skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Friday, September 13 until 2:00 AM ET on Saturday, September 14 due to maintenance. We apologize for the inconvenience.


Title: Wormhole: A Fast Ordered Index for In-memory Data Management
In-memory data management systems, such as key-value stores, have become an essential infrastructure in today's big-data processing and cloud computing. They rely on efficient index structures to access data. While unordered indexes, such as hash tables, can perform point search with O(1) time, they cannot be used in many scenarios where range queries must be supported. Many ordered indexes, such as B+ tree and skip list, have a O(log N) lookup cost, where N is number of keys in an index. For an ordered index hosting billions of keys, it may take more than 30 key-comparisons in a lookup, which is an order of magnitude more expensive than that on a hash table. With availability of large memory and fast network in today's data centers, this O(log N) time is taking a heavy toll on applications that rely on ordered indexes. In this paper we introduce a new ordered index structure, named Wormhole, that takes O(log L) worst-case time for looking up a key with a length of L. The low cost is achieved by simultaneously leveraging strengths of three indexing structures, namely hash table, prefix tree, and B+ tree, to orchestrate a single fast ordered index. Wormhole's range operations can be performed by a linear scan of a list after an initial lookup. This improvement of access efficiency does not come at a price of compromised space efficiency. Instead, Wormhole's index space is comparable to those of B+ tree and skip list. Experiment results show that Wormhole outperforms skip list, B+ tree, ART, and Masstree by up to 8.4x, 4.9x, 4.3x, and 6.6x in terms of key lookup throughput, respectively.  more » « less
Award ID(s):
1815303
NSF-PAR ID:
10119147
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
EuroSys '19 Proceedings of the Fourteenth EuroSys Conference 2019
Page Range / eLocation ID:
1 to 16
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. The performance of today's in-memory indexes is bottlenecked by the memory latency/bandwidth wall. Processing-in-memory (PIM) is an emerging approach that potentially mitigates this bottleneck, by enabling low-latency memory access whose aggregate memory bandwidth scales with the number of PIM nodes. There is an inherent tension, however, between minimizing inter-node communication and achieving load balance in PIM systems, in the presence of workload skew. This paper presents PIM-tree , an ordered index for PIM systems that achieves both low communication and high load balance, regardless of the degree of skew in data and queries. Our skew-resistant index is based on a novel division of labor between the host CPU and PIM nodes, which leverages the strengths of each. We introduce push-pull search , which dynamically decides whether to push queries to a PIM-tree node or pull the node's keys back to the CPU based on workload skew. Combined with other PIM-friendly optimizations ( shadow subtrees and chunked skip lists ), our PIM-tree provides high-throughput, (guaranteed) low communication, and (guaranteed) high load balance, for batches of point queries, updates, and range scans. We implement PIM-tree, in addition to prior proposed PIM indexes, on the latest PIM system from UPMEM, with 32 CPU cores and 2048 PIM nodes. On workloads with 500 million keys and batches of 1 million queries, the throughput using PIM-trees is up to 69.7X and 59.1x higher than the two best prior PIM-based methods. As far as we know these are the first implementations of an ordered index on a real PIM system. 
    more » « less
  2. The skip list is an elegant dictionary data structure that is com- monly deployed in RAM. A skip list with N elements supports searches, inserts, and deletes in O(logN) operations with high probability (w.h.p.) and range queries returning K elements in O(log N + K) operations w.h.p. A seemingly natural way to generalize the skip list to external memory with block size B is to “promote” with probability 1/B, rather than 1/2. However, there are practical and theoretical obsta- cles to getting the skip list to retain its efficient performance, space bounds, and high-probability guarantees. We give an external-memory skip list that achieves write- optimized bounds. That is, for 0 < ε < 1, range queries take O(logBε N + K/B) I/Os w.h.p. and insertions and deletions take O((logBε N)/B1−ε) amortized I/Os w.h.p. Our write-optimized skip list inherits the virtue of simplicity from RAM skip lists. Moreover, it matches or beats the asymptotic bounds of prior write-optimized data structures such as Bε trees or LSM trees. These data structures are deployed in high-performance databases and file systems. 
