Noticeable Network Delay Minimization via Node Upgrades

In several domains, the flow of data is governed by an underlying network. Reduction of delays in end-to-end data flow is an important network optimization task. Reduced delays enable shorter travel times for vehicles in road networks, faster information flow in social networks, and increased rate of packets in communication networks. While techniques for network delay minimization have been proposed, they fail to provide any noticeable reduction in individual data flows. Furthermore, they treat all nodes as equally important, which is often not the case in real-world networks. In this paper, we incorporate these practical aspects and propose a network design problem where the goal is to perform k network upgrades such that it maximizes the number of flows in the network with a noticeable reduction in delay. We show that the problem is NP-hard, APX-hard, and non-submodular. We overcome these computational challenges by designing an importance sampling based algorithm with provable quality guarantees. Through extensive experiments on real and synthetic data sets, we establish that importance sampling imparts up to 1000 times speed-up over the greedy approach, and provides up to 70 times the improvement achieved by the stateof-the-art technique. PVLDB Reference Format: . . PVLDB, (): xxxx-yyyy, .

Related papers:

title: Inferring Uncertain Trajectories from Partial Observations
abstract: The explosion in the availability of GPS-enabled devices has resulted in an abundance of trajectory data. In reality, however, majority of these trajectories are collected at a low sampling rate and only provide partial observations on their actually traversed routes. Consequently, they are mired with uncertainty. In this paper, we develop a technique called Infer Tra to infer uncertain trajectories from network-constrained partial observations. Rather than predicting the most likely route, the inferred uncertain trajectory takes the form of an edge-weighted graph and summarizes all probable routes in a holistic manner. For trajectory inference, Infer Tra employs Gibbs sampling by learning a Network Mobility Model (NMM) from a database of historical trajectories. Extensive experiments on real trajectory databases show that the graph-based approach of Infer Tra is up to 50% more accurate, 20 times faster, and immensely more versatile than state-of-the-art techniques.

title: MANTRA: A Scalable Approach to Mining Temporally Anomalous Sub-trajectories
abstract: In this paper, we study the problem of mining temporally anomalous sub-trajectory patterns from an input trajectory in a scalable manner. Given the prevailing road conditions, a sub-trajectory is temporally anomalous if its travel time deviates significantly from the expected time. Mining these patterns requires us to delve into the sub-trajectory space, which is not scalable for real-time analytics. To overcome this scalability challenge, we design a technique called MANTRA. We study the properties unique to anomalous sub-trajectories and utilize them in MANTRA to iteratively refine the search space into a disjoint set of sub-trajectory islands. The expensive enumeration of all possible sub-trajectories is performed only on the islands to compute the answer set of maximal anomalous sub-trajectories. Extensive experiments on both real and synthetic datasets establish MANTRA as more than 3 orders of magnitude faster than baseline techniques. Moreover, through trajectory classification and segmentation, we demonstrate that the proposed model conforms to human intuition.

title: Route Recommendations for Idle Taxi Drivers: Find Me the Shortest Route to a Customer!
abstract: We study the problem of route recommendation to idle taxi drivers such that the distance between the taxi and an anticipated customer request is minimized. Minimizing the distance to the next anticipated customer leads to more productivity for the taxi driver and less waiting time for the customer. To anticipate when and where future customer requests are likely to come from and accordingly recom- mend routes, we develop a route recommendation engine called MDM: Minimizing Distance through Monte Carlo Tree Search. In contrast to existing techniques, MDM employs a continuous learning platform where the underlying model to predict future customer requests is dynamically updated. Extensive experiments on real taxi data from New York and San Francisco reveal that MDM is up to 70% better than the state of the art and robust to anomalous events such as concerts, sporting events, etc.

title: Upgrading Shortest Paths in Networks
abstract: We introduce the Upgrading Shortest Paths Problem, a new combinatorial problem for improving network connectivity with a wide range of applications from multicast communication to wildlife habitat conservation. We define the problem in terms of a network with node delays and a set of node upgrade actions, each associated with a cost and an upgraded (reduced) node delay. The goal is to choose a set of upgrade actions to minimize the shortest delay paths between demand pairs of terminals in the network, subject to a budget constraint. We show that this problem is NP-hard. We describe and test two greedy algorithms against an exact algorithm on synthetic data and on a real-world instance from wildlife habitat conservation. While the greedy algorithms can do arbitrarily poorly in the worst case, they perform fairly well in practice. For most of the instances, taking the better of the two greedy solutions accomplishes within 5% of optimal on our benchmarks.

