# Graph-Driven Exploration of Issue Handling Schemes in Software Projects
## 4 Exploring and Assessing Issue Handling Processes
### IHM Analysis Algorithms
#### 4.3.3 Supplementary Algorithms (A3)
Timing features include the delay (SD) to the first comment after the issue registration and the duration of the comment sequence (CD). Deeper analysis is targeted at comment sequence distribution in issues. Here, we use aggregated profiles of comment sequences from three perspectives (global, state, and path), defined as follows:  
\[APC=\{[nc_{i};<ct_{i1},\,ct_{i2},\,\ldots\,ct_{i\bar{\jmath}};n_{i}] \colon i\
i C^{*}\}\mid R, \tag{7a}\] \[APC(S_{r})=\{[nc_{i};<ct_{i1},\,ct_{i2},\,\ldots\,ct_{i\bar{\jmath}};n_{i}] \colon i\
i C(S_{r})^{*}\}\mid R,\] (7b) \[APC(P_{s})=\{[nc_{i};<ct_{i1},\,ct_{i2},\,\ldots\,ct_{i\bar{\jmath}};n_{i}] \colon i\
i C(P_{s})^{*}\}\mid R. \tag{7c}\]  
where \(nc_{i}\) is the number of comments in the i-th sequence, \(<ct_{i1},\,ct_{i2},\,\ldots\,ct_{i\bar{\jmath}}\) is the i-th sequence pattern, with \(ct_{k}\) denoting comment type (\(0<k<j\)), \(ns_{i}\) denotes the number of issues comprising i-th sequence type, and restriction R specifies the considered issue types and observation time range. C, \(C(S_{r})\), and \(C(P_{s})\) denote the set of comment sequences correlated with all considered issues, the sequences generated during issue processing in state \(S_{r}\), and the sequences within the whole issue processing path \(P_{s}\), respectively. The sets \(C^{*}\), \(C(S_{r})^{*}\) and \(C(P_{s})^{*}\) comprise indices which label elements of relevant sets of comment sequences. We can focus on some profile features, e.g., dominant sequences, the distribution of comment categories in sequences, etc. Analyzing comment sequences, it is reasonable to use general comment categories (e.g., questions, information, response) to limit the number of possible structures of sequences. Some illustrations are given in Section 5.3. The considered issue set IS needs to be specified by the project repository and additional filtering features (if needed) related to issue types, priorities, timing ranges, etc. The results of the algorithms are presented in an explicit form (derived sets, graphs, etc.) and multicolumn Excel tables comprising many detailed features which can be used by the analyst for deeper studies based on diverse filtering and correlations. Moreover, the available links to individual issues provide capabilities for deeper studies regarding selected paths to drill down and find explanations for strange processing results, diverse deficiencies in issue documentation, etc. Algorithm 1 provides rich data on issue handling in a well-structured way, and it is the basis for further exploration with Algorithms 2 and 3. The number of considered parameters can be adapted to the further analysis goals. The basic list of parameters involves handling times within states and paths, issue features (type, priority, comment characteristics, reporter activity), etc. This list can be extended to cover other details and adapt to the needs of the considered project and the expert's interests. Diverse aggregated statistics are derived for states and paths derived in Algorithm 2. They cover all considered issues (specified by condition R). Issue flow is characterized by the introduced profiles of state or path load, while the issue handling time statistics cover the minimal, maximal, Q1-Q3 quartiles, and distribution of time ranges correlated with the number of relevant issues. Special attention is devoted to issue processing loops, assessed using Algorithm 3, which provides the loop parameters of loop structure, issue coverage, and timing features. The introduced taxonomy of issue handling paths supported by regular expressions and correlated with statistic features facilitates the identification of project deficiencies, anomalies, and good/bad practices (algorithm A3_P). Path exploration is enhanced with issue comment analysis (A3_C). The capabilities and usefulness of the algorithms are illustrated in relation to the provided analysis results in Section 5.