Theoretical Analysis of Git Bisect
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 some...
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| Published in | Algorithmica Vol. 86; no. 5; pp. 1365 - 1399 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.05.2024
Springer Nature B.V Springer Verlag |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0178-4617 1611-3349 0302-9743 1432-0541 |
| DOI | 10.1007/s00453-023-01194-0 |
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| Abstract | 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. |
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| AbstractList | 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. 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 1log2(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. 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 $\frac{1}{\log_2(3/2)}$-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. |
| Author | Lecoq, Romain Dorbec, Paul Courtiel, Julien |
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| Keywords | Worst-case complexity Approximation algorithm Version control system Regression search Graph algorithm |
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| References | Boissinot, B.: Hg Bisect Mercurial Manpage. https://www.mercurial-scm.org/wiki/BisectExtension Ben-Asher, Y., Farchi, E., Newman, I.: Optimal search in trees (1999). https://doi.org/10.1137/S009753979731858X ToveyCAA simplified np-complete satisfiability problemDiscret. Appl. Math.198481858973960110.1016/0166-218X(84)90081-7 Hyafil, L., Rivest, R.L.: Constructing optimal binary decision trees is NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NP$$\end{document}-complete. Inf. Process. Lett. 5(1), 15–17 (1976/77). https://doi.org/10.1016/0020-0190(76)90095-8 Mozes, S., Onak, K., Weimann, O.: Finding an optimal tree searching strategy in linear time, pp. 1096–1105 (2008) CicaleseFJacobsTLaberESMolinaroMOn the complexity of searching in trees and partially ordered structuresTheor. Comput. Sci.201141268796896289435910.1016/j.tcs.2011.08.042 Onak, K., Parys, P.: Generalization of binary search: searching in trees and forest-like partial orders, pp. 379–388 (2006). https://doi.org/10.1109/FOCS.2006.32 Dereniowski, D., Kosowski, A., Uznański, P.A., Zou, M.: Approximation strategies for generalized binary search in weighted trees 80, 84–14 (2017) CarmoRDonadelliJKohayakawaYLaberESearching in random partially ordered setsTheoret. Comput. Sci.200432114157206740010.1016/j.tcs.2003.06.001 LaberESNogueiraLTOn the hardness of the minimum height decision tree problemDiscret. Appl. Math.20041441–2209212209539410.1016/j.dam.2004.06.002 Couder, C.: Fighting regressions with git bisect (2009). https://git-scm.com/docs/git-bisect-lk2009 ArkinEMMeijerHMitchellJSBRappaportDSkienaSSDecision trees for geometric modelsInt. J. Comput. Geom. Appl.199883343363162548010.1142/S0218195998000175 Bendík, J., Benes, N., Cerna, I.: Finding regressions in projects under version control systems. CoRR (2017) arXiv:1708.06623 AdlerMHeeringaBApproximating optimal binary decision treesAlgorithmica2012623–411121121287114010.1007/s00453-011-9510-9 Emamjomeh-Zadeh, E., Kempe, D., Singhal, V.: Deterministic and probabilistic binary search in graphs, pp. 519–532 (2016). https://doi.org/10.1145/2897518.2897656 CA Tovey (1194_CR15) 1984; 8 1194_CR1 M Adler (1194_CR13) 2012; 62 F Cicalese (1194_CR11) 2011; 412 ES Laber (1194_CR7) 2004; 144 EM Arkin (1194_CR14) 1998; 8 R Carmo (1194_CR2) 2004; 321 1194_CR3 1194_CR12 1194_CR4 1194_CR5 1194_CR6 1194_CR8 1194_CR9 1194_CR10 |
