Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Automatic Clustering of Software Systems Using a Genetic Algorithm
STEP '99 Proceedings of the Software Technology and Engineering Practice
Bunch: A Clustering Tool for the Recovery and Maintenance of Software System Structures
ICSM '99 Proceedings of the IEEE International Conference on Software Maintenance
A heuristic search approach to solving the software clustering problem
A heuristic search approach to solving the software clustering problem
Clustering of Software Systems Using New Hybrid Algorithms
CIT '09 Proceedings of the 2009 Ninth IEEE International Conference on Computer and Information Technology - Volume 02
Software Module Clustering as a Multi-Objective Search Problem
IEEE Transactions on Software Engineering
On the NP-Completeness of some graph cluster measures
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Computer Science Review
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The clustering problem has an important application in software engineering, which usually deals with large software systems with complex structures. To facilitate the work of software maintainers, components of the system are divided into groups in such a way that the groups formed contain highly-interdependent modules and the independent modules are placed in different groups. The measure used to analyze the quality of the system partition is called Modularization Quality (MQ). Designers represent the software system as a graph where modules are represented by nodes and relationships between modules are represented by edges. This graph is referred in the literature as Module Dependency Graph (MDG). The Software Clustering Problem (SCP) consists in finding the partition of the MDG that maximizes the MQ.In this paper we present three new mathematical programming formulations for the SCP. Firstly, we formulate the SCP as a sum of linear fractional functions problem and then we apply two different linearization procedures to reformulate the problem as Mixed-Integer Linear Programming (MILP) problems. We discuss a preprocessing technique that reduces the size of the original problem and develop valid inequalities that have been shown to be very effective in tightening the formulations. We present numerical results that compare the formulations proposed and compare our results with the solutions obtained by the exhaustive algorithm supported by the freely available Bunch clustering tool, for benchmark problems.