منابع مشابه
Submodular Percolation
Let f : L → R be a submodular function on a modular lattice L; we show that there is a maximal chain C in L on which the sequence of values of f is minimal among all paths from 0 to 1 in the Hasse diagram of L, in a certain well-behaved partial order on sequences of reals. One consequence is that the maximum value of f on C is minimized over all such paths—i.e., if one can percolate from 0 to 1...
متن کاملSubmodular Optimization with Submodular Cover and Submodular Knapsack Constraints
We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of real-world applications in machine learning including sensor placement and data subset selection, which require ...
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Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displaceme...
متن کاملGreedy approximations for minimum submodular cover with submodular cost
It is well-known that a greedy approximation with an integer-valued polymatroid potential function f is H(γ )-approximation of the minimum submodular cover problem with linear cost where γ is the maximum value of f over all singletons and H(γ ) is the γ -th harmonic number. In this paper, we establish similar results for the minimum submodular cover problem with a submodular cost (possibly nonl...
متن کاملConstrained Robust Submodular Optimization
In this paper, we consider the problem of constrained maximization of the minimum of a set of submodular functions, in which the goal is to find solutions that are robust to worst-case values of the objective functions. Unfortunately, this problem is both non-submodular and inapproximable. In the case where the submodular functions are monotone, an approximate solution can be found by relaxing ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2009
ISSN: 0895-4801,1095-7146
DOI: 10.1137/07069078x