Interactive proofs of proximity: Delegating computation in sublinear time

We study interactive proofs with sublinear-time verifiers. These proof systems can be used to ensure approximate correctness for the results of computations delegated to an untrusted server. Following the literature on property testing, we seek proof systems where with high probability the verifier accepts every input in the language, and rejects every input that is far from the language. The verifier's query complexity (and computation complexity), as well as the communication, should all be sublinear. We call such a proof system an Interactive Proof of Proximity (IPP). On the positive side, our main result is that all languages in NC have Interactive Proofs of Proximity with roughly √n query and communication and complexities, and polylog(n) communication rounds. This is achieved by identifying a natural language, membership in an affine subspace (for a structured class of subspaces), that is complete for constructing interactive proofs of proximity, and providing efficient protocols for it. In building an IPP for this complete language, we show a tradeoff between the query and communication complexity and the number of rounds. For example, we give a 2-round protocol with roughly $n^{3/4}$ queries and communication. On the negative side, we show that there exist natural languages in $NC^1$, for which the sum of queries and communication in any constant-round interactive proof of proximity must be polynomially related to n. In particular, for any 2-round protocol, the sum of queries and communication must be at least ~Ω(√n). Finally, we construct much better IPPs for specific functions, such as bipartiteness on random or well-mixing graphs, and the majority function. The query complexities of these protocols are provably better (by exponential or polynomial factors) than what is possible in the standard property testing model, i.e. without a prover.Engineering and Applied Science

Making Queries Tractable on Big Data with Preprocessing

A query class is traditionally considered tractable if there exists a polynomial-time (PTIME) algorithm to answer its queries. When it comes to big data, however, PTIME al-gorithms often become infeasible in practice. A traditional and effective approach to coping with this is to preprocess data off-line, so that queries in the class can be subsequently evaluated on the data efficiently. This paper aims to pro-vide a formal foundation for this approach in terms of com-putational complexity. (1) We propose a set of Π-tractable queries, denoted by ΠT0Q, to characterize classes of queries that can be answered in parallel poly-logarithmic time (NC) after PTIME preprocessing. (2) We show that several natu-ral query classes are Π-tractable and are feasible on big data. (3) We also study a set ΠTQ of query classes that can be ef-fectively converted to Π-tractable queries by re-factorizing its data and queries for preprocessing. We introduce a form of NC reductions to characterize such conversions. (4) We show that a natural query class is complete for ΠTQ. (5) We also show that ΠT0Q ⊂ P unless P = NC, i.e., the set ΠT0Q of all Π-tractable queries is properly contained in the set P of all PTIME queries. Nonetheless, ΠTQ = P, i.e., all PTIME query classes can be made Π-tractable via proper re-factorizations. This work is a step towards understanding the tractability of queries in the context of big data. 1

Region-Based Image Retrieval Revisited

Region-based image retrieval (RBIR) technique is revisited. In early attempts at RBIR in the late 90s, researchers found many ways to specify region-based queries and spatial relationships; however, the way to characterize the regions, such as by using color histograms, were very poor at that time. Here, we revisit RBIR by incorporating semantic specification of objects and intuitive specification of spatial relationships. Our contributions are the following. First, to support multiple aspects of semantic object specification (category, instance, and attribute), we propose a multitask CNN feature that allows us to use deep learning technique and to jointly handle multi-aspect object specification. Second, to help users specify spatial relationships among objects in an intuitive way, we propose recommendation techniques of spatial relationships. In particular, by mining the search results, a system can recommend feasible spatial relationships among the objects. The system also can recommend likely spatial relationships by assigned object category names based on language prior. Moreover, object-level inverted indexing supports very fast shortlist generation, and re-ranking based on spatial constraints provides users with instant RBIR experiences.Comment: To appear in ACM Multimedia 2017 (Oral

Query-Based Sampling using Only Snippets

Query-based sampling is a popular approach to model the content of an uncooperative server. It works by sending queries to the server and downloading the returned documents in the search results in full. This sample of documents then represents the server’s content. We present an approach that uses the document snippets as samples instead of downloading entire documents. This yields more stable results at the same amount of bandwidth usage as the full document approach. Additionally, we show that using snippets does not necessarily incur more latency, but can actually save time

Ontology-based semantic interpretation of cylindricity specification in the next-generation GPS

Cylindricity specification is one of the most important geometrical specifications in geometrical product development. This specification can be referenced from the rules and examples in tolerance standards and technical handbooks in practice. These rules and examples are described in the form of natural language, which may cause ambiguities since different designers may have different understandings on a rule or an example. To address the ambiguous problem, a categorical data model of cylindricity specification in the next-generation Geometrical Product Specifications (GPS) was proposed at the University of Huddersfield. The modeling language used in the categorical data model is category language. Even though category language can develop a syntactically correct data model, it is difficult to interpret the semantics of the cylindricity specification explicitly. This paper proposes an ontology-based approach to interpret the semantics of cylindricity specification on the basis of the categorical data model. A scheme for translating the category language to the OWL 2 Web Ontology Language (OWL 2) is presented in this approach. Through such a scheme, the categorical data model is translated into a semantically enriched model, i.e. an OWL 2 ontology for cylindricity specification. This ontology can interpret the semantics of cylindricity specification explicitly. As the benefits of such semantic interpretation, consistency checking, inference procedures and semantic queries can be performed on the OWL 2 ontology. The proposed approach could be easily extended to support the semantic interpretations of other kinds of geometrical specifications