Multipass Streaming Algorithms for Regularized Submodular Maximization

In this work,we study a k-Cardinality Constrained Regularized Submodular Maximization(k-CCRSM)problem,in which the objective utility is expressed as the difference between a non-negative submodular and a modular function.No multiplicative approximation algorithm exists for the regularized model,and most works have focused on designing weak approximation algorithms for this problem.In this study,we consider the k-CCRSM problem in a streaming fashion,wherein the elements are assumed to be visited individually and cannot be entirely stored in memory.We propose two multipass streaming algorithms with theoretical guarantees for the above problem,wherein submodular terms are monotonic and nonmonotonic.

Maximizing Submodular+Supermodular Functions Subject to a Fairness Constraint

We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy algorithm.For a streaming model,we propose a one-pass streaming algorithm.We also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular function.The total curvature is computable in polynomial time and widely utilized in the literature.

A Note on Maximizing Regularized Submodular Functions Under Streaming

Recent progress in maximizing submodular functions with a cardinality constraint through centralized and streaming modes has demonstrated a wide range of applications and also developed comprehensive theoretical guarantees.The submodularity was investigated to capture the diversity and representativeness of the utilities,and the monotonicity has the advantage of improving the coverage.Regularized submodular optimization models were developed in the latest studies(such as a house on fire),which aimed to sieve subsets with constraints to optimize regularized utilities.This study is motivated by the setting in which the input stream is partitioned into several disjoint parts,and each part has a limited size constraint.A first threshold-based bicriteria(1/3,2/3/)-approximation for the problem is provided.

Bicriteria Algorithms for Approximately Submodular Cover Under Streaming Model

In this paper,we mainly investigate the optimization model that minimizes the cost function such that the cover function exceeds a required threshold in the set cover problem,where the cost function is additive linear,and the cover function is non-monotone approximately submodular.We study the problem under streaming model and propose three bicriteria approximation algorithms.Firstly,we provide an intuitive streaming algorithm under the assumption of known optimal objective value.The intuitive streaming algorithm returns a solution such that its cover function value is no less thanα(1−ϵ)times threshold,and the cost function is no more than(2+ϵ)^(2)/(ϵ^(2)ω^(2))⋅κ,whereκis a value that we suppose for the optimal solution andαis the approximation ratio of an algorithm for unconstrained maximization problem that we can call directly.Next we present a bicriteria streaming algorithm scanning the ground set multi-pass to weak the assumption that we guess the optimal objective value in advance,and maintain the same bicriteria approximation ratio.Finally we modify the multi-pass streaming algorithm to a single-pass one without compromising the performance ratio.Additionally,we also propose some numerical experiments to test our algorithm’s performance comparing with some existing methods.

多目标跟踪中基于次模优化的轨迹片段生成方法

作为智能视觉任务的基础工作,多目标跟踪(MOT)一直是计算机视觉领域具有挑战性的课题之一。遮挡是影响跟踪准确性的主要因素,为此该文采用基于检测跟踪的思想,以轨迹片段为基础进行关联获取目标的完整轨迹;同时,为提高跟踪鲁棒性,该文将轨迹片段的生成问题转化为运筹学中的设施选址问题,并进而提出基于次模优化的轨迹片段生成方法。该方法融合梯度(HOG)和颜色(CN)两个互补特征进行目标表征,并根据运动信息设计权重系数提高目标匹配准确度,最后提出具有约束的次模最大化算法实现全局范围内的数据关联生成轨迹片段。通过在多个基准数据集上的对比实验,表明该文算法在保证性能的同时能有效处理遮挡问题。

Optimizing top-k retrieval： submodularity analysis and search strategies

The key issue in top-k retrieval, finding a set of k documents （from a large document collection） that can best answer a user＇s query, is to strike the optimal balance between relevance and diversity. In this paper, we study the top-k re- trieval problem in the framework of facility location analysis and prove he submodularity of that objective function which provides a theoretical approximation guarantee of factor 1 -1/ε for the （best-first） greedy search algorithm. Furthermore, we propose a two-stage hybrid search strategy which first ob- tains a high-quality initial set of top-k documents via greedy search, and then refines that result set iteratively via local search. Experiments on two large TREC benchmark datasets show that our two-stage hybrid search strategy approach can supersede the existing ones effectively and efficiently.

能量收集下的D2D-MEC计算卸载

针对移动边缘计算(MEC)在能源消耗和安全性方面的问题,研究具有社会关系和能量收集(EH)的D2D-MEC物联网网络中的任务卸载和资源分配问题,提出基于李雅普诺夫优化的D2D在线决策匹配和资源分配(ODMRA)算法.将用户之间的社会关系量化为社会信任矩阵,将能源消耗、包丢失、社会信任度表述为长期随机优化问题,采用李雅普诺夫优化方法将其分解为一系列子问题后分别求解.对于D2D间的决策选择子问题,结合子模块优化和贪婪算法设计低复杂度的策略选择算法.理论分析和仿真结果表明,所提出的ODMRA算法有效地优化了卸载方案,平衡了系统服务成本和队列长度,在能量消耗、系统服务成本方面优于其他对比算法.

