Abstract
A major issue in software maintenance is change propagation. A software engineer should be able to assess the impact of a change in a software system, so that the effort to accomplish the maintenance may be properly estimated. We define a novel model, named K3B, for estimating change propagation impact. The model aims to predict how far a set of changes will propagate throughout the system. K3B is a stochastic model that has input parameters about the system and the number of modules which will be initially changed. K3B returns the estimated number of change steps, considering that a module may be changed more than once during a modification process. We provide the implementation of K3B for object-oriented programs. We compare our implementation with data from an artificial scenario, given by simulation, as well as with data from a real scenario, given by historical data. We found strong correlation between the results given by K3B and the results observed in the simulation, as well as with historical data of change propagation. K3B may be used for comparing software systems from the viewpoint of change impact. The model may aid software engineers in allocating proper resources to the maintenance tasks.
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Notes
The formula was defined based on the resultant polynomials for n 𝜖{4, 5, 6,..., 11, 20, 25}. Analyzing data for values of n > 25 manually was not viable.
Our implementation of K3B was introduced in Connecta Project and it is available in http://homepages.dcc.ufmg.br/~kecia/connecta.htm.
Geipel and Schweitzer (2012) have found that the probability that two interconnected classes have been modified together is at least once is 0.33, with a standard deviation of 0.12. The weights we used in our study are near to those.
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The authors would like to thank FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais, which has sponsored Bárbara M. Gomes (CEFET-MG) and Luiz F. O. Mendes (UFMG) as undergraduated students.
Appendix A: The expressions obtained
Appendix A: The expressions obtained
This appendix shows the expressions obtained for number of modules from 4 to 7. The symbol a corresponds to the parameters α ϕ, whereas b corresponds to β, respectively.
4 modules
\( \left [ \begin {array}{c} 1+6\,{\dfrac {a}{b}}+12\,{\dfrac {{a}^{2}}{{b}^{2}}}+12\,{\frac {{a}^{3}}{{b}^{3}}}\\[-2pt] 2+10\,{\dfrac {a}{b}}+16\,{\dfrac {{a}^{2}}{{b}^{2}}}+12\,{\frac {{a}^{3}}{{b}^{3}}}\\[-2pt] 3+12\,{\dfrac {a}{b}}+16\,{\dfrac {{a}^{2}}{{b}^{2}}}+12\,{\frac {{a}^{3}}{{b}^{3}}}\\[-2pt] 4+12\,{\dfrac {a}{b}}+16\,{\dfrac {{a}^{2}}{{b}^{2}}}+12\,{\dfrac {{a}^{3}}{{b}^{3}}} \end {array} \right ] \)
5 modules
\( \left [ \begin {array}{c} 1+8\,{\dfrac {a}{b}}+24\,{\dfrac {{a}^{2}}{{b}^{2}}}+48\,{\dfrac {{a}^{3}}{{b}^{3}}}+48\,{\dfrac {{a}^{4}}{{b}^{4}}}\\\noalign {}2+14\,{\dfrac {a}{b}}+36\,{\dfrac {{a}^{2}}{{b}^{2}}}+60\,{\dfrac {{a}^{3}}{{b}^{3}}}+48\,{\dfrac {{a}^{4}}{{b}^{4}}}\\\noalign {}3+18\,{\dfrac {a}{b}}+40\,{\dfrac {{a}^{2}}{{b}^{2}}}+60\,{\dfrac {{a}^{3}}{{b}^{3}}}+48\,{\dfrac {{a}^{4}}{{b}^{4}}}\\\noalign {}4+20\,{\dfrac {a}{b}}+40\,{\dfrac {{a}^{2}}{{b}^{2}}}+60\,{\dfrac {{a}^{3}}{{b}^{3}}}+48\,{\dfrac {{a}^{4}}{{b}^{4}}}\\\noalign {}5+20\,{\dfrac {a}{b}}+40\,{\dfrac {{a}^{2}}{{b}^{2}}}+60\,{\dfrac {{a}^{3}}{{b}^{3}}}+48\,{\dfrac {{a}^{4}}{{b}^{4}}}\end {array} \right ] \)