title: Spontaneous synchrony in power-grid networks
abstract: Power-grid networks must be synchronized in order to function. A condition for the stability of the synchronous state enables identification of network parameters that enhance spontaneous synchronization—heralding the possibility of smart grids that operate optimally in real-world systems.

title: A Hierarchical Framework for Intelligent Traffic Management in Smart Cities
abstract: Transportation infrastructure is undergoing major revolutions in most metropolitan areas, which demands for improved operational strategies to meet requirements of smart cities. Such requirements include more convenience more travelers, and higher levels of security, reliability, economics, and societal sustainability in our communities. Given that the wide-area situational awareness is enabled by advanced information and communication technologies, this paper develops a hierarchical operation framework for regulating traffic signals effectively and flexibly in dynamic traffic conditions. The proposed framework which is based on the multi-agent system manages to mitigate potential traffic congestions and minimize drivers’ average travel time in metropolitan areas. Further traffic efficiency improvements can be achieved by the utilization of a closed-loop management system. Interactive simulations are conducted in this paper to examine the performance of the proposed framework in a real-world transportation system.

title: Towards Scalable Network Delay Minimization
abstract: Reduction of end-to-end network delays is an optimization task with applications in multiple domains. Low delays enable improved information flow in social networks, quick spread of ideas in collaboration networks, low travel times for vehicles on road networks and increased rate of packets in communication networks. Delay reduction can be achieved by both improving the propagation capabilities of individual nodes and adding additional edges in the network. One of the main challenges in such design problems is that the effects of local changes are not independent, and as a consequence, there is a combinatorial search space of possible improvements. Thus, minimizing the cumulative propagation delay requires novel scalable and data-driven approaches. In this paper, we consider the problem of network delay minimization via node upgrades. Although the problem is NP-hard, we show that probabilistic approximation for a restricted version can be obtained. We design scalable and high-quality techniques for the general setting based on sampling that are targeted to different models of delay distribution. Our methods scale almost linearly with the graph size and consistently outperform competitors in quality.

title: Best upgrade plans for single and multiple source-destination pairs
abstract: In this paper, we study Resource Constrained Best Upgrade Plan (BUP) computation in road network databases. Consider a transportation network (weighted graph) G where a subset of the edges are upgradable, i.e., for each such edge there is a cost, which if spent, the weight of the edge can be reduced to a specific new value. In the single-pair version of BUP, the input includes a source and a destination in G, and a budget B (resource constraint). The goal is to identify which upgradable edges should be upgraded so that the shortest path distance between source and destination (in the updated network) is minimized, without exceeding the available budget for the upgrade. In the multiple-pair version of BUP, a set Q of source-destination pairs is given, and the problem is to choose for upgrade those edges that lead to the smallest sum of shortest path distances across all pairs in Q, subject to budget constraint B. In addition to transportation networks, the BUP query arises in other domains too, such as telecommunications. We propose a framework for BUP processing and evaluate it with experiments on large, real road networks.

title: Minimizing Average Shortest Path Distances via Shortcut Edge Addition
abstract: We consider adding k shortcut edges (i.e. edges of small fixed length *** *** 0) to a graph so as to minimize the weighted average shortest path distance over all pairs of vertices. We explore several variations of the problem and give O (1)-approximations for each. We also improve the best known approximation ratio for metric k -median with penalties, as many of our approximations depend upon this bound. We give a $(1+2\frac{(p+1)}{\beta(p+1)-1},\beta)$-approximation with runtime exponential in p . If we set β = 1 (to be exact on the number of medians), this matches the best current k -median (without penalties) result.

title: The Design of Approximation Algorithms
abstract: Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.

title: Greedily Improving Our Own Centrality in A Network
abstract: The closeness and the betweenness centralities are two well-known measures of importance of a vertex within a given complex network. Having high closeness or betweenness centrality can have positive impact on the vertex itself: hence, in this paper we consider the problem of determining how much a vertex can increase its centrality by creating a limited amount of new edges incident to it. We first prove that this problem does not admit a polynomial-time approximation scheme unless $$P=NP$$, and we then propose a simple greedy approximation algorithm with an almost tight approximation ratio, whose performance is then tested on synthetic graphs and real-world networks.

title: Best Algorithms for Approximating the Maximum of a Submodular Set Function
abstract: A real-valued function z whose domain is all of the subsets of N = {1,..., n is said to be submodular if zS + zT ≥ zS ∪ T + zS ∩ T, ∀S, T ⊆ N, and nondecreasing if zS ≤ zT, ∀S ⊂ T ⊆ N. We consider the problem maxS⊂N {zS: |S| ≤ K, z submodular and nondecreasing, zO = 0}. 
 
