Parikh matching in the streaming model

Authors:
Lap-Kei Lee;Moshe Lewenstein;Qin Zhang
Affiliations:
Department of Computer Science, University of Hong Kong, Hong Kong;Department of Computer Science, Bar-Ilan University, Israel;MADALGO, Aarhus University, Denmark
Venue:
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Year:
2012

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Abstract

Let S be a string over an alphabet Σ={σ1, σ2, …}. A Parikh-mapping maps a substring S′ of S to a |Σ|-length vector that contains, in location i of the vector, the count of σi in S′. Parikh matching refers to the problem of finding all substrings of a text T which match to a given input |Σ|-length count vector. In the streaming model one seeks space-efficient algorithms for problems in which there is one pass over the data. We consider Parikh matching in the streaming model. To make this viable we search for substrings whose Parikh-mappings approximately match the input vector. In this paper we present upper and lower bounds on the problem of approximate Parikh matching in the streaming model.