We introduce a new class of functions that can be minimized in polynomial time in the value oracle model. These are functions f satisfying f(x) + f(y) ≥ f(x ∏ y) + f(x ∐ y) where the domain of each variable x i corresponds to nodes of a rooted binary tree, and operations ∏,∐ are defined with respect to this tree. Special cases include previously studied L-convex and bisubmodular functions, which can be obtained with particular choices of trees. We present a polynomial-time algorithm for minimizing functions in the new class. It combines Murota's steepest descent algorithm for L-convex functions with bisubmodular minimization algorithms. © 2011 Springer-Verlag GmbH.
CITATION STYLE
Kolmogorov, V. (2011). Submodularity on a tree: Unifying L-convex and bisubmodular functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6907 LNCS, pp. 400–411). https://doi.org/10.1007/978-3-642-22993-0_37
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