Streaming Algorithms for Some Problems in Log-Space

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.[12](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 DLINs: a randomized one pass algorithm that uses O(log n) 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) sp...

• Type: Conference
• Year: 2010
• Where: TAMC
• Authors: Ajesh Babu, Nutan Limaye, Girish Varma
• Keywords: Algorithm, Deterministic, Deterministic Algorithm, TAMC 2010