Pipage rounding: A new method of constructing algorithms with proven performance guarantee. J.
Randomized Rounding for Routing and Covering Problems: Experiments and Improvements
Then, we go over all the possible values, and we are promised to obtain a solution of high value. A key tool in our derandomization is the pipage rounding technique of Ageev and Sviridenko .
Approximations for Monotone and Non-monotone Submodular Maximization with Knapsack Constraints
Pipage rounding: A new method of constructing algorithms with proven performance guarantee. J.
Approximations for Monotone and Non-monotone Submodular Maximization with Knapsack Constraints
Pipage rounding was originally developed by Ageev and Sviridenko for rounding solutions in the bipartite matching polytope .
Symmetry and approximability of submodular maximization problems
The framework of pipage rounding can be also extended to nonmonotone submodular functions; this presents some additional issues which we discuss in this paper.
Symmetry and approximability of submodular maximization problems
In the case of matroid constraints, this is easy to see, because an approximation to the continuous problem gives the same approximation factor for the discrete problem (by pipage rounding, see Appendix B).
Symmetry and approximability of submodular maximization problems
In the Appendix, we present a few basic facts concerning submodular functions, an extension of pipage rounding to matroid independence polytopes (rather than matroid base polytopes), and other technicalities that would hinder the main exposition.
Symmetry and approximability of submodular maximization problems
If there is no such direction v, apply pipage rounding to x and return the resulting solution.
Symmetry and approximability of submodular maximization problems
Finally, we use pipage rounding to convert a fractional solution into an integral one.
Symmetry and approximability of submodular maximization problems
Finally, we apply the pipage rounding technique which does not lose anything in terms of ob jective value (see Lemma B.3).
Symmetry and approximability of submodular maximization problems
Assume that x ∈ Bt (M); adjust x (using pipage rounding) so that each xi is an integer multiple of δ .
Symmetry and approximability of submodular maximization problems
If there is no such direction v, apply pipage rounding to x and return the resulting solution.
Symmetry and approximability of submodular maximization problems
Finally, we use pipage rounding to convert the fractional solution x into an integral one of value at least F (x) (Lemma B.1 in the Appendix).
Symmetry and approximability of submodular maximization problems
The pipage rounding technique [2, 4, 5] starts with a point in the base polytope y ∈ B (M) and produces an integral solution S ∈ I (in fact, a base) of expected value E[f (S )] ≥ F (y).
Symmetry and approximability of submodular maximization problems
The pipage rounding technique, given a membership oracle for a matroid M = (X, I ), a value oracle for a submodular function f : 2X → R+ , and y in the base polytope B (M), returns a random base B of value E[f (B )] ≥ F (y).
Symmetry and approximability of submodular maximization problems
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