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- W4308171630 abstract "With the rapid popularization of big data, the dichotomy between tractable and intractable problems in big data computing has been shifted. Sublinear time, rather than polynomial time, has recently been regarded as the new standard of tractability in big data computing. This change brings the demand for new methodologies in computational complexity theory in the context of big data. Based on the prior work for sublinear-time complexity classes cite{DBLP:journals/tcs/GaoLML20}, this paper focuses on sublinear-time reductions specialized for problems in big data computing. First, the pseudo-sublinear-time reduction is proposed and the complexity classes Pproblem and PsT are proved to be closed under it. To establish PsT-intractability for certain problems in Pproblem, we find the first problem in $Pproblem setminus PsT$. Using the pseudo-sublinear-time reduction, we prove that the nearest edge query is in PsT but the algebraic equation root problem is not. Then, the pseudo-polylog-time reduction is introduced and the complexity class PsPL is proved to be closed under it. The PsT-completeness under it is regarded as an evidence that some problems can not be solved in polylogarithmic time after a polynomial-time preprocessing, unless PsT = PsPL. We prove that all PsT-complete problems are also Pproblem-complete, which gives a further direction for identifying PsT-complete problems." @default.
- W4308171630 created "2022-11-08" @default.
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- W4308171630 date "2021-11-30" @default.
- W4308171630 modified "2023-09-26" @default.
- W4308171630 title "Sublinear-time Reductions for Big Data Computing" @default.
- W4308171630 doi "https://doi.org/10.48550/arxiv.2111.15330" @default.
- W4308171630 hasPublicationYear "2021" @default.
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