Linear Query Approximation Algorithms for Non-monotone Submodular Maximization under Knapsack Constraint

This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and $\mathsf{RLA}$. $\mathsf{DLA}$ is a deterministic algorithm that provides an approximation factor of $6+\epsilon$ while $\mathsf{RLA}$ is a randomized algorithm with an approximation factor of $4+\epsilon$. Both run in $O(n \log(1/\epsilon)/\epsilon)$ query complexity. The key idea to obtain a constant approximation ratio with linear query lies in: (1) dividing the ground set into two appropriate subsets to find the near-optimal solution over these subsets with linear queries, and (2) combining a threshold greedy with properties of two disjoint sets or a random selection process to improve solution quality. In addition to the theoretical analysis, we have evaluated our proposed solutions with three applications: Revenue Maximization, Image Summarization, and Maximum Weighted Cut, showing that our algorithms not only return comparative results to state-of-the-art algorithms but also require significantly fewer queries

Minimizing cost for influencing target groups in social network: A model and algorithmic approach

Stimulated by practical applications arising from economics, viral marketing, and elections, this paper studies the problem of Groups Influence with Minimum cost (GIM), which aims to find a seed set with the smallest cost that can influence all target groups in a social network, where each user is assigned a cost and a score and a group of users is influenced if the total score of influenced users in the group is at least a certain threshold. As the group influence function, defined as the number of influenced groups or users, is neither submodular nor supermodular, theoretical bounds on the quality of solutions returned by the well-known greedy approach may not be guaranteed.In this work, two efficient algorithms with theoretical guarantees for tackling the GIM problem, named Groups Influence Approximation (GIA) and Exact Groups Influence (EGI), are proposed. GIA is a bi-criteria polynomial-time approximation algorithm and EGI is an (almost) exact algorithm; both can return good approximate solutions with high probability. The novelty of our approach lies in two aspects. Firstly, a novel group reachable reverse sample concept is proposed to estimate the group influence function within an error bound. Secondly, a framework algorithmic is designed to find serial candidate solutions with checking theoretical guarantees at the same time. Besides theoretical results, extensive experiments conducted on real social networks show our algorithms' performance. In particular, both EGI and GIA provide the solution quality several times better, while GIA is up to 800 times faster than the state-of-the-art algorithms.Web of Science21219718

Competitive Influence Maximization within Time and Budget Constraints in Online Social Networks: An Algorithmic Approach

Competitive Influence Maximization ( CIM ) problem, which seeks a seed set nodes of a player or a company to propagate their product’s information while at the same time their competitors are conducting similar strategies, has been paid much attention recently due to its application in viral marketing. However, existing works neglect the fact that the limited budget and time constraints can play an important role in competitive influence strategy of each company. In addition, based on the the assumption that one of the competitors dominates in the competitive influence process, the majority of prior studies indicate that the competitive influence function (objective function) is monotone and submodular.This led to the fact that CIM can be approximated within a factor of 1 − 1 / e − ϵ by a Greedy algorithm combined with Monte Carlo simulation method. Unfortunately, in a more realistic scenario where there is fair competition among competitors, the objective function is no longer submodular. In this paper, we study a general case of CIM problem, named Budgeted Competitive Influence Maximization ( BCIM ) problem, which considers CIM with budget and time constraints under condition of fair competition. We found that the objective function is neither submodular nor suppermodular. Therefore, it cannot admit Greedy algorithm with approximation ratio of 1 − 1 / e . We propose Sandwich Approximation based on Polling-Based Approximation ( SPBA ), an approximation algorithm based on Sandwich framework and polling-based method. Our experiments on real social network datasets showed the effectiveness and scalability of our algorithm that outperformed other state-of-the-art methods. Specifically, our algorithm is scalable with million-scale networks in only 1.5 min

