Theoretical analysis of git bisect - Archive ouverte HAL
Article Dans Une Revue Algorithmica Année : 2023

Theoretical analysis of git bisect

Résumé

In this paper, we consider the problem of finding a regression in a version control system (VCS), such as \texttt{git}. The set of versions is modelled by a Directed Acyclic Graph (DAG) where vertices represent versions of the software, and arcs are the changes between different versions. We assume that somewhere in the DAG, a bug was introduced, which persists in all of its subsequent versions. It is possible to query a vertex to check whether the corresponding version carries the bug. Given a DAG and a bugged vertex, the Regression Search Problem consists in finding the first vertex containing the bug in a minimum number of queries in the worst-case scenario. This problem is known to be NP-complete. We study the algorithm used in \texttt{git} to address this problem, known as \texttt{git bisect}. We prove that in a general setting, \texttt{git bisect} can use an exponentially larger number of queries than an optimal algorithm. We also consider the restriction where all vertices have indegree at most 2 (i.e. where merges are made between at most two branches at a time in the VCS), and prove that in this case, \texttt{git bisect} is a $\frac{1}{\log_2(3/2)}$-approximation algorithm, and that this bound is tight. We also provide a better approximation algorithm for this case. Finally, we give an alternative proof of the NP-completeness of the Regression Search Problem, via a variation with bounded indegree.
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Dates et versions

hal-04354327 , version 1 (19-12-2023)
hal-04354327 , version 2 (02-10-2024)

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Julien Courtiel, Paul Dorbec, Romain Lecoq. Theoretical analysis of git bisect. Algorithmica, In press, ⟨10.1007/s00453-023-01194-0⟩. ⟨hal-04354327v1⟩
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