Many combinatorial optimization problems can be posed in this framework. For example, a well-known location problem and the maximization of certain boolean polynomials are in this class. 
 
We present a family of algorithms that involve the partial enumeration of all sets of cardinality q and then a greedy selection of the remaining elements, q = 0,..., K-1. For fixed K, the qth member of this family requires Onq+1 computations and is guaranteed to achieve at least $$\biggl[1-\biggl\frac{K-q}{K}\biggr\biggl\frac{K-q-1}{K-q}\biggr^{K-q}\biggr]\times100 \quad\mbox {percent of the optimum value}.$$ Our main result is that this is the best performance guarantee that can be obtained by any algorithm whose number of computations does not exceed Onq+1.

title: Greedily Improving Our Own Closeness Centrality in a Network
abstract: The closeness centrality is a well-known measure of importance of a vertex within a given complex network. Having high closeness centrality can have positive impact on the vertex itself: hence, in this paper we consider the optimization problem of determining how much a vertex can increase its centrality by creating a limited amount of new edges incident to it. We will consider both the undirected and the directed graph cases. In both cases, we first prove that the optimization problem does not admit a polynomial-time approximation scheme (unless P = NP), and then propose a greedy approximation algorithm (with an almost tight approximation ratio), whose performance is then tested on synthetic graphs and real-world networks.

title: Probability Inequalities for sums of Bounded Random Variables
abstract: Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr {S – ES ≥ nt} depend only on the endpoints of the ranges of the summands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.

title: A Framework for the Evaluation and Management of Network Centrality
abstract: Network-analysis literature is rich in node-centrality measures that quantify the centrality of a node as a function of the (shortest) paths of the network that go through it. Existing work focuses on defining instances of such measures and designing algorithms for the specific combinatorial problems that arise for each instance. In this work, we propose a unifying definition of centrality that subsumes all path-counting based centrality definitions: e.g., stress, betweenness or paths centrality. We also define a generic algorithm for computing this generalized centrality measure for every node and every group of nodes in the network. Next, we define two optimization problems: k-Group Centrality Maximization and k-Edge Centrality Boosting. In the former, the task is to identify the subset of k nodes that have the largest group centrality. In the latter, the goal is to identify up to k edges to add to the network so that the centrality of a node is maximized. We show that both of these problems can be solved efficiently for arbitrary centrality definitions using our general framework. In a thorough experimental evaluation we show the practical utility of our framework and the efficacy of our algorithms.

title: People in motion: Spatio-temporal analytics on Call Detail Records
abstract: The data about how people move in a city can be potentially used by various enterprises and government organizations to strategically optimize their operations and maximize their revenue. However, fine-grained and real-time data is currently unavailable to the enterprises. We believe that Cellular Network operators can deliver such data and insights to enterprises. Call records collected in the networks embed a wealth of information about where, when and how a large fraction of the city moves. However, this information is untapped; a majority of the cellular operators are not deriving spatio-temporal insights or monetizing the data that is already available. In this paper, we demonstrate “People in Motion”: an end-to-end Hadoop-based system with a library of spatio-temporal algorithms that operates on the call record data to derive business insights. We identify the hangouts and trajectories of users with different interests. Finally, we demonstrate a visual analytics tool that facilitates business users to compute, compare and contrast the importance of spatial regions at different times for different categories of users.

title: {35 () Approximation Algorithms for Certain Network Improvement Problems
abstract: We study budget constrained network upgrading problems. Such problems aim at nding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V; E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function ce(t) that speciies the cost of upgrading the edge by an amount t. A reduction strategy speciies for each edge e the amount by which the length`(e) is to be reduced. In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v. For a given budget B, the goal is to nd an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e.g. minimum spanning tree) under the modiied edge lengths is the best over all possible strategies which obey the budget constraint. After providing a brief overview of the models and deenitions of the various problems considered, we present several new results on the complexity and approximability of network improvement problems.

title: From Competition to Complementarity: Comparative Influence Diffusion and Maximization
abstract: Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization, in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation" strategy. The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines on four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.

