Efficient and Effective Query Auto-Completion

Query Auto-Completion (QAC) is an ubiquitous feature of modern textual search systems, suggesting possible ways of completing the query being typed by the user. Efficiency is crucial to make the system have a real-time responsiveness when operating in the million-scale search space. Prior work has extensively advocated the use of a trie data structure for fast prefix-search operations in compact space. However, searching by prefix has little discovery power in that only completions that are prefixed by the query are returned. This may impact negatively the effectiveness of the QAC system, with a consequent monetary loss for real applications like Web Search Engines and eCommerce. In this work we describe the implementation that empowers a new QAC system at eBay, and discuss its efficiency/effectiveness in relation to other approaches at the state-of-the-art. The solution is based on the combination of an inverted index with succinct data structures, a much less explored direction in the literature. This system is replacing the previous implementation based on Apache SOLR that was not always able to meet the required service-level-agreement.Comment: Published in SIGIR 202

Counting, Fanout, and the Complexity of Quantum ACC

We propose definitions of \QAC^0, the quantum analog of the classical class \AC^0 of constant-depth circuits with AND and OR gates of arbitrary fan-in, and \QACC[q], the analog of the class \ACC[q] where \Mod_q gates are also allowed. We prove that parity or fanout allows us to construct quantum \MOD_q gates in constant depth for any $q$, so \QACC[2] = \QACC. More generally, we show that for any $q,p > 1$, \MOD_q is equivalent to \MOD_p (up to constant depth). This implies that \QAC^0 with unbounded fanout gates, denoted \QACwf^0, is the same as \QACC[q] and \QACC for all $q$. Since \ACC[p] \ne \ACC[q] whenever $p$ and $q$ are distinct primes, \QACC[q] is strictly more powerful than its classical counterpart, as is \QAC^0 when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. We also develop techniques for proving upper bounds for \QACC^0 in terms of related language classes. We define classes of languages \EQACC, \NQACC and \BQACC_{\rats}. We define a notion of $\log$-planar \QACC operators and show the appropriately restricted versions of \EQACC and \NQACC are contained in \P/\poly. We also define a notion of $\log$-gate restricted \QACC operators and show the appropriately restricted versions of \EQACC and \NQACC are contained in \TC^0

Evaluations of series of the qq-Watson, qq-Dixon, and qq-Whipple type

Using $q$-series identities and series rearrangement, we establish several extensions of $q$-Watson formulas with two extra integer parameters. Then they and Sears' transformation formula are utilized to derive some generalizations of $q$-Dixon formulas and $q$-Whipple formulas with two extra integer parameters. As special cases of these results, many interesting evaluations of series of $q$-Watson,$q$-Dixon, and $q$-Whipple type are displayed