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The author completed this work in 2017. It was recognized with University Research Honors in 2018.


Symmetry occurs in many constraint satisfaction problems, and it is important to deal with it efficiently and effectively, as it often leads to an exponential number of isomorphic assignments. Symmetric rows and columns in matrices are an important class of symmetries in constraint programming. In this work, we develop a new SAT encoding for partial lexicographical ordering constraints to break symmetries in such places. We also survey all the previous complete lex-leader encodings in literature and translate them into SAT encodings. We perform experimental analysis on how these lex-leader constraints impact the solving of Balanced Incomplete Block Design (BIBD) instances. Each encoding is able to outperform the other encodings on some instances, and they all perform close to each other; no clear winner can be drawn. Finally, the result shows that though using any lex-leader constraints is detrimental to finding a single BIBD, they are necessary in enumerating all BIBDs and proving non-existing designs.


Computer Sciences