Recognizing the tractability in big data computing

Gao, Xiangyu; Li, Jianzhong; Miao, Dongjing; Liu, Xianmin

doi:10.1016/j.tcs.2020.07.026

Cited by 11 publications

(10 citation statements)

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“…We have shown that PPL is closed under DLOGTIME reduction and defined PPLcompleteness in [9]. However, we did not manage to find the first natural PPLcomplete problem.…”

Section: Complete Problems In Pplmentioning

confidence: 89%

“…In this section, we briefly review the sublinear-time complexity classes introduced in [9] and the basic concepts of reductions.…”

Section: Preliminariesmentioning

confidence: 99%

“…M has a special random access state which, when entered, moves the head of each non-index tape to the cell described by the respective index tape in one step. Based on RATM, a series of pure-sublinear-time complexity classes are proposed in [9] to include problems that are solvable in sublinear time.…”

Section: Preliminariesmentioning

confidence: 99%

“…In the last few years, many complexity classes were proposed to formalize tractable problems in big data computing [8,9,19]. The first attempt was made by Fan et al in 2013 [8], which focuses on tractable boolean query classes with the help of preprocessing.…”

Section: Introductionmentioning

confidence: 99%

“…A year ago, to completely describe the scope of sublinear-time tractable problems, the authors of this paper proposed two categories of sublinear-time complexity classes [9]. One kind characterizes the problems that are directly feasible in sublinear time, while the other describes the problems that are solvable in sublinear time after a PTIME preprocessing.…”

Section: Introductionmentioning

confidence: 99%

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Sublinear-time Reductions for Big Data Computing

Gao¹,

Li²,

Miao³

2021

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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 [9], this paper focuses on sublineartime reductions specialized for problems in big data computing. First, the pseudo-sublinear-time reduction is proposed and the complexity classes P and PsT are proved to be closed under it. To establish PsT-intractability for certain problems in P, we find the first problem in P \ 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 pseudopolylog-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 P-complete, which gives a further direction for identifying PsT-complete problems.

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“…We have shown that PPL is closed under DLOGTIME reduction and defined PPLcompleteness in [9]. However, we did not manage to find the first natural PPLcomplete problem.…”

Section: Complete Problems In Pplmentioning

confidence: 89%

“…In this section, we briefly review the sublinear-time complexity classes introduced in [9] and the basic concepts of reductions.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%