Set variable is essential for the modelling of some classes of combinatorial problem. It captures more semantics of the problem than finite domain variables, hence lead to better domain reduction during search. Expressing the domain of set variable is not trivial, existing methods either consume too much space, or is difficult to achieve adaquate level of consistency. This line of research tries to remedy these problems by proposing a domain representation (the Length-Lex set representation) that requires small storage space and allows achieving bound consistency effectively. The empirical evaluation shows that Length-Lex is very robust across a number of standard CSP benchmarks.

• Bound Consistency for Binary Length-Lex Set Constraints. Pascal Van Hentenryck, Justin Yip, Carmen Gervet, and Gregoire Dooms. In Twenty-Third AAAI Conference on Artificial Intelligence (AAAI-08), Chicago, July 2008. (pdf)
• Length-Lex Bound Consistency for Knapsack Constraints. Justin Yip, Pascal Van Hentenryck. In ACM SAC 2009, Hawaii, March 2009. (pdf)
• The Evaluation of Length-Lex Set Variables. Justin Yip, Pascal Van Hentenryck. In CP 2009, Lisbon, Sept 2009. (pdf)
• Length-Lex Set Variables (Poster). Justin Yip. In CP 2009 Doctoral Program, Lisbon, Sept 2009. (pdf)
• Boosting Set Constraint Propagation for Network Design. Justin Yip, Pascal Van Hentenryck, Carmen Gervet. In CPAIOR 2010, Bologna, June 2010. (pdf)
• Exponential Propagation for Set Variables. Justin Yip, Pascal Van Hentenryck. In CP 2010, St. Andrews, Sept 2010. (pdf)
• Exponential Propagation for Set-CSPs. Justin Yip, Pascal Van Hentenryck. Constraints, submitted. (pdf)
• Boosting Network Design with Set Constraint Propagation. Justin Yip, Pascal Van Hentenryck, Carmen Gervet. Constraints, submitted. (pdf)

Symmetry breaking plays an important role in complete search. By eliminating symmetric subtrees, the search space can be exponentially reduced. In the problem where both variables and values are interchangeable, given a symmetry breaking constraint, different postings w.r.t different variable partitions orderings greatly affect the search space.

• Model Restarts for Structural Symmetry Breaking Proceedings of the 14th intern. Daniel Heller, Aurojit Panda, Meinolf Sellmann, Justin Yip. Conference on the Principles and Practice of Constraint Programming (CP), Springer LNCS 5202, pp. 539-544, 2008. (pdf)
• Breaking Symmetry of Interchangeable Variables and Values. Y. C. Law, J. H. M. Lee, T. Walsh, and J.Y.K. Yip. In Proceedings of the 13th International Conference of Principles and Practise of Constraint Programming (CP-2007), pp. 423-437, 2007. (pdf)

One picture is worth a thousand words. The internet is flooded with enormous amount of information. Grasping general idea of a lengthy text at a glance is difficult. By performing a lightweight analysis of the wikipedia text of a series of historial events, and a database consist of the information of relationship between different entities over time was constructed. The database was then depicted in a specially designed format to give a big picture of the event. A user studied was performed to evaluate the effectiveness of the visualization approach.

• Cheung Kwok Kuen, Yip Yue Kwen Justin. Making Pictures from Text, Final Year Project of Department of Computer Science and Engineering, The Chinese University of Hong Kong, 2006. (pdf)