Adopting Metamorphic Relations to Verify Non-Testable Graph theory Algorithms

Test oracles are playing a vital role in automated software testing to determine whether the test cases are succeeded or not. Designing the test cases become rigid in some areas of application testing due to the complexity and unavailability. Metamorphic testing emerged as an alternate to alleviate the test oracle problems in testing, by implementing metamorphic relations instead of test oracles. Many researchers were applied metamorphic testing to various real time applications like Machine Learning, bioinformatics, Network simulations, Computer graphics and compilers to overcome the test oracle problem and to feasible result verification. Graph Theory is a prominent non-numeric technology of mathematics and widely used in many gaming and other real time applications. Testing and verifying these combinatorial graph theory applications with test oracle is a very expensive and inaccurate process under many circumstances. In this paper we proposed metamorphic testing to address the problems of testing graph theory applications. This process employs the metamorphic relations of graph theory to simplify testing and alleviates the expensive test oracle utilization. Our case studies on shortest path and minimal spanning tree testing explains the applicability and advantages of metamorphic relations in the area of graph theory in detail.