An Approximation Algorithm for the Dynamic Facility Location Problem with Submodular Penalties

In this paper, we study the dynamic facility location problem with submodular penalties （DFLPSP）. We present a combinatorial primal-dual 3-approximation algorithm for the DFLPSP.

A Note on Submodularity Preserved Involving the Rank Functions

In many kinds of games with economic significance,it is very important to study the submodularity of functions.In this paper,wemainly study the problem of maximizing a concave function over an intersection of two matroids.We obtain that the submod-ularity may not be preserved,but it involves one maximal submodular problem(or minimal supermodular problem)with some conditions.Moreover,we also present examples showing that these conditions can be satisfied.

Simultaneous Approximation of Multi-criteria Submodular Function Maximization

Recently intensive interest has been raised on approximation of the NPhard submodular maximization problem due to their theoretical and practical significance.In this work,we extend this line of research by focusing on the simultaneous approximation of multiple submodular function maximization.We address the existence and nonexistence results for both deterministic and randomized approximation when the submodular functions are symmetric and asymmetric,respectively,along with algorithmic corollaries.We offer complete characterization of the symmetric case and partial results on the asymmetric case.

An Approximation Algorithm for the Generalized Prize-Collecting Steiner Forest Problem with Submodular Penalties

In this paper,we consider the generalized prize-collecting Steiner forest problem with submodular penalties(GPCSF-SP problem).In this problem,we are given an undirected connected graph G=(V,E)and a collection of disjoint vertex subsets V={V_(1),V_(2),…,V_(l)}.Assume c:E→R_(+)is an edge cost function andπ:2^(V)→R_(+)is a submodular penalty function.The objective of the GPCSF-SP problem is to find an edge subset F such that the total cost including the edge cost in F and the penalty cost of the subcollection S containing these Vi not connected by F is minimized.By using the primal-dual technique,we give a 3-approximation algorithm for this problem.

Performance bounds for Nash equilibria in submodular utility systems with user groups

It is shown that for a valid non-cooperative utility system,if the social utility function is submodular,then any Nash equilibrium achieves at least 1/2 of the optimal social utility,subject to a function-dependent additive term.Moreover,if the social utility function is nondecreasing and submodular,then any Nash equilibrium achieves at least 1/(1+c)of the optimal social utility,where c is the curvature of the social utility function.In this paper,we consider variations of the utility system considered by Vetta,in which users are grouped together.Our aim is to establish how grouping and cooperation among users affect performance bounds.We consider two types of grouping.The first type is from a previous paper,where each user belongs to a group of users having social ties with it.For this type of utility system,each user’s strategy maximises its social group utility function,giving rise to the notion of social-aware Nash equilibrium.We prove that this social utility system yields to the bounding results of Vetta for non-cooperative system,thus establishing provable performance guarantees for the social-aware Nash equilibria.For the second type of grouping we consider,the set of users is partitioned into l disjoint groups,where the users within a group cooperate to maximise their group utility function,giving rise to the notion of group Nash equilibrium.In this case,each group can be viewed as a new user with vector-valued actions,and a 1/2 bound for the performance of group Nash equilibria follows from the result of Vetta.But as we show tighter bounds involving curvature can be established.By defining the group curvature cki associated with group i with ki users,we show that if the social utility function is nondecreasing and submodular,then any group Nash equilibrium achieves at least 1/(1+max1≤i≤l cki)of the optimal social utility,which is tighter than that for the case without grouping.As a special case,if each user has the same action space,then we have that any group Nash equilibrium achieves at least 1/(1+ck∗)of the optimal social utility,where k∗is the least number of users among the l groups.Finally,we present an example of a utility system for database-assisted spectrum access to illustrate our results.

基于边缘智能计算的城市交通感知数据自适应恢复

智能交通系统(intelligent transportation systems,ITSs)被广泛用于智慧城市中,却普遍存在感知数据缺失问题.而交通感知站点有限的存储计算能力严重制约感知数据的恢复,极大影响ITSs的正常使用.虽然可以利用边缘节点强大的存储计算能力解决这个困境,但边缘节点部署的高复杂性和感知数据时空相关性的高动态性对数据精确恢复提出挑战.为了解决上述挑战,提出基于边缘智能计算的城市交通感知数据自适应恢复系统.具体地,首先利用子模优化理论,提出具有理论下界的边缘节点次优部署分配算法.然后,基于低秩理论恢复感知数据,并基于恢复结果估计非缺失下限,通过反馈自适应调整感知站点的数据上传比例,从而保证数据精确恢复.最后,基于澳大利亚600个交通站点1年的感知数据构建原型系统,对所提算法进行评估.实验结果表明,所提算法的边缘节点部署性能达到最优性能的90%以上,缺失数据恢复精度比3种对比方法提高43.8%以上.同时,自适应数据恢复能够平均提高精度40.3%.

