Much research has been done on studying the diffusion of ideas or technologies on social networks including the textit{Influence Maximization} problem and many of its variations. Here, we investigate a type of inverse problem. Given a snapshot of the
diffusion process, we seek to understand if the snapshot is feasible for a given dynamic, i.e., whether there is a limited number of nodes whose initial adoption can result in the snapshot in finite time. While similar questions have been considered for epidemic dynamics, here, we consider this problem for variations of the deterministic Linear Threshold Model, which is more appropriate for modeling strategic agents. Specifically, we consider both sequential and simultaneous dynamics when deactivations are allowed and when they are not. Even though we show hardness results for all variations we consider, we show that the case of sequential dynamics with deactivations allowed is significantly harder than all others. In contrast, sequential dynamics make the problem trivial on cliques even though its complexity for simultaneous dynamics is unknown. We complement our hardness results with structural insights that can help better understand diffusions of social networks under various dynamics.
We study decentralized markets with the presence of middlemen, modeled by a non-cooperative bargaining game in trading networks. Our goal is to investigate how the network structure of the market and the role of middlemen influence the markets effici
ency and fairness. We introduce the concept of limit stationary equilibrium in a general trading network and use it to analyze how competition among middlemen is influenced by the network structure, how endogenous delay emerges in trade and how surplus is shared between producers and consumers.
In this paper we characterise the maximal convex subsets of the (non-convex) rate region in 802.11 WLANs. In addition to being of intrinsic interest as a fundamental property of 802.11 WLANs, this characterisation can be exploited to allow the wealth
of convex optimisation approaches to be applied to 802.11 WLANs.
In this paper we establish the log-convexity of the rate region in 802.11 WLANs. This generalises previous results for Aloha networks and has immediate implications for optimisation based approaches to the analysis and design of 802.11 wireless networks.
In this paper we build upon the recent observation that the 802.11 rate region is log-convex and, for the first time, characterise max-min fair rate allocations for a large class of 802.11 wireless mesh networks. By exploiting features of the 802.11e
/n MAC, in particular TXOP packet bursting, we are able to use this characterisation to establish a straightforward, practically implementable approach for achieving max-min throughput fairness. We demonstrate that this approach can be readily extended to encompass time-based fairness in multi-rate 802.11 mesh networks.
In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and where the s
ervice discipline is the max-weight policy. Under the assumption that the arrival processes satisfy a many-sources LDP, this is accomplished by employing Garcias extended contraction principle that is applicable to quasi-continuous mappings. For the simplex rate-region, an LDP for the stationary workload is also established under the additional requirements that the scheduling policy be work-conserving and that the arrival processes satisfy certain mixing conditions. The LDP results can be used to calculate asymptotic buffer overflow probabilities accounting for the multiplexing gain, when the arrival process is an average of emph{i.i.d.} processes. The rate function for the stationary workload is expressed in term of the rate functions of the finite-horizon workloads when the arrival processes have emph{i.i.d.} increments.
