Results 171 to 180 of about 9,676,389 (199)

Maximizing Submodular Set Functions: Formulations and Analysis of Algorithms

1981
We consider integer programming formulations of problems that involve the maximization of submodular functions. A location problem and a 0–1 quadratic program are well-known special cases. We give a constraint generation algorithm and a branch-and-bound algorithm that uses linear programming relaxations.
G.L. Nemhauser, L.A. Wolsey
openaire   +1 more source

Matroids and Submodular Functions for Covering-Based Rough Sets

2019
Covering-based rough set theory is an extension of Pawlak’s rough set theory, and it was proposed to expand the applications of the latter to more general contexts. In this case a covering is used instead of the partition obtained from an equivalence relation.
Mauricio Restrepo, John Fabio Aguilar
openaire   +1 more source

Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)

2007
Let $f:2^{N} \rightarrow \cal R^{+}$ be a non-decreasing submodular set function, and let $(N,\cal I)$ be a matroid. We consider the problem $\max_{S \in \cal I} f(S)$. It is known that the greedy algorithm yields a 1/2-approximation [9] for this problem. It is also known, via a reduction from the max-k-cover problem, that there is no (1 i¾?
Gruia Calinescu, Chandra Chekuri, Martin Pál, Jan Vondrák   +3 more
openaire   +1 more source

Accelerated greedy algorithms for maximizing submodular set functions

2005
Given a finite set E and a real valued function f on P(E) (the power set of E) the optimal subset problem (P) is to find S ⊂ E maximizing f over P(E). Many combinatorial optimization problems can be formulated in these terms. Here, a family of approximate solution methods is studied : the greedy algorithms.
openaire   +1 more source

Approximation Operators in Covering Based Rough Sets from Submodular Functions

2017
We present a new collection of upper approximation operators for covering based rough sets, obtained from sub modular functions and closure operators. Each non decreasing submodular function defines a closure operator that can be considered as an approximation operator. The construction allows us to define several upper approximation operators.
openaire   +1 more source

On greedy algorithms, partially ordered sets, and submodular functions

IBM Journal of Research and Development, 2003
Brenda L. Dietrich, Alan J. Hoffman
openaire   +2 more sources

Submodular set functions and monotone systems in aggregation problems. II

[For part I see Autom. Remote Control 48, No.5, 679-689 (1987; Zbl 0639.90077).] The relationship from part I between submodular functions and functions determining the extremal properties of monotone sytems is applied to prove that, on the chain of any set-theoretical interval, the submodular function varies more slowly than the linear function of the
Muchnik, I. B., Shvartser, L. V.
openaire   +2 more sources

Approximability of Monotone Submodular Function Maximization under Cardinality and Matroid Constraints in the Streaming Model

SIAM Journal on Discrete Mathematics, 2022
Yuichi Yoshida, Naonori Kakimura, Simon Mauras   +2 more
exaly  

Improved Randomized Algorithm for k-Submodular Function Maximization

SIAM Journal on Discrete Mathematics, 2021
exaly  

Maximizing a non-decreasing non-submodular function subject to various types of constraints

Journal of Global Optimization, 2022
Wenguo Yang
exaly