title: Scalable Betweenness Centrality Maximization via Sampling
abstract: Betweenness centrality (BWC) is a fundamental centrality measure in social network analysis. Given a large-scale network, how can we find the most central nodes? This question is of great importance to many key applications that rely on BWC, including community detection and understanding graph vulnerability. Despite the large amount of work on scalable approximation algorithm design for BWC, estimating BWC on large-scale networks remains a computational challenge. In this paper, we study the Centrality Maximization problem (CMP): given a graph G = (V,E) and a positive integer k, find a set S* ⊆ V that maximizes BWC subject to the cardinality constraint |S*| ≤ k. We present an efficient randomized algorithm that provides a (1 -- 1/e -- ε)-approximation with high probability, where ε > 0. Our results improve the current state-of-the-art result [40]. Furthermore, we provide the first theoretical evidence for the validity of a crucial assumption in betweenness centrality estimation, namely that in real-world networks O(|V|2) shortest paths pass through the top-k central nodes, where k is a constant. This also explains why our algorithm runs in near linear time on real-world networks. We also show that our algorithm and analysis can be applied to a wider range of centrality measures, by providing a general analytical framework. On the experimental side, we perform an extensive experimental analysis of our method on real-world networks, demonstrate its accuracy and scalability, and study different properties of central nodes. Then, we compare the sampling method used by the state-of-the-art algorithm with our method. Furthermore, we perform a study of BWC in time evolving networks, and see how the centrality of the central nodes in the graphs changes over time. Finally, we compare the performance of the stochastic Kronecker model [28] to real data, and observe that it generates a similar growth pattern.

title: Recommendations to boost content spread in social networks
abstract: Content sharing in social networks is a powerful mechanism for discovering content on the Internet. The degree to which content is disseminated within the network depends on the connectivity relationships among network nodes. Existing schemes for recommending connections in social networks are based on the number of common neighbors, similarity of user profiles, etc. However, such similarity-based connections do not consider the amount of content discovered.
 In this paper, we propose novel algorithms for recommending connections that boost content propagation in a social network without compromising on the relevance of the recommendations. Unlike existing work on influence propagation, in our environment, we are looking for edges instead of nodes, with a bound on the number of incident edges per node. We show that the content spread function is not submodular, and develop approximation algorithms for computing a near-optimal set of edges. Through experiments on real-world social graphs such as Flickr and Twitter, we show that our approximation algorithms achieve content spreads that are as much as 90 times higher compared to existing heuristics for recommending connections.

title: Stochastic simulation - algorithms and analysis
abstract: General Methods and Algorithms.- Generating Random Objects.- Output Analysis.- Steady-State Simulation.- Variance-Reduction Methods.- Rare-Event Simulation.- Derivative Estimation.- Stochastic Optimization.- Algorithms for Special Models.- Numerical Integration.- Stochastic Di3erential Equations.- Gaussian Processes.- Levy Processes.- Markov Chain Monte Carlo Methods.- Selected Topics and Extended  What This  What This Book Is About.

title: Hierarchical in-network attribute compression via importance sampling
abstract: Many real-world complex systems can be modeled as dynamic networks with real-valued vertex/edge attributes. Examples include users' opinions in social networks and average speeds in a road system. When managing these large dynamic networks, compressing attribute values becomes a key requirement, since it enables the answering of attribute-based queries regarding a node/edge or network region based on a compact representation of the data. To address this problem, we introduce a lossy network compression scheme called Slice Tree (ST), which partitions a network into smooth regions with respect to node/edge values and compresses each value as the average of its region. ST applies a compact representation for network partitions, called slices, that are defined as a center node and radius distance. We propose an importance sampling algorithm to efficiently prune the search space of candidate slices in the ST construction by biasing the sampling process towards the node values that most affect the compression error. The effectiveness of ST in terms of compression error, compression rate, and running time is demonstrated using synthetic and real datasets. ST scales to million-node instances and removes up to 87% of the error in attribute values with a 103 compression ratio. We also illustrate how ST captures relevant phenomena in real networks, such as research collaboration patterns and traffic congestions.

title: Almost linear-time algorithms for adaptive betweenness centrality using hypergraph sketches
abstract: Betweenness centrality measures the importance of a vertex by quantifying the number of times it acts as a midpoint of the shortest paths between other vertices. This measure is widely used in network analysis. In many applications, we wish to choose the k vertices with the maximum adaptive betweenness centrality, which is the betweenness centrality without considering the shortest paths that have been taken into account by already-chosen vertices. All previous methods are designed to compute the betweenness centrality in a fixed graph. Thus, to solve the above task, we have to run these methods $k$ times. In this paper, we present a method that directly solves the task, with an almost linear runtime no matter how large the value of k. Our method first constructs a hypergraph that encodes the betweenness centrality, and then computes the adaptive betweenness centrality by examining this graph. Our technique can be utilized to handle other centrality measures. We theoretically prove that our method is very accurate, and experimentally confirm that it is three orders of magnitude faster than previous methods. Relying on the scalability of our method, we experimentally demonstrate that strategies based on adaptive betweenness centrality are effective in important applications studied in the network science and database communities.

