We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

We introduce a system for sensing complex social systems with data collected from 100 mobile phones over the course of 9 months. We demonstrate the ability to use standard Bluetooth-enabled mobile telephones to measure information access and use in different contexts, recognize social patterns in daily user activity, infer relationships, identify socially significant locations, and model organizational rhythms.

/pdf/reality-mining-sensing-complex-social-systems-2gf3rdnw3x.pdf

Reality mining: sensing complex social systems

National Institute of Standards and Technology における超伝導研究及び生活

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems In many cases, however, the edges are not continuously active As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts In some cases, edges are active for non-negligible periods of time: eg, the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

Temporal Networks

Pocket Switched Networks (PSN) make use of both human mobility and local/global connectivity in order to transfer data between mobile users' devices. This falls under the Delay Tolerant Networking (DTN) space, focusing on the use of opportunistic networking. One key problem in PSN is in designing forwarding algorithms which cope with human mobility patterns. We present an experiment measuring forty-one humans' mobility at the Infocom 2005 conference. The results of this experiment are similar to our previous experiments in corporate and academic working environments, in exhibiting a power-law distrbution for the time between node contacts. We then discuss the implications of these results on the design of forwarding algorithms for PSN.

/pdf/pocket-switched-networks-and-human-mobility-in-conference-3if076v0nc.pdf

Pocket switched networks and human mobility in conference environments

We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes; 1 day]. This observation is confirmed using eight distinct experimental data sets. It is at odds with the exponential decay implied by the most commonly used mobility models. In this paper, we study how this newly uncovered characteristic of human mobility impacts one class of forwarding algorithms previously proposed. We use a simplified model based on the renewal theory to study how the parameters of the distribution impact the performance in terms of the delivery delay of these algorithms. We make recommendations for the design of well-founded opportunistic forwarding algorithms in the context of human-carried devices

/pdf/impact-of-human-mobility-on-opportunistic-forwarding-46zeuyk4ja.pdf

Impact of Human Mobility on Opportunistic Forwarding Algorithms

Studying transfer opportunities between wireless devices carried by humans, we observe that the distribution of the inter-contact time, that is the time gap separating two contacts of the same pair of devices, exhibits a heavy tail such as one of a power law, over a large range of value. This observation is confirmed on six distinct experimental data sets. It is at odds with the exponential decay implied by most mobility models. In this paper, we study how this new characteristic of human mobility impacts a class of previously proposed forwarding algorithms. We use a simplified model based on the renewal theory to study how the parameters of the distribution impact the delay performance of these algorithms. We make recommendation for the design of well founded opportunistic forwarding algorithms, in the context of human carried devices.

/pdf/impact-of-human-mobility-on-the-design-of-opportunistic-1vnrx9ap6z.pdf

Impact of Human Mobility on the Design of Opportunistic Forwarding Algorithms

Mobile opportunistic networks are characterized by unpredictable mobility, heterogeneity of contact rates and lack of global information. Successful delivery of messages at low costs and delays in such networks is thus challenging. Most forwarding algorithms avoid the cost associated with flooding the network by forwarding only to nodes that are likely to be good relays, using a quality metric associated with nodes. However it is non-trivial to decide whether an encountered node is a good relay at the moment of encounter. Thus the problem is in part one of online inference of the quality distribution of nodes from sequential samples, and has connections to optimal stopping theory. Based on these observations we develop a new strategy for forwarding, which we refer to as delegation forwarding.We analyse two variants of delegation forwarding and show that while naive forwarding to high contact rate nodes has cost linear in the population size, the cost of delegation forwarding is proportional to the square root of population size. We then study delegation forwarding with different metrics using real mobility traces and show that delegation forwarding performs as well as previously proposed algorithms at much lower cost. In particular we show that the delegation scheme based on destination contact rate does particularly well.

Delegation forwarding

We study the dissemination of dynamic content, such as news or traffic information, over a mobile social network. In this application, mobile users subscribe to a dynamic-content distribution service, offered by their service provider. To improve coverage and increase capacity, we assume that users share any content updates they receive with other users they meet. We make two contributions. First, we determine how the service provider can allocate its bandwidth optimally to make the content at users as "fresh" as possible. More precisely, we define a global fairness objective (namely, maximizing the aggregate utility over all users) and prove that the corresponding optimization problem can be solved by gradient descent. Second, we specify a condition under which the system is highly scalable: even if the total bandwidth dedicated by the service provider remains fixed, the expected content age at each user grows slowly (as log(n)) with the number of users n. To the best of our knowledge, our work is the first to address these two aspects (optimality and scalability) of the distribution of dynamic content over a mobile social network.

/pdf/optimal-and-scalable-distribution-of-content-updates-over-a-143dwf5w5f.pdf

Augustin Chaintreau

Papers

Pocket switched networks and human mobility in conference environments

Impact of Human Mobility on Opportunistic Forwarding Algorithms

Impact of Human Mobility on the Design of Opportunistic Forwarding Algorithms

Delegation forwarding

Optimal and scalable distribution of content updates over a mobile social network