4 research outputs found
Approximate Query Processing over Static Sets and Sliding Windows
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to support approximate versions of the operations rank(i) (i.e., computing sum_{j = i}) queries. We study multiple types of approximations (allowing an error in the query or the result) and present lower bounds and succinct data structures for several variants of the problem. We also extend our model to sliding windows, in which we process a stream of elements and compute suffix sums. This is a generalization of the window summation problem that allows the user to specify the window size at query time. Here, we provide an algorithm that supports updates and queries in constant time while requiring just (1+o(1)) factor more space than the fixed-window summation algorithms
TeAAL: A Declarative Framework for Modeling Sparse Tensor Accelerators
Over the past few years, the explosion in sparse tensor algebra workloads has
led to a corresponding rise in domain-specific accelerators to service them.
Due to the irregularity present in sparse tensors, these accelerators employ a
wide variety of novel solutions to achieve good performance. At the same time,
prior work on design-flexible sparse accelerator modeling does not express this
full range of design features, making it difficult to understand the impact of
each design choice and compare or extend the state-of-the-art.
To address this, we propose TeAAL: a language and compiler for the concise
and precise specification and evaluation of sparse tensor algebra
architectures. We use TeAAL to represent and evaluate four disparate
state-of-the-art accelerators--ExTensor, Gamma, OuterSPACE, and SIGMA--and
verify that it reproduces their performance with high accuracy. Finally, we
demonstrate the potential of TeAAL as a tool for designing new accelerators by
showing how it can be used to speed up Graphicionado--by on BFS and
on SSSP.Comment: 14 pages, 12 figure
Approximate query processing over static sets and sliding windows
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to support approximate versions of the operations rank(i) (i.e., computing ∑ j≤i B[ j]) and select(i) (i.e., finding min{p | rank(p) ≥ i}) queries. We study multiple types of approximations (allowing an error in the query or the result) and present lower bounds and succinct data structures for several variants of the problem. We also extend our model to sliding windows, in which we process a stream of elements and compute suffix sums. This is a generalization of the window summation problem that allows the user to specify the window size at query time. Here, we provide an algorithm that supports updates and queries in constant time while requiring just (1 + o(1)) factor more space than the fixed-window summation algorithm