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A Complementary Column Generation Approach for the Graph Equipartition Problem
Volume 31, Issue 1 (2020), pp. 1–20
Pub. online: 23 March 2020      Type: Research Article      Open accessOpen Access
Received
1 May 2019
Accepted
1 September 2019
Published
23 March 2020

Abstract

This paper investigates the problem of partitioning a complete weighted graph into complete subgraphs, each having the same number of vertices, with the objective of minimizing the sum of edge weights of the resulting subgraphs. This NP-complete problem arises in many applications such as assignment and scheduling-related group partitioning problems and micro-aggregation techniques. In this paper, we present a mathematical programming model and propose a complementary column generation approach to solve the resulting model. A dual based lower bounding feature is also introduced to curtail the notorious tailing-off effects often induced when using column generation methods. Computational results are presented for a wide range of test problems.

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Biographies

Al-Ykoob Salem M.
smalyakoob@gmail.com

S.M. Al-Yakoob is an associate professor at the Department of Mathematics, Kuwait University. His research interests include mathematical programming and optimization with applications to real world problems such as location, transportation, scheduling, and timetabling problems.

Sherali Hanif D.
hanifs@vt.edu

H.D. Sherali is a University Distinguished Professor Emeritus at the Industrial and Systems Engineering Department, Virginia Polytechnic Institute and State University. His areas of research interest are in mathematical optimization modelling, analysis, and design of algorithms for specially structured linear, nonlinear, and continuous and discrete nonconvex programs, with applications to transportation, location, engineering and network design, production, economics, and energy systems. He has published over 351 refereed articles in various operations research journals and has (co-)authored nine books, with a total Google Scholar citation count of over 35,700 and an H-index of 75. He is an elected member of the National Academy of Engineering, a fellow of both INFORMS and IIE, and a member of the Virginia Academy of Science Engineering and Medicine.


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Copyright
© 2020 Vilnius University
Open access article under the CC BY license.

Keywords
graph partitioning column generation complementary column generation mixed-integer programming

Funding
This work was supported by Kuwait University under Research Grant No. [SM03/14].

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