Greedily Improving Our Own Centrality in A Network

International audienceThe closeness and the betweenness centralities are two well knownmeasures of importance of a vertex within a given complex network.Having high closeness or betweenness centrality can have positiveimpact on the vertex itself: hence, in this paper we consider the problemof determining how much a vertex can increase its centrality by creatinga limited amount of new edges incident to it. We first prove that thisproblem does not admit a polynomial-time approximation scheme (unlessP = NP), and we then propose a simple greedy approximation algorithm(with an almost tight approximation ratio), whose performance is thentested on synthetic graphs and real-world networks

Improving information centrality of a node in complex networks by adding edges

The problem of increasing the centrality of a network node arises in many practical applications. In this paper, we study the optimization problem of maximizing the information centrality $I_v$ of a given node $v$ in a network with $n$ nodes and $m$ edges, by creating $k$ new edges incident to $v$. Since $I_v$ is the reciprocal of the sum of resistance distance $\mathcal{R}_v$ between $v$ and all nodes, we alternatively consider the problem of minimizing $\mathcal{R}_v$ by adding $k$ new edges linked to $v$. We show that the objective function is monotone and supermodular. We provide a simple greedy algorithm with an approximation factor $\left(1-\frac{1}{e}\right)$ and $O(n^3)$ running time. To speed up the computation, we also present an algorithm to compute $\left(1-\frac{1}{e}-\epsilon\right)$-approximate resistance distance $\mathcal{R}_v$ after iteratively adding $k$ edges, the running time of which is $\widetilde{O} (mk\epsilon^{-2})$ for any $\epsilon>0$, where the $\widetilde{O} (\cdot)$ notation suppresses the ${\rm poly} (\log n)$ factors. We experimentally demonstrate the effectiveness and efficiency of our proposed algorithms.Comment: 7 pages, 2 figures, ijcai-201

On the fixed-parameter tractability of the maximum connectivity improvement problem

In the Maximum Connectivity Improvement (MCI) problem, we are given a directed graph $G=(V,E)$ and an integer $B$ and we are asked to find $B$ new edges to be added to $G$ in order to maximize the number of connected pairs of vertices in the resulting graph. The MCI problem has been studied from the approximation point of view. In this paper, we approach it from the parameterized complexity perspective in the case of directed acyclic graphs. We show several hardness and algorithmic results with respect to different natural parameters. Our main result is that the problem is $W[2]$-hard for parameter $B$ and it is FPT for parameters $|V| - B$ and $\nu$, the matching number of $G$. We further characterize the MCI problem with respect to other complementary parameters.Comment: 15 pages, 1 figur

Coverage Centrality Maximization in Undirected Networks

Centrality metrics are among the main tools in social network analysis. Being central for a user of a network leads to several benefits to the user: central users are highly influential and play key roles within the network. Therefore, the optimization problem of increasing the centrality of a network user recently received considerable attention. Given a network and a target user $v$, the centrality maximization problem consists in creating $k$ new links incident to $v$ in such a way that the centrality of $v$ is maximized, according to some centrality metric. Most of the algorithms proposed in the literature are based on showing that a given centrality metric is monotone and submodular with respect to link addition. However, this property does not hold for several shortest-path based centrality metrics if the links are undirected. In this paper we study the centrality maximization problem in undirected networks for one of the most important shortest-path based centrality measures, the coverage centrality. We provide several hardness and approximation results. We first show that the problem cannot be approximated within a factor greater than $1-1/e$, unless $P=NP$, and, under the stronger gap-ETH hypothesis, the problem cannot be approximated within a factor better than $1/n^{o(1)}$, where $n$ is the number of users. We then propose two greedy approximation algorithms, and show that, by suitably combining them, we can guarantee an approximation factor of $\Omega(1/\sqrt{n})$. We experimentally compare the solutions provided by our approximation algorithm with optimal solutions computed by means of an exact IP formulation. We show that our algorithm produces solutions that are very close to the optimum.Comment: Accepted to AAAI 201

The Parameterized Complexity of Centrality Improvement in Networks

The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact on the network or less transportation or administration cost. In this work we study the parameterized complexity of the NP-complete problems Closeness Improvement and Betweenness Improvement in which we ask to improve a given vertex' closeness or betweenness centrality by a given amount through adding a given number of edges to the network. Herein, the closeness of a vertex v sums the multiplicative inverses of distances of other vertices to v and the betweenness sums for each pair of vertices the fraction of shortest paths going through v. Unfortunately, for the natural parameter "number of edges to add" we obtain hardness results, even in rather restricted cases. On the positive side, we also give an island of tractability for the parameter measuring the vertex deletion distance to cluster graphs

Socially-Aware Distributed Hash Tables for Decentralized Online Social Networks

Many decentralized online social networks (DOSNs) have been proposed due to an increase in awareness related to privacy and scalability issues in centralized social networks. Such decentralized networks transfer processing and storage functionalities from the service providers towards the end users. DOSNs require individualistic implementation for services, (i.e., search, information dissemination, storage, and publish/subscribe). However, many of these services mostly perform social queries, where OSN users are interested in accessing information of their friends. In our work, we design a socially-aware distributed hash table (DHTs) for efficient implementation of DOSNs. In particular, we propose a gossip-based algorithm to place users in a DHT, while maximizing the social awareness among them. Through a set of experiments, we show that our approach reduces the lookup latency by almost 30% and improves the reliability of the communication by nearly 10% via trusted contacts.Comment: 10 pages, p2p 2015 conferenc