40,719 research outputs found
Faster Query Answering in Probabilistic Databases using Read-Once Functions
A boolean expression is in read-once form if each of its variables appears
exactly once. When the variables denote independent events in a probability
space, the probability of the event denoted by the whole expression in
read-once form can be computed in polynomial time (whereas the general problem
for arbitrary expressions is #P-complete). Known approaches to checking
read-once property seem to require putting these expressions in disjunctive
normal form. In this paper, we tell a better story for a large subclass of
boolean event expressions: those that are generated by conjunctive queries
without self-joins and on tuple-independent probabilistic databases. We first
show that given a tuple-independent representation and the provenance graph of
an SPJ query plan without self-joins, we can, without using the DNF of a result
event expression, efficiently compute its co-occurrence graph. From this, the
read-once form can already, if it exists, be computed efficiently using
existing techniques. Our second and key contribution is a complete, efficient,
and simple to implement algorithm for computing the read-once forms (whenever
they exist) directly, using a new concept, that of co-table graph, which can be
significantly smaller than the co-occurrence graph.Comment: Accepted in ICDT 201
Competitive Boolean Function Evaluation: Beyond Monotonicity, and the Symmetric Case
We study the extremal competitive ratio of Boolean function evaluation. We
provide the first non-trivial lower and upper bounds for classes of Boolean
functions which are not included in the class of monotone Boolean functions.
For the particular case of symmetric functions our bounds are matching and we
exactly characterize the best possible competitiveness achievable by a
deterministic algorithm. Our upper bound is obtained by a simple polynomial
time algorithm.Comment: 15 pages, 1 figure, to appear in Discrete Applied Mathematic
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