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The software system under test can be modeled as a graph comprising of a setof vertices, (V) and a set of edges, (E). Test Cases are Test Paths over thegraph meeting a particular test criterion. In this paper, we present a methodto achieve the minimum number of Test Paths needed to cover differentstructural coverage criteria. Our method can accommodate Prime Path, Edge-Pair,Simple & Complete Round Trip, Edge and Node coverage criteria. Our methodobtains the optimal solution by transforming the graph into a flow graph andsolving the minimum flow problem. We present an algorithm for the minimum flowproblem that matches the best known solution complexity of $O(|V| |E|)$. Ourmethod is evaluated through two sets of tests. In the first, we test againstgraphs representing actual software. In the second test, we create randomgraphs of varying complexity. In each test we measure the number of Test Paths,the length of Test Paths, the lower bound on minimum number of Test Paths andthe execution time.

Minimum Number of Test Paths for Prime Path and other Structural Coverage Criteria