Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence-Invariant Algebraic Provenance for Hyperplane Update Queries   The algebraic approach for provenance tracking, originating in the semiring
model of Green et. al, has proven useful as an abstract way of handling
metadata. Commutative Semirings were shown to be the "correct" algebraic
structure for Union of Conjunctive Queries, in the sense that its use allows
provenance to be invariant under certain expected query equivalence axioms.
  In this paper we present the first (to our knowledge) algebraic provenance
model, for a fragment of update queries, that is invariant under set
equivalence. The fragment that we focus on is that of hyperplane queries,
previously studied in multiple lines of work. Our algebraic provenance
structure and corresponding provenance-aware semantics are based on the sound
and complete axiomatization of Karabeg and Vianu. We demonstrate that our
construction can guide the design of concrete provenance model instances for
different applications. We further study the efficient generation and storage
of provenance for hyperplane update queries. We show that a naive algorithm can
lead to an exponentially large provenance expression, but remedy this by
presenting a normal form which we show may be efficiently computed alongside
query evaluation. We experimentally study the performance of our solution and
demonstrate its scalability and usefulness, and in particular the effectiveness
of our normal form representation.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio