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FastMapSVM for Predicting CSP Satisfiability

Authors Kexin Zheng, Ang Li, Han Zhang, T. K. Satish Kumar

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Author Details

Kexin Zheng
  • University of Southern California, Los Angeles, CA, USA
Ang Li
  • University of Southern California, Los Angeles, CA, USA
Han Zhang
  • University of Southern California, Los Angeles, CA, USA
T. K. Satish Kumar
  • University of Southern California, Los Angeles, CA, USA

Funding

This work at the University of Southern California is supported by DARPA under grant number HR001120C0157 and by NSF under grant number 2112533. The views, opinions, and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the sponsoring organizations, agencies, or the U.S. Government.

Cite AsGet BibTex

Kexin Zheng, Ang Li, Han Zhang, and T. K. Satish Kumar. FastMapSVM for Predicting CSP Satisfiability. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CP.2023.40

Abstract

Recognizing the satisfiability of Constraint Satisfaction Problems (CSPs) is NP-hard. Although several Machine Learning (ML) approaches have attempted this task by casting it as a binary classification problem, they have had only limited success for a variety of challenging reasons. First, the NP-hardness of the task does not make it amenable to straightforward approaches. Second, CSPs come in various forms and sizes while many ML algorithms impose the same form and size on their training and test instances. Third, the representation of a CSP instance is not unique since the variables and their domain values are unordered. In this paper, we propose FastMapSVM, a recently developed ML framework that leverages a distance function between pairs of objects. We define a novel distance function between two CSP instances using maxflow computations. This distance function is well defined for CSPs of different sizes. It is also invariant to the ordering on the variables and their domain values. Therefore, our framework has broader applicability compared to other approaches. We discuss various representational and combinatorial advantages of FastMapSVM. Through experiments, we also show that it outperforms other state-of-the-art ML approaches.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Machine learning
Keywords
  • Constraint Satisfaction Problems
  • Machine Learning
  • FastMapSVM

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References

  1. Abder-Rahman Ali, Micael S Couceiro, Aboul Ella Hassanien, and D Jude Hemanth. Fuzzy c-means based on Minkowski distance for liver CT image segmentation. Intelligent Decision Technologies, 2016. Google Scholar
  2. Alejandro Arbelaez, Youssef Hamadi, and Michele Sebag. Continuous search in constraint programming. In Proceedings of the 22nd IEEE International Conference on Tools with Artificial Intelligence, 2010. Google Scholar
  3. Liron Cohen, Tansel Uras, Shiva Jahangiri, Aliyah Arunasalam, Sven Koenig, and T. K. Satish Kumar. The FastMap algorithm for shortest path computations. In Proceedings of the International Joint Conference on Artificial Intelligence, 2018. Google Scholar
  4. Rina Dechter. Constraint processing. Morgan Kaufmann, 2003. Google Scholar
  5. Christos Faloutsos and King-Ip Lin. FastMap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets. In Proceedings of the ACM SIGMOD International Conference on Management of Data, 1995. Google Scholar
  6. Ian Philip Gent, Christopher Anthony Jefferson, Lars Kotthoff, Ian James Miguel, Neil Charles Armour Moore, Peter Nightingale, and Karen Petrie. Learning when to use lazy learning in constraint solving. In Proceedings of the 19th European Conference on Artificial Intelligence, 2010. Google Scholar
  7. Alessio Guerri and Michela Milano. Learning techniques for automatic algorithm portfolio selection. In Proceedings of the 16th European Conference on Artificial Intelligence, 2004. Google Scholar
  8. Serdar Kadioglu, Yuri Malitsky, Meinolf Sellmann, and Kevin Tierney. ISAC-instance-specific algorithm configuration. In Proceedings of the 19th European Conference on Artificial Intelligence, 2010. Google Scholar
  9. Lars Kotthoff. Algorithm selection for combinatorial search problems: A survey. Data Mining and Constraint Programming: Foundations of a Cross-Disciplinary Approach, 2016. Google Scholar
  10. Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Communications of the ACM, 2017. Google Scholar
  11. Ang Li, Peter Stuckey, Sven Koenig, and T. K. Satish Kumar. A FastMap-based algorithm for block modeling. In Proceedings of the International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, 2022. Google Scholar
  12. Jiaoyang Li, Ariel Felner, Sven Koenig, and T. K. Satish Kumar. Using FastMap to solve graph problems in a Euclidean space. In Proceedings of the International Conference on Automated Planning and Scheduling, 2019. Google Scholar
  13. Eoin O'Mahony, Emmanuel Hebrard, Alan Holland, Conor Nugent, and Barry O'Sullivan. Using case-based reasoning in an algorithm portfolio for constraint solving. In Proceedings of the Irish Conference on Artificial Intelligence and Cognitive Science, 2008. Google Scholar
  14. Arti Patle and Deepak Singh Chouhan. SVM kernel functions for classification. In Proceedings of the International Conference on Advances in Technology and Engineering, 2013. Google Scholar
  15. Luca Pulina and Armando Tacchella. A multi-engine solver for quantified boolean formulas. In Proceedings of the 13th International Conference on Principles and Practice of Constraint Programming, 2007. Google Scholar
  16. Faisal Rahutomo, Teruaki Kitasuka, and Masayoshi Aritsugi. Semantic cosine similarity. In Proceedings of the International Student Conference on Advanced Science and Technology, 2012. Google Scholar
  17. V David Sánchez A. Advanced support vector machines and kernel methods. Neurocomputing, 2003. Google Scholar
  18. Barbara M Smith and Martin E Dyer. Locating the phase transition in binary constraint satisfaction problems. Artificial Intelligence, 1996. Google Scholar
  19. Malcolm White, Kushal Sharma, Ang Li, T. K. Satish Kumar, and Nori Nakata. FastMapSVM: Classifying complex objects using the FastMap algorithm and support-vector machines. arXiv preprint arXiv:2204.05112, 2022. Google Scholar
  20. Hong Xu, Sven Koenig, and T. K. Satish Kumar. Towards effective deep learning for constraint satisfaction problems. In Proceedings of the 24th International Conference on Principles and Practice of Constraint Programming, 2018. Google Scholar
  21. Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? arXiv preprint arXiv:1810.00826, 2018. Google Scholar
  22. Lin Xu, Frank Hutter, Holger H Hoos, and Kevin Leyton-Brown. SATzilla: portfolio-based algorithm selection for SAT. Journal of Artificial Intelligence Research, 2008. Google Scholar
  23. Muhan Zhang, Zhicheng Cui, Marion Neumann, and Yixin Chen. An end-to-end deep learning architecture for graph classification. In Proceedings of the AAAI Conference on Artificial Intelligence, 2018. Google Scholar
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