An improved branch-and-bound method for maximum monomial agreement

Jonathan Eckstein, Noam Goldberg

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The NP-hard maximum monomial agreement problem consists of finding a single logical conjunction that is most consistent with or "best fits" a weighted data set of "positive" and "negative" binary vectors. Computing weighted voting classifiers using boosting methods involves a maximum agreement subproblem at each iteration, although such subproblems are typically solved in practice by heuristic methods. Here, we describe an exact branch-and-bound method for maximum agreement over Boolean monomials, improving on the earlier work of Goldberg and Shan [Goldberg, N., C. Shan. 2007. Boosting optimal logical patterns. Proc. 7th SIAM Internat. Conf. Data Mining, SIAM, Philadelphia, 228-236]. Specifically, we develop a tighter upper bounding function and an improved branching procedure that exploits knowledge of the bound and the particular data set, while having a lower branching factor. Experimental results show that the new method is able to solve larger problem instances and runs faster within a linear programming boosting procedure applied to medium-sized data sets from the UCI Machine Learning Repository. The new algorithm also runs much faster than applying a commercial mixed-integer programming solver, which uses linear programming relaxation-based bounds, to an integer linear programming formulation of the problem.

Original languageEnglish
Pages (from-to)328-341
Number of pages14
JournalINFORMS Journal on Computing
Issue number2
StatePublished - Mar 2012
Externally publishedYes


  • Branch and bound
  • Combinatorial optimization
  • Machine Learning


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