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As a fundamental topic in graph mining, Densest Subgraph Discovery (DSD) has found a wide spectrum of real applications. Several DSD algorithms, including exact and approximation algorithms, have been proposed in the literature. However, these algorithms have not been systematically and comprehensively compared under the same experimental settings. In this paper, we first propose a unified framework to incorporate all DSD algorithms from a high-level perspective. We then extensively compare representative DSD algorithms over a range of graphs -- from small to billion-scale -- and examine the effectiveness of all methods. Moreover, we suggest new variants of the DSD algorithms by combining the existing techniques, which are up to 10 X faster than the state-of-the-art algorithm with the same accuracy guarantee. Finally, based on the findings, we offer promising research opportunities. We believe that a deeper understanding of the behavior of existing algorithms can provide new valuable insights for future research. The codes are released at https://anonymous.4open.science/r/DensestSubgraph-245A, Comment: 19pages, 27 figures

A test oracle serves as a criterion or mechanism to assess the correspondence between software output and the anticipated behavior for a given input set. In automated testing, black-box techniques, known for their non-intrusive nature in test oracle construction, are widely used, including notable methodologies like differential testing and metamorphic testing. Inspired by the mathematical concept of inverse function, we present Retromorphic Testing, a novel black-box testing methodology. It leverages an auxiliary program in conjunction with the program under test, which establishes a dual-program structure consisting of a forward program and a backward program. The input data is first processed by the forward program and then its program output is reversed to its original input format using the backward program. In particular, the auxiliary program can operate as either the forward or backward program, leading to different testing modes. The process concludes by examining the relationship between the initial input and the transformed output within the input domain. For example, to test the implementation of the sine function $\sin(x)$, we can employ its inverse function, $\arcsin(x)$, and validate the equation $x = \sin(\arcsin(x)+2k\pi), \forall k \in \mathbb{Z}$. In addition to the high-level concept of Retromorphic Testing, this paper presents its three testing modes with illustrative use cases across diverse programs, including algorithms, traditional software, and AI applications.