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A test coverage criterion defines a set Er of entities of the program flowgraph and requires that every entity in this set is covered under some test Case. Coverage criteria are also used to measure the adequacy of the executed test cases. In this paper, we introduce the notion of spanning sets of entities for coverage testing. A spanning set is a minimum subset of Er, such that a test suite covering the entities in this subset is guaranteed to cover every entity in Er. When the coverage of an entity always guarantees the coverage of another entity, the former is said to subsume the latter. Based on the subsumption relation between entities, we provide a generic algorithm to find spanning sets for control flow and data flow-based test coverage criteria. We suggest several useful applications of spanning sets: They help reduce and estimate the number of test cases needed to satisfy coverage criteria. We also empirically investigate how the use of spanning sets affects the fault detection effectiveness.