    more » « less
  3. For nearly six decades, the central open question in the study of hash tables has been to determine the optimal achievable tradeoff curve between time and space. State-of-the-art hash tables offer the following guarantee: If keys/values are Θ(logn) bits each, then it is possible to achieve constant-time insertions/deletions/queries while wasting only O(loglogn) bits of space per key when compared to the information-theoretic optimum. Even prior to this bound being achieved, the target of O(log log n) wasted bits per key was known to be a natural end goal, and was proven to be optimal for a number of closely related problems (e.g., stable hashing, dynamic retrieval, and dynamically-resized filters). This paper shows that O(log log n) wasted bits per key is not the end of the line for hashing. In fact, for any k ∈ [log∗ n], it is possible to achieve O(k)-time insertions/deletions, O(1)-time queries, and O(log(k) n) = Ologlog···logn 􏰟 􏰞􏰝 􏰠 k wasted bits per key (all with high probability in n). This means that, each time we increase inser- tion/deletion time by an additive constant, we reduce the wasted bits per key exponentially. We further show that this tradeoff curve is the best achievable by any of a large class of hash tables, including any hash table designed using the current framework for making constant-time hash tables succinct. Our results hold not just for fixed-capacity hash tables, but also for hash tables that are dynamically resized (this is a fundamental departure from what is possible for filters); and for hash tables that store very large keys/values, each of which can be up to no(1) bits (this breaks with the conventional wisdom that larger keys/values should lead to more wasted bits per key). For very small keys/values, we are able to tighten our bounds to o(1) wasted bits per key, even when k = O(1). Building on this, we obtain a constant-time dynamic filter that uses n􏰕logε−1􏰖+nloge+o(n) bits of space for a wide choice of 
    more » « less
  4. Hash tables are a ubiquitous class of dictionary data structures. However, standard hash table implementations do not translate well into the external memory model, because they do not incorporate locality for insertions. Iacono and Pătraşu established an update/query tradeoff curve for external-hash tables: a hash table that performs insertions in O(λ/B) amortized IOs requires Ω(logλ N) expected IOs for queries, where N is the number of items that can be stored in the data structure, B is the size of a memory transfer, M is the size of memory, and λ is a tuning parameter. They provide a complicated hashing data structure, which we call the IP hash table, that meets this curve for λ that is Ω(loglogM +logM N). In this paper, we present a simpler external-memory hash table, the Bundle of Arrays Hash Table (BOA), that is optimal for a narrower range of λ. The simplicity of BOAs allows them to be readily modified to achieve the following results: A new external-memory data structure, the Bundle of Trees Hash Table (BOT), that matches the performance of the IP hash table, while retaining some of the simplicity of the BOAs. The Cache-Oblivious Bundle of Trees Hash Table (COBOT), the first cache-oblivious hash table. This data structure matches the optimality of BOTs and IP hash tables over the same range of λ. 
    more » « less
  5. We present Recipe, a principled approach for converting concurrent DRAM indexes into crash-consistent indexes for persistent memory (PM). The main insight behind Recipe is that isolation provided by a certain class of concurrent in-memory indexes can be translated with small changes to crash-consistency when the same index is used in PM. We present a set of conditions that enable the identification of this class of DRAM indexes, and the actions to be taken to convert each index to be persistent. Based on these conditions and conversion actions, we modify five different DRAM indexes based on B+ trees, tries, radix trees, and hash tables to their crash-consistent PM counterparts. The effort involved in this conversion is minimal, requiring 30--200 lines of code. We evaluated the converted PM indexes on Intel DC Persistent Memory, and found that they outperform state-of-the-art, hand-crafted PM indexes in multi-threaded workloads by up-to 5.2x. For example, we built P-CLHT, our PM implementation of the CLHT hash table by modifying only 30 LOC. When running YCSB workloads, P-CLHT performs up to 2.4x better than Cacheline-Conscious Extendible Hashing (CCEH), the state-of-the-art PM hash table. 
    more » « less