14

Cited by 13 publications

(18 citation statements)

References 29 publications

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“…In particular, we require that c < 1/(q(q − 1)), which results in an underlying hypergraph that is all trees and unicyclic components with high probability. See [11] for a discussion of and definitions for trees an unicyclic components in the hypergraph.…”

Section: Invertible Bloom Lookup Tablesmentioning

confidence: 99%

Robust Set Reconciliation via Locality Sensitive Hashing

Mitzenmacher

Morgan

2019

Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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We consider variations of set reconciliation problems where two parties, Alice and Bob, each hold a set of points in a metric space, and the goal is for Bob to conclude with a set of points that is close to Alice's set of points in a well-defined way. This setting has been referred to as robust set reconciliation. More specifically, in one variation we examine the goal is for Bob to end with a set of points that is close to Alice's in earth mover's distance, and in another the goal is for Bob to have a point that is close to each of Alice's. The first problem has been studied before; our results scale better with the dimension of the space. The second problem appears new.Our primary novelty is utilizing Invertible Bloom Lookup Tables in combination with locality sensitive hashing. This combination allows us to cope with the geometric setting in a communication-efficient manner.Gap Guarantee model. In the second model, which we introduce, we aim for a stronger guarantee of closeness for every point, and consider the necessary communication. Here Bob's final point set S B will be of the form S B ∪ T A , where T A ⊂ S A includes every point in S A which is at least some chosen distance r 2 from every point in S B . Note that T A is allowed to contain additional points from S A beyond these. That is, Bob is guaranteed that every point in the union of Alice's and Bob's original sets is close to some point in his final set. In order to achieve nontrivial 1 We note that Definition 2 of [7] makes the additional stipulation that S B ⊂ SA ∪SB, however neither our protocol nor the protocol of [7] meet this requirement. Both include points in S B that approximate, without necessarily equaling, points from SA.2 TheÕ here hides log factors of n and log factors of parameters depending on the metric space, in particular |U |.

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Section: Invertible Bloom Lookup Tablesmentioning

confidence: 99%

Robust Set Reconciliation via Locality Sensitive Hashing

Mitzenmacher

Morgan

2019

Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…Prior work [7,21,25,38,39,47] has studied read-write asymmetries in NAND flash memory, but this work has focused on (i) the asymmetric granularity of reads and writes in NAND flash chips: bits can only be cleared by incurring the overhead of erasing a large block of memory, and/or (ii) the asymmetric endurance of reads and writes: individual cells wear out after tens of thousands of writes to the cell. Emerging memories, in contrast, can read and write arbitrary bytes in-place and have many orders of magnitude higher write endurance, enabling system software to readily balance application writes across individual physical cells by adjusting its virtual-to-physical mapping.…”

Section: Related Workmentioning

confidence: 99%

Efficient Algorithms with Asymmetric Read and Write Costs

Blelloch¹,

Fineman²,

Gibbons³

et al. 2015

Preprint

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In several emerging technologies for computer memory (main memory), the cost of reading is significantly cheaper than the cost of writing. Such asymmetry in memory costs poses a fundamentally different model from the RAM for algorithm design. In this paper we study lower and upper bounds for various problems under such asymmetric read and write costs. We consider both the case in which all but O(1) memory has asymmetric cost, and the case of a small cache of symmetric memory. We model both cases using the (M, ω)-ARAM, in which there is a small (symmetric) memory of size M and a large unbounded (asymmetric) memory, both random access, and where reading from the large memory has unit cost, but writing has cost ω 1. For FFT and sorting networks we show a lower bound cost of Ω(ωn log ωM n), which indicates that it is not possible to achieve asymptotic improvements with cheaper reads when ω is bounded by a polynomial in M . Moreover, there is an asymptotic gap (of min(ω, log n)/ log(ωM )) between the cost of sorting networks and comparison sorting in the model. This contrasts with the RAM, and most other models, in which the asymptotic costs are the same. We also show a lower bound for computations on an n × n diamond DAG of Ω(ωn 2 /M ) cost, which indicates no asymptotic improvement is achievable with fast reads. However, we show that for the minimum edit distance problem (and related problems), which would seem to be a diamond DAG, we can beat this lower bound with an algorithm with only O(ωn 2 /(M min(ω 1/3 , M 1/2 ))) cost. To achieve this we make use of a "path sketch" technique that is forbidden in a strict DAG computation. Finally, we show several interesting upper bounds for shortest path problems, minimum spanning trees, and other problems. A common theme in many of the upper bounds is that they require redundant computation and a tradeoff between reads and writes.

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“…1 This trend poses the interesting question of how to design algorithms that are more efficient in the number of writes than in the number of reads. To this end recent works have studied models that account for asymmetric read-write costs and have analyzed a variety of algorithms in these models [8,9,12,13,15,17,24,25,31,38,46,47].…”

Section: Introductionmentioning

confidence: 99%

Implicit Decomposition for Write-Efficient Connectivity Algorithms

Ben-David

Blelloch

Fineman

et al. 2018

2018 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

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The future of main memory appears to lie in the direction of new technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of latency, bandwidth, and energy. Motivated by this trend, we propose sequential and parallel algorithms to solve graph connectivity problems using significantly fewer writes than conventional algorithms. Our primary algorithmic tool is the construction of an o(n)-sized implicit decomposition of a bounded-degree graph G on n nodes, which combined with read-only access to G enables fast answers to connectivity and biconnectivity queries on G. The construction breaks the linear-write "barrier", resulting in costs that are asymptotically lower than conventional algorithms while adding only a modest cost to querying time. For general non-sparse graphs on m edges, we also provide the first o(m) writes and O(m) operations parallel algorithms for connectivity and biconnectivity. These algorithms provide insight into how applications can efficiently process computations on large graphs in systems with read-write asymmetry.

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Wear Minimization for Cuckoo Hashing: How Not to Throw a Lot of Eggs into One Basket

Cited by 13 publications

References 29 publications

Robust Set Reconciliation via Locality Sensitive Hashing

Robust Set Reconciliation via Locality Sensitive Hashing

Efficient Algorithms with Asymmetric Read and Write Costs

Implicit Decomposition for Write-Efficient Connectivity Algorithms

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