EnumCC

Efficient Enumeration of Correlation Clustering Optimal Solution Space

• Copyright 2020-21 Nejat Arınık

EnumCC is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation. For source availability and license information see the file LICENCE

• GitHub repo: https://github.com/arinik9/EnumCC
• Contact: Nejat Arınık arinik9@gmail.com

Description

EnumCC is an optimal solution space enumeration method for the Correlation Clustering (CC) problem. It relies on two essential tasks: Recurrent neighborhood search (RNS) and jumping onto an undiscovered solution. The former is performed by the component RNSCC, whereas the latter is done by the commercial solver Cplex.

In the first step, instead of directly jumping onto undiscovered optimal solutions one by one through Cplex, as in a traditional sequential approach, its component RNSCC discovers the recurrent neighborhood of the current optimal solution P with the hope of discovering new optimal solutions. The recurrent neighborhood of an optimal solution P, represents the set of optimal solutions, reached directly or indirectly from P depending on the maximum distance parameter maxNbEdit. Whether a new solution is found or not through RNSCC, the jumping process into a new solution P is performed. If P is not empty, the workflow of RNS and jumping is repeated again. Otherwise, the enumeration process stops. See Chapter 5 of [Arınık'21] for more details.

EnumCC performs the enumeration process based on two different formulation types: 1) decision variables defined on vertex-pair (Fv: "vertex" formulation type) or 2) edge (Fe: "edge" formulation type). If we denote "n" by the number of vertices in the graph and "m" by the number of edges, there are (n(n-1)/2) variables in Fv, whereas there are m variables in Fe.

So, which one would be preferable over the other one? We have not answered this question yet. However, some small experiments show that the resolution method relying on the Fv formulation is in general more efficient, especially if EnumCC needs to perform a large number of "jumps". Because, the resolution method relying on the Fe formulation performs these jumps through lazy callback, and this can worsen the performance.

Another remark of performance issue concerns the "triangleIneqReducedForm" parameter, which concerns only the Fv formulation. See the description of this parameter for more information.

Input parameters

• formulationType: ILP formulation type. Either "vertex" for Fv or "edge" for Fe.

• inFile: Input file path. See in/exemple.G for the input graph format.

• outDir: Output directory path. Default "." (i.e. the current directory).

• initMembershipFilePath: The membership file path, from which the RNSCC starts. It must be an optimal solution of the given signed graph. Moreover, It must be named as membership0.txt or something different than membership.txt. See out/exemple/membership0.txt for its format. This file can be obtained through ExCC by running the script run-cp-bb.sh.

• java.library.path: The Cplex java library path. It is usually found in <YOUR_CPLEX_PATH>/cplex/lib/cplex.jar.

• maxNbEdit The maximum value edit distance value to be considered in edit operations. We show in our experiments that maxNbEdit=3 is usually more appropriate.

• tilim: Time limit in seconds for the whole program.Default -1, which means no time limit.

• solLim Maximum number of optimal solutions to be discovered. This can be useful when there is a huge number of optimal solutions, e.g. 50,000. Default -1.

• JAR_filepath_RNSCC: The jar file path for RNSCC.

• LPFilePath It allows to import a Cplex LP file, corresponding to a ILP formulation of a signed graph for the CC problem. Remark: Such a file is obtained through Cplex by doing exportModel(). This file can be obtained through ExCC by running the script run-cp-bb.sh. In ExCC, the name of this file is *strengthedModelAfterRootRelaxation.lp.

• lazyInBB: Used only for the Fe formulation type. True if adding lazily triangle constraints (i.e. lazy callback approach) is used during the branching phase when trying to find a new optimal solution. Default false.

• userCutInBB: True if adding user cuts during the branching phase is desired, when trying to find a new optimal solution. Based on our experiments, we can say that it does not yield any advantage, and it might even slow down the optimization process. Default false.

