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An Abortion Based Search Method for Optimal Coalition Structure Generation

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Abstract

The Coalition Structure Generation (CSG) problem is a partitioning of a set of agents into exhaustive and disjoint subsets to maximize social welfare. This NP-complete problem arises in many practical scenarios. Prominent examples are included in the field of transportation, e-Commerce, distributed sensor networks, and others. The fastest exact algorithm to solve the CSG problem is ODP-IP, which is a hybrid version of two previously established algorithms, namely Improved Dynamic Programming (IDP) and IP. In this paper, we show that the ODP-IP algorithm performs many redundant operations. To improve ODP-IP, we propose a faster abortion mechanism to speed up IP’s search. Our abortion mechanism decides at runtime which of the IP’s operations are redundant to skip them. Then, we propose a modified version of IDP (named MIDP) and an improved version of IP (named IIP). Based on these two improved algorithms, we develop a hybrid version (MIDP-IIP) to solve the CSG problem. After a detailed description of the new algorithm MIDP-IIP, an experimental comparison is conducted against ODP-IP. Our analysis shows that MIDP-IIP performs fewer operations than ODP-IP. In addition, MIDP-IIP reduced significantly many problem instances running times (11–37%).

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Notes

  1. For n agents, we have total \(\Omega ((\frac{n}{\ln n})^n)\) search spaces, that is, the \(n^{th}\) Bell number (Berend and Tassa 2010)

  2. A detailed presentation of IP is proposed in Rahwan et al. (2007).

  3. For the techniques used in IP algorithm in the hybrid ODP-IP algorithm, we recommend readers to refer to the novel techniques to improve IP’s search process using the branch and bound techniques proposed by Michalak et al. (2016).

  4. More details are provided in Michalak et al. (2016).

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Acknowledgements

The research presented in this article is funded by “Visvesvaraya Ph.D. Scheme for Electronics & IT”, Grant No: PhD-MLA/4(29)/2015-16.

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Authors and Affiliations

  1. National Institute of Technology Durgapur, Durgapur, West Bengal, India

    Changder Narayan & Dutta Animesh

  2. LIRIS Lab., Lyon 1 University, Lyon, France

    Aknine Samir

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  1. Changder Narayan
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  2. Aknine Samir
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  3. Dutta Animesh
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Correspondence to Changder Narayan.

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Narayan, C., Samir, A. & Animesh, D. An Abortion Based Search Method for Optimal Coalition Structure Generation. Group Decis Negot 31, 747–768 (2022). https://doi.org/10.1007/s10726-022-09781-2

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