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Identifying time periods with a burst of activities related to a topic has been an important problem in analyzing time-stamped documents. In this paper, we propose an approach to extract a hot spot of a given topic in a time-stamped document set. Topics can be basic, containing a simple list of keywords, or complex. Logical relationships such as and, or, and not are used to build complex topics from basic topics. A concept of presence measure of a topic based on fuzzy set theory is introduced to compute the amount of information related to the topic in the document set. Each interval in the time period of the document set is associated with a numeric value which we call the discrepancy score. A high discrepancy score indicates that the documents in the time interval are more focused on the topic than those outside of the time interval. A hot spot of a given topic is defined as a time interval with the highest discrepancy score. We first describe a naive implementation for extracting hot spots. We then construct an algorithm called EHE (Efficient Hot Spot Extraction) using several efficient strategies to improve performance. We also introduce the notion of a topic DAG to facilitate an efficient computation of presence measures of complex topics. The proposed approach is illustrated by several experiments on a subset of the TDT-Pilot Corpus and DBLP conference data set. The experiments show that the proposed EHE algorithm significantly outperforms the naive one, and the extracted hot spots of given topics are meaningful.