Abstract
In this paper, we give streaming algorithms for some problems which are known to be in deterministic log-space, when the number of passes made on the input is unbounded. If the input data is massive, the conventional deterministic log-space algorithms may not run efficiently. We study the complexity of the problems when the number of passes is bounded.
The first problem we consider is the membership testing problem for deterministic linear languages, DLIN. Extending the recent work of Magniez et al.[11](to appear in STOC 2010), we study the use of fingerprinting technique for this problem. We give the following streaming algorithms for the membership testing of DLIN s: a randomized one pass algorithm that uses O(logn) space (one-sided error, inverse polynomial error probability), and also a p-pass O(n/p)-space deterministic algorithm. We also prove that there exists a language in DLIN, for which any p-pass deterministic algorithm for membership testing, requires Ω(n/p) space. We also study the application of fingerprinting technique to visibly pushdown languages, VPL s.
The other problem we consider is, given a degree sequence and a graph, checking whether the graph has the given degree sequence, Deg-Seq. We prove that, any p-pass deterministic algorithm that takes as its input a degree sequence, followed by an adjacency list of a graph, requires Ω(n/p) space to decide Deg-Seq. However, using randomness, for a more general input format: degree sequence, followed by a list of edges in any arbitrary order, Deg-Seq can be decided in O(logn) space. We also give a p-pass, O(n/p)-space deterministic algorithm for Deg-Seq.
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References
Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. In: STOC 1996: Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, pp. 20–29 (1996)
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC, pp. 202–211 (2004)
Alur, R., Madhusudan, P.: Adding nesting structure to words. J. ACM 56(3) (2009)
Nanongkai, D., Sarma, A.D., Lipton, R.J.: Best-order streaming model. In: Chen, J., Cooper, S.B. (eds.) TAMC 2009. LNCS, vol. 5532, pp. 178–191. Springer, Heidelberg (2009)
Von Braunmühl, B., Verbeek, R.: Input-driven languages are recognized in logn space. In: Karpinski, M. (ed.) FCT 1983. LNCS, vol. 158, pp. 40–51. Springer, Heidelberg (1983)
Dymond, P.W.: Input-driven languages are in logn depth. Information Processing Letters 26, 247–250 (1988)
Feigenbaum, J., Kannan, S., Strauss, M., Viswanathan, M.: Testing and spot-checking of data streams. Algorithmica 34(1), 67–80 (2002)
Holzer, M., Lange, K.-J.: On the complexities of linear LL(1) and LR(1) grammars. In: Ésik, Z. (ed.) FCT 1993. LNCS, vol. 710, pp. 299–308. Springer, Heidelberg (1993)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 3rd edn. Addison-Wesley Longman Publishing Co., Inc., Boston (2006)
Ibarra, O.H., Jiang, T., Ravikumar, B.: Some subclasses of context-free languages in NC 1. Information Processing Letters 29, 111–117 (1988)
Magniez, F., Mathieu, C., Nayak, A.: Recognizing well-parenthesized expressions in the streaming model. In: STOC (2010)
Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL recognition. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 422–432. Springer, Heidelberg (1980)
Motwani, R., Raghavan, P.: Randomized algorithms. ACM Comput. Surv. 28(1), 33–37 (1996)
Muthukrishnan, S.: Data streams: algorithms and applications. In: SODA 2003: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, p. 413 (2003)
Vollmer, H.: Introduction to Circuit Complexity: A Uniform Approach. Springer, New York (1999)
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Babu, A., Limaye, N., Varma, G. (2010). Streaming Algorithms for Some Problems in Log-Space. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_10
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DOI: https://doi.org/10.1007/978-3-642-13562-0_10
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