• triangleIneqReducedForm : Used only for the Fv formulation type. It requires the knowledge of the user. Because, when it is set to true, this indicates that the parameter "LPFilePath" contains the reduced number ("non-redundant") of triangle inequalities in the formulation. It is important to know this information, because the way the partition information is extracted from an optimal solution is slightly different. This extraction step is explained in [Miyaichi'18]. Default value is false, which keeps the whole set of triangle constraints. It is worth noting that removing redundant triangle inequalities from the ILP formulation can be very beneficial for complete or very dense signed graphs, when enumerating all optimal solutions. See some small experiments conducted in Chapter 2 of [Arınık'21] based on complete random signed networks. However, removing such inequalities from the ILP formulation in sparse signed graphs can substantially worsen the performance of this optimization process. This is because Cplex can find many optimal solutions which actually correspond to a same optimal partition.

Instructions & Use

Use 1

• Install IBM CPlex. The default installation location is: /opt/ibm/ILOG/CPLEX_Studio<YOUR_VERSION>. Tested with Cplex 12.8 and 20.1.
• Put /opt/ibm/ILOG/CPLEX_Studio<YOUR_VERSION>/cplex/lib/cplex.jar into the lib folder in this repository.
• Compile and get the jar file for RNSCC: ant -v -buildfile build-rns.xml compile jar.
• Compile and get the jar file for EnumCC ant -v -buildfile build.xml compile jar.
• We need a starting optimal solution and the ILP model of the given signed graph. We can obtain them by running the script run-cp-bb.sh in the ExCC repository.
• Run the script run.sh.

Use 2

• Put /opt/ibm/ILOG/CPLEX_Studio<YOUR_VERSION>/cplex/lib/cplex.jar into the lib folder in this repository.
• Compile and get the jar file for RNSCC: ant -v -buildfile build-rns.xml compile jar.
• Compile and get the jar file for EnumCC: ant -v -buildfile build.xml compile jar.
• Download the BenchmarkCC repository and put these jar files into the lib folder. Then, run the program for the ExCC and EnumCC(3) methods. See the instructions of the BenchmarkCC repository for more details.

Example command for the Fv formulation:

ant -v -buildfile build.xml compile jar;
ant -v -buildfile build.xml -DformulationType="vertex" -DinFile="in/example.G" -DoutDir="out/example-vertex" -DmaxNbEdit=3 -DinitMembershipFilePath="out/example-vertex/membership0.txt" -DLPFilePath="in/strengthedModel_vertex.lp" -DJAR_filepath_RNSCC="RNSCC.jar" -DnbThread=4 -Dtilim=-1 -DsolLim=5000 -DtriangleIneqReducedForm=false -DlazyCB=false -DuserCutCB=false run

Example command for the Fe formulation:

ant -v -buildfile build.xml compile jar;
ant -v -buildfile build.xml -DformulationType="edge" -DinFile="in/example.G" -DoutDir="out/example-edge" -DmaxNbEdit=3 -DinitMembershipFilePath="out/example-edge/membership0.txt" -DLPFilePath="in/strengthedModel_edge.lp" -DJAR_filepath_RNSCC="RNSCC.jar" -DnbThread=4 -Dtilim=-1 -DsolLim=5000 -DtriangleIneqReducedForm=false -DlazyCB=true -DuserCutCB=false run

Output

• : Folder , where is a numerical value starting from 1. Each folder contains the result of a RNSCC execution and possesses one or multiple optimal solutions.

• allResults.txt File storing all absolute paths of the discovered optimal solutions.

• exec-time.txt Execution time for the whole enumeration process.

• jump-exec-time.txt Execution time for the x.th jumping process through Cplex.

• jump-log.txt Cplex log file regarding the the x.th jumping process.

• jump-status.txt The Cplex status result in the end of the jumoing process. Three values are possible: Optimal, SolLim, Infeasible

• membership.txt The starting membership file for the (x+1).th RNSCC process.

References

• [Arınık'21] N. Arınık, Multiplicity in the Partitioning of Signed Graphs. PhD thesis in Avignon Université (2021).
• [Miyauchi'18] A. Miyauchi, T. Sonobe, and N. Sukegawa, Exact Clustering via Integer Programming and Maximum Satisfiability, in: AAAI Conference on Artificial Intelligence 32.1 (2018).