带线性惩罚的次模边点控制集问题的近似算法

考虑带线性惩罚的次模边点控制集问题,给定一个无向图G=(V,E),且V中每个顶点都有一个非负惩罚,E的每个边子集都有一个非负权值.称e={u,v}∈E为边点控制顶点w,如果w∈N[u]∪N[v],这里N[u],N[v]分别为顶点u,v的闭邻域.带线性惩罚的次模边点控制集问题的目标是寻找一个边子集D,使得D的权值与未被D边点控制的顶点的惩罚费用之和最小.利用原始对偶技巧给出此问题的一个k-近似算法,其中k=maxv∈V|N[v]|.

一般图中的最小概要表示集问题

在一般图中,通常基于图的拓扑结构来刻画任意2个节点之间的相似度。基于节点相似度提出概要表示集SRS的概念,从图中寻找最少节点数的概要表示集称为最小概要表示集问题。证明了在一般图中求解最小概要表示集问题是NP(非确定性多项式)难的,不太可能存在多项式时间复杂度的精确算法。基于次模函数提出了多项式时间复杂度的贪心近似算法,用于求解最小概要表示集问题,得出近似比结果。

基于数据摘要的流式子模优化算法研究

针对如何从数据中提取出公平摘要的问题,文中采用流式子模最大化方法来解决该问题,并对其算法进行改进,提出一种公平约束下的流式子模最大化算法。该算法根据摘要的个数以及数据属性范围设置上下界构成公平约束,能够确保提取出代表性子集涵盖原始数据集的所有属性范围。仿真结果表明,该文算法与其他流式子模最大化算法相比,不仅时间复杂度减少了8.6%以上,而且在不同数据集下都能保证数据摘要结果的公平性与多样性。

临近最优主动学习的藏语语音识别方法研究

语音识别模型需要大量带标注语音语料进行训练,作为少数民族语言的藏语,由于语音标注专家十分匮乏,人工标注语音语料是一件非常费时费力的工作。然而,主动学习方法可以根据语音识别的目标从大量未标注的语音数据中挑选一些具有价值的样本交给用户进行标注,以便利用少量高质量的训练样本构建与大数据量训练方式一样精准的识别模型。研究了基于主动学习的藏语拉萨话语音语料选择方法,提出了一种临近最优的批量样本选择目标函数,并验证了其具有submodular函数性质。通过实验验证,该方法能够使用较少的训练数据保证语音识别模型的精度,从而减少了人工标注语料的工作量。

一种高效有向无线充电器的布置算法

传统的传感器节点通常采用电池供电,有限的电池能量限制了传感器网络整体的寿命.无线能量传输技术可将能量以无线方式从充电器发送至传感器,从而可以彻底解决这一问题.无线可充电传感网中的一个重要问题是无线充电器的布置问题,即,如何有效地布置充电器,使得传感器网络的整体充电效用最大化.已有的工作主要考虑的是全向充电器的布置问题,且充电器可布置的位置受限,如只能布置在三角形顶点或网格中的格点处,因此具有相当的局限性.首次考虑了有向充电器的一般布置问题,即,充电器充电区域为扇形,并且充电器可布置在区域内任何位置处,其朝向可任意调节.另外,首次基于实测数据建立了有向充电器的充电模型,并提出一系列创新方法将问题进行转化,设计了一种近似比为(1-1/e)/(1+ε)的高效算法——CDG(charger deployment-greedy)算法来解决这一问题.仿真实验结果说明了CDG算法的有效性.与其他提出的两种随机算法相比,CDG算法的性能分别提升了将近300%和100%.

社会网络中影响力传播的鲁棒抑制方法

社会网络中影响力传播的有效抑制是当前社会网络影响力传播机制研究关注的问题之一.针对不确定性、策略性负影响源的影响力传播抑制,讨论社会网络中影响力传播的鲁棒抑制问题.首先,作为提高算法运行效率的有效途径,讨论在竞争性线性阈值传播模型下,负种子集传播能力的近似估计方法,以此为基础,提出不确定性负影响源情况下,期望抑制效果最大化的抑制种子集挖掘算法.然后,对于策略性传播源,以最小化最坏情况下的影响力传播范围为目标,基于极小极大优化作为抑制决策准则,提出了一个随机抑制策略的多项式时间近似求解算法.最后,在真实的社会网络数据集上,通过实验验证了所提出方法的有效性.

基于图割与泛形信息的对象分割方法

针对交互式图像对象分割对用户交互性、分割速度和精度的需求,提出一种融合用户交互中泛化形状(简称泛形)信息的方法.该方法通过能量函数将用户交互中包含的泛形信息(包括区域、边界泛形)与对象、背景外观颜色以及图像梯度信息有机地融合,建立了从全局优化到局部优化的分割框架,并利用高效的图割优化方法进行求解.在全局优化过程中,利用超像素代替像素作为处理的基本单元,在保留原图像空间结构特征的同时大幅降低了全局优化计算的复杂度,并通过区域泛形保证全局整体分割的质量.局部优化过程对全局分割结果边界处的错误进行修正,仅处理某段边界局部范围内的像素,保证了分割速度;同时,边界泛形约束进一步确保了最终分割结果在边界处的准确性.实验结果证明了文中方法在用户交互性、分割速度和精度方面的良好性能.