Theoretical Analysis of Git Bisect

• Published in: Algorithmica Vol. 86; no. 5; pp. 1365 - 1399
• Main Authors: Courtiel, Julien, Dorbec, Paul, Lecoq, Romain
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2024; Springer Nature B.V; Springer Verlag
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Apexes; Approximation; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Algorithms; Data Structures and Information Theory; Discrete Mathematics; Graph theory; Mathematical analysis; Mathematics of Computing; Queries; Regression; Theory of Computation; Version control; Worst-case complexity; Approximation algorithm; Version control system; Regression search; Graph algorithm
• ISSN: 0178-4617; 1611-3349; 0302-9743; 1432-0541
• DOI: 10.1007/s00453-023-01194-0

In this paper, we consider the problem of finding a regression in a version control system (VCS), such as 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 git to address this problem, known as git bisect. We prove that in a general setting, 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, git bisect is a 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.