mathematics, a submodular set function (also known as a submodular function) is a set function that, informally, describes the relationship between a set of inputs...

(strictly) supermodular then f is called (strictly) submodular. A function that is both submodular and supermodular is called modular. This corresponds...

flow out, and have minimum total cost. In submodular flow, as well, one is given a submodular set function on sets of vertices of the graph. Instead of obeying...

naturally model summarization problems are TextRank and PageRank, Submodular set function, Determinantal point process, maximal marginal relevance (MMR)...

mathematics Submodular set function – Set-to-real map with diminishing returns Subadditive set function τ-additivity ba space – The set of bounded charges...

mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values...

submodular set function is subadditive (the family of non-negative submodular functions is strictly contained in the family of subadditive functions)...

may be axiomatized. Matroid rank functions form an important subclass of the submodular set functions. The rank functions of matroids defined from certain...

solve it optimally. A function f {\displaystyle f} defined on subsets of a set Ω {\displaystyle \Omega } is called submodular if for every S , T ⊆ Ω...

of resources Self-organized criticality – Concept in physics Submodular set function – Set-to-real map with diminishing returns Sunk-cost fallacy – Cost...

submodular agent has a utility function that is a submodular set function. This means that the agent's utility has decreasing marginals. Submodular utilities...

a pseudo-Boolean function. The submodular set functions can be viewed as a special class of pseudo-Boolean functions, which is equivalent to the condition...

knapsack problems, interval scheduling, and the optimization of submodular set functions. She is a professor of computer science at the Technion – Israel...

been defined over sets, through a submodular set function which is known as the discrete analog of a convex function. The submodular Bregman divergences...

Theory of Greedy Algorithms Archived 2016-03-04 at the Wayback Machine Submodular Functions and Optimization Matchings, Matroids and Submodular Functions...

{\displaystyle u} is a subadditive set function. Assuming u ( ∅ ) {\displaystyle u(\emptyset )} is non-negative, every submodular function is subadditive. However...

submodular set functions I, Mathematical Programming 14 (1978), 265–294 Hochbaum, Dorit S. (1997). "Approximating Covering and Packing Problems: Set Cover...

In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also a generalization...

_{i}v(T_{i})} . Every submodular set function is XOS, and every XOS function is a subadditive set function. See also: Utility functions on indivisible goods...

game is called submodular if (a) the set of feasible joint decisions is a sublattice; (b) the cost function of each player is submodular and has antitone...

functions on indivisible goods Independent goods Submodular set function Supermodular set function Brandt, Felix; Conitzer, Vincent; Endriss, Ulle; Lang...

valuation is a submodular set function. The converse is not necessarily true. This is shown by the example on the right. The utility is submodular since it...

allows for simpler optimization while maintaining sparsity. See: Submodular set function Besides the norms discussed above, other norms used in structured...

is bounded in several cases. For example, when the cost function is a submodular set function (as in the above example), the correlation gap is at most...

is an extreme case of a submodular set function. It is characteristic of items that are pure substitute goods. Utility functions on indivisible goods Matching...

Fisher (1978). "An analysis of approximations for maximizing submodular set functions I". Mathematical Programming A. 14: 265–294. doi:10.1007/BF01588971...

−sur(G; X)] In a bipartite graph G = (X+Y, E), the surplus function is a submodular set function: for every two subsets X1, X2 of X: sur G ⁡ ( X 1 ∪ X 2...

Kulik, Ariel; Shachnai, Hadas; Tamir, Tami (2009), "Maximizing submodular set functions subject to multiple linear constraints", in Mathieu, Claire (ed...

theory", as well as matchings in graphs, include incidence matrices, submodular set functions, independent matchings in matroids, the Birkhoff–von Neumann theorem...

Fisher, M. L. (1978), "An analysis of approximations for maximizing submodular set functions I", Mathematical Programming, 14 (1): 265–294, doi:10.1007/BF01588971...