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Cost-based query optimization remains a critical task in relational databases even after decades of research and industrial development. Query optimizers rely on a large range of statistical synopses for accurate cardinality estimation. As the complexity of selections and the number of join predicates increase, two problems arise. First, statistics cannot be incrementally composed to effectively estimate the cost of the sub-plans generated in plan enumeration. Second, small errors are propagated exponentially through joins, which can lead to severely sub-optimal plans. In this paper, we introduce COMPASS, a novel query optimization paradigm for in-memory databases based on a single type of statistics---Fast-AGMS sketches. In COMPASS, query optimization and execution are intertwined. Selection predicates and sketch updates are pushed-down and evaluated online during query optimization. This allows Fast-AGMS sketches to be computed only over the relevant tuples---which enhances cardinality estimation accuracy. Plan enumeration is performed over the query join graph by incrementally composing attribute-level sketches---not by building a separate sketch for every sub-plan. We prototype COMPASS in MapD -- an open-source parallel database -- and perform extensive experiments over the complete JOB benchmark. The results prove that COMPASS generates better execution plans -- both in terms of cardinality and runtime -- compared to four other database systems. Overall, COMPASS achieves a speedup ranging from 1.35X to 11.28X in cumulative query execution time over the considered competitors. Supplementary Material Read me (3448016.3452840_readme.pdf) Download 472.23 KB Source Code (3448016.3452840_source_code.zip) Download 6.94 MB MP4 File (3448016.3452840.mp4) Cost-based query optimization remains a critical task in relational databases even after decades of research and industrial development. Query optimizers rely on a large range of statistical synopses -- including attribute-level histograms and table-level samples -- for accurate cardinality estimation. As the complexity of selection predicates and the number of join predicates increase, two problems arise. First, statistics cannot be incrementally composed to effectively estimate the cost of the sub-plans generated in plan enumeration. Second, small errors are propagated exponentially through joins, which can lead to severely sub-optimal plans. In this paper, we introduce COMPASS, a novel query optimization paradigm for in-memory databases based on a single type of statistics---Fast-AGMS sketches. In COMPASS, query optimization and execution are intertwined. Selection predicates and sketch updates are pushed-down and evaluated online during query optimization. This allows Fast-AGMS sketches to be computed only over the relevant tuples---which enhances cardinality estimation accuracy. Plan enumeration is performed over the query join graph by incrementally composing attribute-level sketches---not by building a separate sketch for every sub-plan.We prototype COMPASS in MapD -- an open-source parallel database -- and perform extensive experiments over the complete JOB benchmark. The results prove the reduced overhead COMPASS incurs, while generating better execution plans -- both in terms of cardinality and runtime -- compared to four other database systems. Overall, COMPASS achieves a speedup ranging from 1.89X to 7.09X in cumulative query execution time over the considered competitors. Moreover, COMPASS is the only optimizer that consistently generates effective plans for complex queries with 10 or more joins.