Deterministic approximation algorithm for submodular maximization subject to a matroid constraint

Abstract We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency.

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k-Submodular maximization with two kinds of constraints

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830921500361 ◽

2020 ◽

pp. 2150036

Author(s):

Ganquan Shi ◽

Shuyang Gu ◽

Weili Wu

Keyword(s):

Approximation Algorithm ◽

Submodular Function ◽

Approximation Ratio ◽

Size Difference ◽

Total Size ◽

Difference Constraints ◽

Submodular Maximization ◽

Individual Size

[Formula: see text]-submodular maximization is a generalization of submodular maximization, which requires us to select [Formula: see text] disjoint subsets instead of one subset. Attracted by practical values and applications, we consider [Formula: see text]-submodular maximization with two kinds of constraints. For total size and individual size difference constraints, we present a [Formula: see text]-approximation algorithm for maximizing a nonnegative k-submodular function, running in time [Formula: see text] at worst. Specially, if [Formula: see text] is multiple of [Formula: see text], the approximation ratio can reduce to [Formula: see text], running in time [Formula: see text] at worst. Besides, this algorithm can be applied to [Formula: see text]-bisubmodular achieving [Formula: see text]-approximation running in time [Formula: see text]. Furthermore, if [Formula: see text] is multiple of 2, the approximation ratio can reduce to [Formula: see text], running in time [Formula: see text] at worst. For individual size constraint, there is a [Formula: see text]-approximation algorithm for maximizing a nonnegative [Formula: see text]-submodular function and an nonnegative [Formula: see text]-bisubmodular function, running in time [Formula: see text] and [Formula: see text] respectively, at worst.

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Monotone submodular maximization over the bounded integer lattice with cardinality constraints

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830919500757 ◽

2019 ◽

Vol 11 (06) ◽

pp. 1950075

Author(s):

Lei Lai ◽

Qiufen Ni ◽

Changhong Lu ◽

Chuanhe Huang ◽

Weili Wu

Keyword(s):

Approximation Algorithm ◽

Greedy Algorithm ◽

Deterministic Algorithm ◽

Submodular Function ◽

Integer Lattice ◽

Cardinality Constraint ◽

Cardinality Constraints ◽

Definition Of ◽

Deterministic Formula ◽

Submodular Maximization

We consider the problem of maximizing monotone submodular function over the bounded integer lattice with a cardinality constraint. Function [Formula: see text] is submodular over integer lattice if [Formula: see text], [Formula: see text], where ∨ and ∧ represent elementwise maximum and minimum, respectively. Let [Formula: see text], and [Formula: see text], we study the problem of maximizing submodular function [Formula: see text] with constraints [Formula: see text] and [Formula: see text]. A random greedy [Formula: see text]-approximation algorithm and a deterministic [Formula: see text]-approximation algorithm are proposed in this paper. Both algorithms work in value oracle model. In the random greedy algorithm, we assume the monotone submodular function satisfies diminishing return property, which is not an equivalent definition of submodularity on integer lattice. Additionally, our random greedy algorithm makes [Formula: see text] value oracle queries and deterministic algorithm makes [Formula: see text] value oracle queries.

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An Approximation Algorithm for Distributed Resilient Submodular Maximization: Extended Abstract

2019 International Symposium on Multi-Robot and Multi-Agent Systems (MRS) ◽

10.1109/mrs.2019.8901088 ◽

2019 ◽

Author(s):

Lifeng Zhou ◽

Pratap Tokekar

Keyword(s):

Approximation Algorithm ◽

Submodular Maximization

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Finite High Order Approximation Algorithm for Joint Frequency Tracking and Channel Estimation in OFDM Systems

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e95.a.1676 ◽

2012 ◽

Vol E95.A (10) ◽

pp. 1676-1682 ◽

Cited By ~ 1

Author(s):

Rainfield Y. YEN ◽

Hong-Yu LIU ◽

Chia-Sheng TSAI

Keyword(s):

Channel Estimation ◽

Approximation Algorithm ◽

Order Approximation ◽

High Order ◽

Ofdm Systems ◽

High Order Approximation ◽

Frequency Tracking ◽

Joint Frequency

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Adaptive tracking for NARX system based on stochastic approximation algorithm

2020 39th Chinese Control Conference (CCC) ◽

10.23919/ccc50068.2020.9188818 ◽

2020 ◽

Author(s):

Wenhui Feng ◽

Han-Fu Chen

Keyword(s):

Approximation Algorithm ◽

Stochastic Approximation ◽

Stochastic Approximation Algorithm ◽

Adaptive Tracking

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An Improved Sequential Polygonal Approximation Algorithm on Skeleton Curves

ACTA AUTOMATICA SINICA ◽

10.3724/sp.j.1004.2008.01467 ◽

2009 ◽

Vol 34 (12) ◽

pp. 1467-1474

Author(s):

Zhe LV ◽

Fu-Li WANG ◽

Yu-Qing CHANG ◽

Yang LIU

Keyword(s):

Approximation Algorithm ◽

Polygonal Approximation

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The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219858855 ◽

2019 ◽

Vol 41 (15) ◽

pp. 4380-4386

Author(s):

Tu Xianping ◽

Lei Xianqing ◽

Ma Wensuo ◽

Wang Xiaoyi ◽

Hu Luqing ◽

...

Keyword(s):

Approximation Algorithm ◽

Evaluation Method ◽

Geometry Optimization ◽

Reference Points ◽

Approximation Technique ◽

Error Evaluation ◽

Iterative Approximation ◽

Logarithmic Curve ◽

Normal Distance ◽

Minimum Zone

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

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