2,976 research outputs found
Optimal Hierarchical Layouts for Cache-Oblivious Search Trees
This paper proposes a general framework for generating cache-oblivious
layouts for binary search trees. A cache-oblivious layout attempts to minimize
cache misses on any hierarchical memory, independent of the number of memory
levels and attributes at each level such as cache size, line size, and
replacement policy. Recursively partitioning a tree into contiguous subtrees
and prescribing an ordering amongst the subtrees, Hierarchical Layouts
generalize many commonly used layouts for trees such as in-order, pre-order and
breadth-first. They also generalize the various flavors of the van Emde Boas
layout, which have previously been used as cache-oblivious layouts.
Hierarchical Layouts thus unify all previous attempts at deriving layouts for
search trees.
The paper then derives a new locality measure (the Weighted Edge Product)
that mimics the probability of cache misses at multiple levels, and shows that
layouts that reduce this measure perform better. We analyze the various degrees
of freedom in the construction of Hierarchical Layouts, and investigate the
relative effect of each of these decisions in the construction of
cache-oblivious layouts. Optimizing the Weighted Edge Product for complete
binary search trees, we introduce the MinWEP layout, and show that it
outperforms previously used cache-oblivious layouts by almost 20%.Comment: Extended version with proofs added to the appendi
Cache-Oblivious Persistence
Partial persistence is a general transformation that takes a data structure
and allows queries to be executed on any past state of the structure. The
cache-oblivious model is the leading model of a modern multi-level memory
hierarchy.We present the first general transformation for making
cache-oblivious model data structures partially persistent
DeltaTree: A Practical Locality-aware Concurrent Search Tree
As other fundamental programming abstractions in energy-efficient computing,
search trees are expected to support both high parallelism and data locality.
However, existing highly-concurrent search trees such as red-black trees and
AVL trees do not consider data locality while existing locality-aware search
trees such as those based on the van Emde Boas layout (vEB-based trees), poorly
support concurrent (update) operations.
This paper presents DeltaTree, a practical locality-aware concurrent search
tree that combines both locality-optimisation techniques from vEB-based trees
and concurrency-optimisation techniques from non-blocking highly-concurrent
search trees. DeltaTree is a -ary leaf-oriented tree of DeltaNodes in which
each DeltaNode is a size-fixed tree-container with the van Emde Boas layout.
The expected memory transfer costs of DeltaTree's Search, Insert, and Delete
operations are , where are the tree size and the unknown
memory block size in the ideal cache model, respectively. DeltaTree's Search
operation is wait-free, providing prioritised lanes for Search operations, the
dominant operation in search trees. Its Insert and {\em Delete} operations are
non-blocking to other Search, Insert, and Delete operations, but they may be
occasionally blocked by maintenance operations that are sometimes triggered to
keep DeltaTree in good shape. Our experimental evaluation using the latest
implementation of AVL, red-black, and speculation friendly trees from the
Synchrobench benchmark has shown that DeltaTree is up to 5 times faster than
all of the three concurrent search trees for searching operations and up to 1.6
times faster for update operations when the update contention is not too high
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