title: T-drive: driving directions based on taxi trajectories
abstract: GPS-equipped taxis can be regarded as mobile sensors probing traffic flows on road surfaces, and taxi drivers are usually experienced in finding the fastest (quickest) route to a destination based on their knowledge. In this paper, we mine smart driving directions from the historical GPS trajectories of a large number of taxis, and provide a user with the practically fastest route to a given destination at a given departure time. In our approach, we propose a time-dependent landmark graph, where a node (landmark) is a road segment frequently traversed by taxis, to model the intelligence of taxi drivers and the properties of dynamic road networks. Then, a Variance-Entropy-Based Clustering approach is devised to estimate the distribution of travel time between two landmarks in different time slots. Based on this graph, we design a two-stage routing algorithm to compute the practically fastest route. We build our system based on a real-world trajectory dataset generated by over 33,000 taxis in a period of 3 months, and evaluate the system by conducting both synthetic experiments and in-the-field evaluations. As a result, 60-70% of the routes suggested by our method are faster than the competing methods, and 20% of the routes share the same results. On average, 50% of our routes are at least 20% faster than the competing approaches.

title: Trajectory aware macro-cell planning for mobile users
abstract: We handle the problem of efficient user-mobility driven macro-cell planning in cellular networks. As cellular networks embrace heterogeneous technologies (including long range 3G/4G and short range WiFi, Femto-cells, etc.), most traffic generated by static users gets absorbed by the short-range technologies, thereby increasingly leaving mobile user traffic to macro-cells. To this end, we consider a novel approach that factors in the trajectories of mobile users as well as the impact of city geographies and their associated road networks for macro-cell planning. Given a budget k of base-stations that can be upgraded, our approach selects a deployment that improves the most number of user trajectories. The generic formulation incorporates the notion of quality of service of a user trajectory as a parameter to allow different application-specific requirements, and operator choices. We show that the proposed trajectory utility maximization problem is NP-hard, and design multiple heuristics. We evaluate our algorithms with real and synthetic datasets emulating different city geographies to demonstrate their efficacy. For instance, with an upgrade budget k of 20%, our algorithms perform 3-8 times better in improving the user quality of service on trajectories when compared to greedy location-based base-station upgrades.

title: Network upgrading problems
abstract: Graphs with weights and delays associated with their edges and/or vertices are often used to model communication and signal flow networks. Network performance can be improved by upgrading the network vertices. Such an upgrade reduces the edge/vertex delays and comes at a cost. We study different formulations of this network performance improvement problem and show that these are NP-hard. We then consider one of the formulations and develop polynomial time algorithms for some special cases and pseudopolynomial time algorithms for others.

title: Suggesting ghost edges for a smaller world
abstract: Small changes in the network topology can have dramatic effects on its capacity to disseminate information. In this paper, we consider the problem of adding a small number of ghost edges in the network in order to minimize the average shortest-path distance between nodes, towards a smaller-world network. We formalize the problem of suggesting ghost edges and we propose a novel method for quickly evaluating the importance of ghost edges in sparse graphs. Through experiments on real and synthetic data sets, we demonstrate that our approach performs very well, for a varying range of conditions, and it outperforms sensible baselines.

title: Selecting Shortcuts for a Smaller World
abstract: The small world phenomenon is a desirable property of social networks, since it guarantees short paths between the nodes of the social graph and thus efficient information spread on the network. It is thus in the benefit of both network users and network owners to enforce and maintain this property. In this work, we study the problem of finding a subset of k edges from a set of candidate edges whose addition to a network leads to the greatest reduction in its average shortest path length. We formulate the problem as a combinatorial optimization problem, and show that it is NP-hard and that known approximation techniques are not applicable. We describe an efficient method for computing the exact effect of a single edge insertion on the average shortest path length, as well as several heuristics for efficiently estimating this effect. We perform experiments on real data to study the performance of our algorithms in practice.

