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In this work we propose MementoMap, a flexible and adaptive framework to efficiently summarize holdings of a web archive. We described a simple, yet extensible, file format suitable for MementoMap. We used the complete index of the arquivo.pt comprising 5B mementos (archived web pages/files) to understand the nature and shape of its holdings. We generated MementoMaps with varying amount of detail from its HTML pages that have an HTTP status code of 200 OK. Additionally, we designed a single-pass, memory-efficient, and parallelization-friendly algorithm to compact a large MementoMap into a small one and an in-file binary search method for efficient lookup. We analyzed more than three years of MemGator (a Memento aggregator) logs to understand the response behavior of 14 public web archives. We evaluated MementoMaps by measuring their Accuracy using 3.3M unique URIs from MemGator logs. We found that a MementoMap of less than 1.5% Relative Cost (as compared to the comprehensive listing of all the unique original URIs) can correctly identify the presence or absence of 60% of the lookup URIs in the corresponding archive while maintaining 100% Recall (i.e., zero false negatives).