A data structure A is said to be dynamically optimal over a class of data structures C if A is constant- competitive with every data structure C ∈ C. Much of the research on binary search trees in the past forty years has focused on studying dynamic optimality over the class of binary search trees that are modified via rotations (and indeed, the question of whether splay trees are dynamically optimal has gained notoriety as the so-called dynamic-optimality conjecture). Recently, researchers have extended this to consider dynamic optimality over certain classes of external-memory search trees. In particular, Demaine, Iacono, Koumoutsos, and Langerman propose a class of external-memory trees that support a notion of tree rotations, and then give an elegant data structure, called the Belga B-tree, that is within an O(log log N )-factor of being dynamically optimal over this class. In this paper, we revisit the question of how dynamic optimality should be defined in external memory. A defining characteristic of external-memory data structures is that there is a stark asymmetry between queries and inserts/updates/deletes: by making the former slightly asymptotically slower, one can make the latter significantly asymptotically faster (even allowing for operations with sub-constant amortized I/Os). Thismore »
The LSM RUM-Tree: A Log Structured Merge R-Tree for Update-intensive Spatial Workloads
Many applications require update-intensive work-loads on spatial objects, e.g., social-network services and shared-riding services that track moving objects (devices). By buffering insert and delete operations in memory, the Log Structured Merge Tree (LSM) has been used widely in various systems because of its ability to handle insert-intensive workloads. While the focus on LSM has been on key-value stores and their optimizations, there is a need to study how to efficiently support LSM-based secondary indexes. We investigate the augmentation of a main-memory-based memo structure into an LSM secondary index structure to handle update-intensive workloads efficiently. We conduct this study in the context of an R-tree-based secondary index. In particular, we introduce the LSM RUM-tree that demonstrates the use of an Update Memo in an LSM-based R-tree to enhance the performance of the R-tree's insert, delete, update, and search operations. The LSM RUM-tree introduces novel strategies to reduce the size of the Update Memo to be a light-weight in-memory structure that is suitable for handling update-intensive workloads without introducing significant over-head. Experimental results using real spatial data demonstrate that the LSM RUM-tree achieves up to 9.6x speedup on update operations and up to 2400x speedup on query processing over the existing LSM more »
- Publication Date:
- NSF-PAR ID:
- 10301807
- Journal Name:
- 2021 IEEE 37th International Conference on Data Engineering (ICDE)
- Page Range or eLocation-ID:
- 2285 to 2290
- Sponsoring Org:
- National Science Foundation
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Multicopy search structures such as log-structured merge (LSM) trees are optimized for high insert/update/delete (collectively known as upsert) performance. In such data structures, an upsert on key k , which adds ( k , v ) where v can be a value or a tombstone, is added to the root node even if k is already present in other nodes. Thus there may be multiple copies of k in the search structure. A search on k aims to return the value associated with the most recent upsert. We present a general framework for verifying linearizability of concurrent multicopy search structures that abstracts from the underlying representation of the data structure in memory, enabling proof-reuse across diverse implementations. Based on our framework, we propose template algorithms for (a) LSM structures forming arbitrary directed acyclic graphs and (b) differential file structures, and formally verify these templates in the concurrent separation logic Iris. We also instantiate the LSM template to obtain the first verified concurrent in-memory LSM tree implementation.
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Big spatial data has become ubiquitous, from mobile applications to satellite data. In most of these applications, data is continuously growing to huge volumes. Existing systems for big spatial data organize records at either the record-level or block-level. Systems that use record-level structures include key-value stores and LSM-Tree stores, which support insert and delete operations and they are optimized for highly-selective queries. On the other hand, systems like GeoSpark that use block-level structures (e.g. 128 MB each) are more efficient for analytical queries, but they cannot incrementally maintain the partitioned data and do not support delete operations. This paper proposes a general framework that enables block-level systems to incrementally maintain spatial partitions, in the presence of bulk insertions and deletions, in distributed file system (DFS) blocks. We first formally study the incremental spatial partitioning problem for big data and demonstrate its NP-hardness. Then, we propose a cost model to estimate the performance of queries on the partitioned data and the effect of modifying it as the data grows. After that, we provide three different implementations of the incremental partitioning framework. Comprehensive experiments on large real datasets show that our proposed partitioning algorithms outperforms state-of-the-art spatial partitioning methods.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1109/ICDE51399.2021.00238