title: Minimizing Eccentricity in Composite Networks via Constrained Edge Additions
abstract: In practical military or first responder deployment scenarios, information flows need to adhere to specified policies regardless of the physical connectivity of nodes. Nodes in such networks are associated with various levels in a command-and-control hierarchy, and therefore typically form a logical hierarchical tree network that is used to route both command and data traffic. Associated with this logical hierarchical network is a communication network that represents the connectivity of these nodes in the deployed scenario. Such composite networks introduce constraints that can result in information flows having to traverse much longer paths in the underlying communication network. In this paper, we look at the problem of adding edges to a logical hierarchical network (or any other social network) so as to minimize the number of hops required to route data traffic in the underlying communication network from a node to other specified nodes. The edges added are a subset of all possible edges in the complementary logical hierarchical graph and have to satisfy specified hierarchical constraints. First, we consider the general problem of minimizing the eccentricity of a source node 's' (where eccentricity of 's' is the maximum of the shortest paths from 's' to all other nodes) in a metric graph on adding upto 'B' unequal cost metric edges from the set of all edges in the complementary graph. We develop an efficient constant factor approximation algorithm for this case that outperforms existing constant factor algorithms for eccentricity minimization. Here the added edge metric cost as well as the graph edge metric cost correspond to the number of hops in the shortest path required to route traffic in the actual deployed topology (i.e., underlying communication network). Next, we consider the case where the set of possible added edges is a specified subset of the edges in the complementary graph and the set of destinations is a subset of the graph nodes. For this case, we develop heuristic algorithms based on the previous eccentricity minimizing algorithm that show good performance. We validate our algorithms using two realistic military deployment scenarios. We find that adding even a low number of hierarchically constrained edges (of the order of 10) can cause a significant decrease (around 50%) in the eccentricity of a node in the logical hierarchical network and thus can reduce the number of hops required for data traffic traversal.

title: Fast approximation of betweenness centrality through sampling
abstract: Betweenness centrality is a fundamental measure in social network analysis, expressing the importance or influence of individual vertices in a network in terms of the fraction of shortest paths that pass through them. Exact computation in large networks is prohibitively expensive and fast approximation algorithms are required in these cases. We present two efficient randomized algorithms for betweenness estimation. The algorithms are based on random sampling of shortest paths and offer probabilistic guarantees on the quality of the approximation. The first algorithm estimates the betweenness of all vertices: all approximated values are within an additive factor ɛ from the real values, with probability at least 1-δ. The second algorithm focuses on the top-K vertices with highest betweenness and approximate their betweenness within a multiplicative factor ɛ, with probability at least $1-δ. This is the first algorithm that can compute such approximation for the top-K vertices. We use results from the VC-dimension theory to develop bounds to the sample size needed to achieve the desired approximations. By proving upper and lower bounds to the VC-dimension of a range set associated with the problem at hand, we obtain a sample size that is independent from the number of vertices in the network and only depends on a characteristic quantity that we call the vertex-diameter, that is the maximum number of vertices in a shortest path. In some cases, the sample size is completely independent from any property of the graph. The extensive experimental evaluation that we performed using real and artificial networks shows that our algorithms are significantly faster and much more scalable as the number of vertices in the network grows than previously presented algorithms with similar approximation guarantees.

title: Group Centrality Maximization via Network Design
abstract: Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors. In hyperlinked environments, such as the Web, where users navigate via clicks, central content receives high traffic, becoming target for advertising campaigns. While there is an extensive amount of work on centrality measures and their efficient computation, controlling nodes’ centrality via network updates is a more recent and challenging task. Performing minimal modifications to a network to achieve a desired property falls under the umbrella of network design problems. This paper is focused on improving group (coverage and betweenness) centrality, which is a function of the shortest paths passing through a set of nodes, by adding edges to the network. Several variations of the problem, which are NP-hard as well as APX-hard, are introduced. We present a greedy algorithm, and even faster sampling algorithms, for group centrality maximization with theoretical quality guarantees under realistic constraints. The experimental results show that our sampling algorithms outperform the best baseline solution in terms of centrality by up to 5 times while being 2-3 orders of magnitude faster than our greedy approach.

title: On the Construction of Covert Networks
abstract: Centrality measures are widely used to identify leaders of covert networks. We study how a group of such leaders can avoid being detected by such measures. More concretely, we study the hardness of choosing a set of edges that can be added to the network in order to decrease the leaders' ranking according to two fundamental centrality measures, namely degree, and closeness. We prove that this problem is NP-complete for each measure. We then study how the leaders can construct a network from scratch, designed specifically for them to hide in disguise. We identify a network structure that not only guarantees to hide the leaders to a certain extent, but also allows them to spread their influence across the network.