| References_xml | – reference: AdlerMHeeringaBApproximating optimal binary decision treesAlgorithmica2012623–411121121287114010.1007/s00453-011-9510-9 – reference: Boissinot, B.: Hg Bisect Mercurial Manpage. https://www.mercurial-scm.org/wiki/BisectExtension – reference: CarmoRDonadelliJKohayakawaYLaberESearching in random partially ordered setsTheoret. Comput. Sci.200432114157206740010.1016/j.tcs.2003.06.001 – reference: CicaleseFJacobsTLaberESMolinaroMOn the complexity of searching in trees and partially ordered structuresTheor. Comput. Sci.201141268796896289435910.1016/j.tcs.2011.08.042 – reference: Emamjomeh-Zadeh, E., Kempe, D., Singhal, V.: Deterministic and probabilistic binary search in graphs, pp. 519–532 (2016). https://doi.org/10.1145/2897518.2897656 – reference: Mozes, S., Onak, K., Weimann, O.: Finding an optimal tree searching strategy in linear time, pp. 1096–1105 (2008) – reference: Bendík, J., Benes, N., Cerna, I.: Finding regressions in projects under version control systems. CoRR (2017) arXiv:1708.06623 – reference: Ben-Asher, Y., Farchi, E., Newman, I.: Optimal search in trees (1999). https://doi.org/10.1137/S009753979731858X – reference: Onak, K., Parys, P.: Generalization of binary search: searching in trees and forest-like partial orders, pp. 379–388 (2006). https://doi.org/10.1109/FOCS.2006.32 – reference: ArkinEMMeijerHMitchellJSBRappaportDSkienaSSDecision trees for geometric modelsInt. J. Comput. Geom. Appl.199883343363162548010.1142/S0218195998000175 – reference: LaberESNogueiraLTOn the hardness of the minimum height decision tree problemDiscret. Appl. Math.20041441–2209212209539410.1016/j.dam.2004.06.002 – reference: Couder, C.: Fighting regressions with git bisect (2009). https://git-scm.com/docs/git-bisect-lk2009 – reference: Hyafil, L., Rivest, R.L.: Constructing optimal binary decision trees is NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NP$$\end{document}-complete. Inf. Process. Lett. 5(1), 15–17 (1976/77). https://doi.org/10.1016/0020-0190(76)90095-8 – reference: ToveyCAA simplified np-complete satisfiability problemDiscret. Appl. Math.198481858973960110.1016/0166-218X(84)90081-7 – reference: Dereniowski, D., Kosowski, A., Uznański, P.A., Zou, M.: Approximation strategies for generalized binary search in weighted trees 80, 84–14 (2017) – volume: 412 start-page: 6879 year: 2011 ident: 1194_CR11 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2011.08.042 – volume: 62 start-page: 1112 issue: 3–4 year: 2012 ident: 1194_CR13 publication-title: Algorithmica doi: 10.1007/s00453-011-9510-9 – ident: 1194_CR4 doi: 10.1109/FOCS.2006.32 – volume: 144 start-page: 209 issue: 1–2 year: 2004 ident: 1194_CR7 publication-title: Discret. Appl. Math. doi: 10.1016/j.dam.2004.06.002 – ident: 1194_CR6 doi: 10.1016/0020-0190(76)90095-8 – volume: 8 start-page: 343 issue: 3 year: 1998 ident: 1194_CR14 publication-title: Int. J. Comput. Geom. Appl. doi: 10.1142/S0218195998000175 – ident: 1194_CR5 – volume: 321 start-page: 41 issue: 1 year: 2004 ident: 1194_CR2 publication-title: Theoret. Comput. Sci. doi: 10.1016/j.tcs.2003.06.001 – ident: 1194_CR8 – ident: 1194_CR12 – volume: 8 start-page: 85 issue: 1 year: 1984 ident: 1194_CR15 publication-title: Discret. Appl. Math. doi: 10.1016/0166-218X(84)90081-7 – ident: 1194_CR1 – ident: 1194_CR9 doi: 10.1145/2897518.2897656 – ident: 1194_CR3 doi: 10.1137/S009753979731858X – ident: 1194_CR10 doi: 10.5220/0006864401860197 |
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| SubjectTerms | 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 |
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| Title | Theoretical Analysis of Git Bisect |
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