Paper Info
Title
Recognizing the Tractability in Big Data Computing.
Abstract
Due to the limitation on computational power of existing computers, the polynomial time does not works for identifying the tractable problems in big data computing. This paper adopts the sublinear time as the new tractable standard to recognize the tractability in big data computing, and the random-access Turing machine is used as the computational model to characterize the problems that are tractable on big data. First, two pure-tractable classes are first proposed. One is the class \(\mathrm {PL}\) consisting of the problems that can be solved in polylogarithmic time by a RATM. The another one is the class \(\mathrm {ST}\) including all the problems that can be solved in sublinear time by a RATM. The structure of the two pure-tractable classes is deeply investigated and they are proved \(\mathrm {PL^i} \subsetneq \mathrm {PL^{i+1}}\) and \(\mathrm {PL} \subsetneq \mathrm {ST}\). Then, two pseudo-tractable classes, \(\mathrm {PTR}\) and \(\mathrm {PTE}\), are proposed. \(\mathrm {PTR}\) consists of all the problems that can solved by a RATM in sublinear time after a PTIME preprocessing by reducing the size of input dataset. \(\mathrm {PTE}\) includes all the problems that can solved by a RATM in sublinear time after a PTIME preprocessing by extending the size of input dataset. The relations among the two pseudo-tractable classes and other complexity classes are investigated and they are proved that \(\mathrm {PT} \subseteq \mathrm {P}\), \(\sqcap u0027\mathrm {T^0_Q} \subsetneq \mathrm {PTR^0_Q}\) and \(\mathrm {PT_P} = \mathrm {P}\).
Year
DOI
Venue
2019
10.1007/978-3-030-36412-0_18
COCOA
Field
DocType
Citations 
Complexity class,Sublinear function,Discrete mathematics,Combinatorics,Sublinear time,Computer science,P,Turing machine,Time complexity
Conference
0
PageRank 
References 
Authors
0.34
12
4
Name
Order
Citations
PageRank
Xiangyu Gao111.03
Jianzhong Li23196304.46
Dongjing Miao3189.91
Xianmin Liu400.34