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 \(\mathrm {PT} \subseteq \mathrm {P}\), \(\sqcap '\mathrm {T^0_Q} \subsetneq \mathrm {PTR^0_Q}\) and \(\mathrm {PT_P} = \mathrm {P}\).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press, Cambridge (2009)
Mix Barrington, D.A., Immerman, N., Straubing, H.: On uniformity within NC1. J. Comput. Syst. Sci. 41(3), 274–306 (1990)
Buss, S.R.: The Boolean formula value problem is in ALOGTIME. In: Nineteenth ACM Symposium on Theory of Computing (1987)
Chazelle, B., Liu, D., Magen, A.: Sublinear geometric algorithms. SIAM J. Comput. 35(3), 627–646 (2005)
Czumaj, A., Sohler, C.: Sublinear-time algorithms. In: Property Testing-current Research & Surveys (2010)
Dowd, M.: Notes on log space representation (1986)
Du, D.-Z., Ko, K.-I.: Theory of Computational Complexity, vol. 58. Wiley, New York (2011)
Fan, W., Geerts, F., Neven, F.: Making queries tractable on big data with preprocessing: (through the eyes of complexity theory). Proc. VLDB Endow. 6(9), 685–696 (2013)
Gao, X., Li, J., Miao, D., Liu, X.: Recognizing the tractability in big data computing (2019)
Greenlaw, R.: Breadth-depth search is \(\cal{P}\)-complete. Parallel Process. Lett. 3(03), 209–222 (1993)
Liu, X., Cai, Z., Miao, D., Li, J.: Tree size reduction with keeping distinguishability. Theor. Comput. Sci. 749, 26–35 (2018)
Miao, D., Cai, Z., Li, J.: On the complexity of bounded view propagation for conjunctive queries. IEEE Trans. Knowl. Data Eng. 30(1), 115–127 (2018)
Miao, D., Cai, Z., Li, Y.: SEF view deletion under bounded condition. Theor. Comput. Sci. 749, 17–25 (2018)
Miao, D., Cai, Z., Jiguo, Y., Li, Y.: Triangle edge deletion on planar glasses-free RGB-digraphs. Theor. Comput. Sci. 788, 2–11 (2019)
Miao, D., Liu, X., Li, J.: On the complexity of sampling query feedback restricted database repair of functional dependency violations. Theor. Comput. Sci. 609, 594–605 (2016)
Miao, D., Liu, X., Li, Y., Li, J.: Vertex cover in conflict graphs. Theor. Comput. Sci. 774, 103–112 (2019)
Rubinfeld, R.: Sublinear time algorithms. Marta Sanz Solé 34(2), 1095–1110 (2011)
Van Leeuwen, J., Leeuwen, J.: Handbook of Theoretical Computer Science, vol. 1. Elsevier, Amsterdam (1990)
Yang, J., Wang, H., Cao, Y.: Tractable queries on big data via preprocessing with logarithmic-size output. Knowl. Inf. Syst. 56(12), 1–23 (2017)
Acknowledgment
This work was supported by the National Natural Science Foundation of China under grants 61732003, 61832003, 61972110 and U1811461.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Gao, X., Li, J., Miao, D., Liu, X. (2019). Recognizing the Tractability in Big Data Computing. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-36412-0_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36411-3
Online ISBN: 978-3-030-36412-0
eBook Packages: Computer ScienceComputer Science (R0)