6 modules
\( \left [ \begin {array}{c} 1+10\,{\dfrac {a}{b}}+40\,{\dfrac {{a}^{2}}{{b}^{2}}}+120\,{\dfrac {{a}^{3}}{{b}^{3}}}+240\,{\dfrac {{a}^{4}}{{b}^{4}}}+240\,{\dfrac {{a}^{5}}{{b}^{5}}}\\\noalign {}2+18\,{\dfrac {a}{b}}+64\,{\dfrac {{a}^{2}}{{b}^{2}}}+168\,{\dfrac {{a}^{3}}{{b}^{3}}}+288\,{\dfrac {{a}^{4}}{{b}^{4}}}+240\,{\dfrac {{a}^{5}}{{b}^{5}}}\\\noalign {}3+24\,{\dfrac {a}{b}}+76\,{\dfrac {{a}^{2}}{{b}^{2}}}+180\,{\dfrac {{a}^{3}}{{b}^{3}}}+288\,{\dfrac {{a}^{4}}{{b}^{4}}}+240\,{\dfrac {{a}^{5}}{{b}^{5}}}\\\noalign {}4+28\,{\dfrac {a}{b}}+80\,{\dfrac {{a}^{2}}{{b}^{2}}}+180\,{\dfrac {{a}^{3}}{{b}^{3}}}+288\,{\dfrac {{a}^{4}}{{b}^{4}}}+240\,{\dfrac {{a}^{5}}{{b}^{5}}}\\\noalign {}5+30\,{\dfrac {a}{b}}+80\,{\dfrac {{a}^{2}}{{b}^{2}}}+180\,{\dfrac {{a}^{3}}{{b}^{3}}}+288\,{\dfrac {{a}^{4}}{{b}^{4}}}+240\,{\dfrac {{a}^{5}}{{b}^{5}}}\\\noalign {}6+30\,{\dfrac {a}{b}}+80\,{\dfrac {{a}^{2}}{{b}^{2}}}+180\,{\dfrac {{a}^{3}}{{b}^{3}}}+288\,{\dfrac {{a}^{4}}{{b}^{4}}}+240\,{\dfrac {{a}^{5}}{{b}^{5}}}\end {array} \right ] \)
7 modules
\( \left [ \begin {array}{c} 1+12\,{\dfrac {a}{b}}+60\,{\dfrac {{a}^{2}}{{b}^{2}}}+240\,{\dfrac {{a}^{3}}{{b}^{3}}}+720\,{\dfrac {{a}^{4}}{{b}^{4}}}+1440\,{\dfrac {{a}^{5}}{{b}^{5}}}+1440\,{\dfrac {{a}^{6}}{{b}^{6}}}\\\noalign {}2+22\,{\dfrac {a}{b}}+100\,{\dfrac {{a}^{2}}{{b}^{2}}}+360\,{\dfrac {{a}^{3}}{{b}^{3}}}+960\,{\dfrac {{a}^{4}}{{b}^{4}}}+1680\,{\dfrac {{a}^{5}}{{b}^{5}}}+1440\,{\dfrac {{a}^{6}}{{b}^{6}}}\\\noalign {}3+30\,{\dfrac {a}{b}}+124\,{\dfrac {{a}^{2}}{{b}^{2}}}+408\,{\dfrac {{a}^{3}}{{b}^{3}}}+1008\,{\dfrac {{a}^{4}}{{b}^{4}}}+1680\,{\dfrac {{a}^{5}}{{b}^{5}}}+1440\,{\dfrac {{a}^{6}}{{b}^{6}}}\\\noalign {}4+36\,{\dfrac {a}{b}}+136\,{\dfrac {{a}^{2}}{{b}^{2}}}+420\,{\dfrac {{a}^{3}}{{b}^{3}}}+1008\,{\dfrac {{a}^{4}}{{b}^{4}}}+1680\,{\dfrac {{a}^{5}}{{b}^{5}}}+1440\,{\dfrac {{a}^{6}}{{b}^{6}}}\\\noalign {}5+40\,{\dfrac {a}{b}}+140\,{\dfrac {{a}^{2}}{{b}^{2}}}+420\,{\dfrac {{a}^{3}}{{b}^{3}}}+1008\,{\dfrac {{a}^{4}}{{b}^{4}}}+1680\,{\dfrac {{a}^{5}}{{b}^{5}}}+1440\,{\dfrac {{a}^{6}}{{b}^{6}}}\\\noalign {}6+42\,{\dfrac {a}{b}}+140\,{\dfrac {{a}^{2}}{{b}^{2}}}+420\,{\dfrac {{a}^{3}}{{b}^{3}}}+1008\,{\dfrac {{a}^{4}}{{b}^{4}}}+1680\,{\dfrac {{a}^{5}}{{b}^{5}}}+1440\,{\dfrac {{a}^{6}}{{b}^{6}}}\\\noalign {}7+42\,{\dfrac {a}{b}}+140\,{\dfrac {{a}^{2}}{{b}^{2}}}+420\,{\dfrac {{a}^{3}}{{b}^{3}}}+1008\,{\dfrac {{a}^{4}}{{b}^{4}}}+1680\,{\dfrac {{a}^{5}}{{b}^{5}}}+1440\,{\dfrac {{a}^{6}}{{b}^{6}}}\end {array} \right ] \)
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M. Ferreira, K.A., S. Bigonha, M.A., S. Bigonha, R. et al. A model for estimating change propagation in software. Software Qual J 26, 217–248 (2018). https://doi.org/10.1007/s11219-017-9358-6
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DOI: https://doi.org/10.1007/s11219-017-9358-6