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As remarked earlier, quantified pattern matching is (mathsf {DP} -complete for patterns with possibly negated edges, and real-life graphs are often big.
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(1) Using a uniform form of counting quantifiers, quantified patterns support numeric and ratio aggregates (e.g., at least p friends and 80% of friends), and universal (100%) and existential quantification ((ge 1)).
More specifically, the quantified matching problem is (mathsf {DP} -complete for general quantified patterns and (mathsf {DP} -complete for positive quantified patterns.
(mathsf {NP} -complete for positive quantified patterns.
We define quantified patterns to strike a balance between their expressive power and complexity.
(1) Without the restriction, quantified patterns can express first-order logic ((mathsf {FO})) on graphs.
We revise the statement of the graph pattern matching problem given in Sect. 2 for quantified patterns as follows.
As will be seen shortly, the restriction makes discovery and applications of quantified patterns feasible in large-scale graphs.
We quantified patterns of streamflow using probabilities of joint or sequential appearances of the binary symbol sequences.
This study quantified patterns of fish response to flow regime alteration in a sub-tropical region where many rivers have regulated flow regimes but 57% of ecologically relevant flow metrics have changed by <20%.
Few studies have quantified patterns of harvest selection and compare these with associated trait changes over time, especially for multiple stocks of the same species that are differentially harvested.
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