Influence Maximization with Priority in Online Social Networks

The Influence Maximization (IM) problem, which finds a set of k nodes (called seedset) in a social network to initiate the influence spread so that the number of influenced nodes after propagation process is maximized, is an important problem in information propagation and social network analysis. However, previous studies ignored the constraint of priority that led to inefficient seed collections. In some real situations, companies or organizations often prioritize influencing potential users during their influence diffusion campaigns. With a new approach to these existing works, we propose a new problem called Influence Maximization with Priority (IMP) which finds out a set seed of k nodes in a social network to be able to influence the largest number of nodes subject to the influence spread to a specific set of nodes U (called priority set) at least a given threshold T in this paper. We show that the problem is NP-hard under well-known IC model. To find the solution, we propose two efficient algorithms, called Integrated Greedy (IG) and Integrated Greedy Sampling (IGS) with provable theoretical guarantees. IG provides a 1−(1−1k)t-approximation solution with t is an outcome of algorithm and t≥1. The worst-case approximation ratio is obtained when t=1 and it is equal to 1/k. In addition, IGS is an efficient randomized approximation algorithm based on sampling method that provides a 1−(1−1k)t−ϵ-approximation solution with probability at least 1−δ with ϵ>0,δ∈(0,1) as input parameters of the problem. We conduct extensive experiments on various real networks to compare our IGS algorithm to the state-of-the-art algorithms in IM problem. The results indicate that our algorithm provides better solutions interns of influence on the priority sets when approximately give twice to ten times higher than threshold T while running time, memory usage and the influence spread also give considerable results compared to the others

VIETNAMESE MIGRATION IN THE CONTEXT OF CLIMATE CHANGE

The paper examines emigration from Vietnam in the context of global climate change. Vietnam is among the five countries, most vulnerable to water level rise in the oceans associated with global warming. The areas of potential flooding include territories with most dense population and are extremity important for the economy of Vietnam. The country has a significant demographic potential exceeding 90 mln people. Vietnamese migration has a relatively long history. Large Vietnamese communities have grown in the countries of Eastern Europe; these communities are relatively well integrated into the host countries. Increase in global mean temperatures could lead to severe storms, tsunamis, and flooding and force significant portion of the population out of the Mekong Delta regions and Central provinces of Vietnam. The paper discusses the potential of Atlas Information Systems (AISs) for the assessment of social-economic and demographic consequences of climate change in Vietnam. The authors describe an AIS they are developing. This AIS consists of blocks that provide for a close link between socio-political, economic (production), natural resource, and environmental components for the integrated assessment of the provinces of Vietnam. Simulation of events shows that the flood zone could affect such populated provinces as An Giang, Kien Giang, Hau Giang, Dong Thap, Long An, Tien Giang, Vinh Long and Can Tho. To address this problem, the Vietnamese authorities, in 2008, approved the state target program to respond to climate change. The Ministry of Natural Resources and Environment was commissioned to create a scenario of climate change and sea level rise in Vietnam. However, the problem requires an immediate response at the international level, as the threat cannot be localized within the borders of Vietnam. Flooding may require mandatory relocation of the population in the country and, possibly, beyond its borders. If people are not relocated gradually, a reduction in the country’s territory with high population density, considering the specifics of the settlement pattern and reproduction trends, could result in a significant migration flow of forced migrants - environmental refugees. The territory of Vietnam may not be sufficient to absorb the entire flow of immigrants and, as a result, the flow would be directed out of the country. However, if the resettlement program starts now in the form of organized labor migration, it may be possible to anticipate and mitigate the negative scenario. Besides, organized labor emigration would be even beneficial for Vietnam in the socio-economic respect. The paper suggests measures to improve Russia’s migration policy aimed at attracting and using Vietnamese workers in a regulated way that would benefit Russia socially and economically

Some Problems of Extracting Level Density and Radiative Strength Functions from the gamma Spectra in Nuclear Reactions

The most important systematical errors in determination of level density and radiative strength functions for deformed nuclei have been estimated from the gamma-ray spectra in nuclear reactions like the stripping or pickup reactions