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

Monitoring applications define an important class of applications used in wireless sensor networks In these applications the network perceives the environment and searches for event occurrences (phenomena) by sensing different physical properties, such as temperature, humidity, pressure, ambient light, movement, and presence (for target tracking) In such cases the location information of both phenomena and nodes is usually required for tracking and correlation purposes In this work we summarize most of the concepts related to localization systems for WSNs as well as how to localize the nodes in these networks (which allows the localization of phenomena) By dividing the localization systems into three distinct components -distance/angle estimation, position computation, and localization algorithm - besides providing a didactic viewpoint, we show that these components can be seen as subareas of the localization problem that need to be analyzed and studied separately

http://sarstudent.persiangig.com/Book/search2/11_localization%20system%20for%20wsn.pdf

Localization systems for wireless sensor networks

The usefulness of mobile devices has increased greatly in recent years allowing users to perform more tasks in a mobile context. This increase in usefulness has come at the expense of the usability of these devices in some contexts. We conducted a small review of mobile usability models and found that usability is usually measured in terms of three attributes; effectiveness, efficiency and satisfaction. Other attributes, such as cognitive load, tend to be overlooked in the usability models that are most prominent despite their likely impact on the success or failure of an application. To remedy this we introduces the PACMAD (People At the Centre of Mobile Application Development) usability model which was designed to address the limitations of existing usability models when applied to mobile devices. PACMAD brings together significant attributes from different usability models in order to create a more comprehensive model. None of the attributes that it includes are new, but the existing prominent usability models ignore one or more of them. This could lead to an incomplete usability evaluation. We performed a literature search to compile a collection of studies that evaluate mobile applications and then evaluated the studies using our model.

/pdf/usability-of-mobile-applications-literature-review-and-2sgkvggy18.pdf

Usability of mobile applications: literature review and rationale for a new usability model

Ingredients of Locational Analysis (J. Krarup & P. Pruzan). The p-Median Problem and Generalizations (P. Mirchandani). The Uncapacitated Facility Location Problem (G. Cornuejols, et al.). Multiperiod Capacitated Location Models (S. Jacobsen). Decomposition Methods for Facility Location Problems (T. Magnanti & R. Wong). Covering Problems (A. Kolen & A. Tamir). p-Center Problems (G. Handler). Duality: Covering and Constraining p-Center Problems on Trees (B. Tansel, et al.). Locations with Spatial Interactions: The Quadratic Assignment Problem (R. Burkard). Locations with Spatial Interactions: Competitive Locations and Games (S. Hakimi). Equilibrium Analysis for Voting and Competitive Location Problems (P. Hansen, et al.). Location of Mobile Units in a Stochastic Environment (O. Berman, et al.). Index.

https://link.springer.com/content/pdf/10.1057%2Fjors.1991.208.pdf

Discrete location theory

The concept of physical-layer network coding (PNC) was proposed in 2006 for application in wireless networks. Since then it has developed into a subfield of network coding with wide followings. The basic idea of PNC is to exploit the network coding operation that occurs naturally when electromagnetic (EM) waves are superimposed on one another. This simple idea turns out to have profound and fundamental ramifications. Subsequent works by various researchers have led to many new results in the domains of 1) wireless communication; 2) wireless information theory; and 3) wireless networking. The purpose of this paper is fourfold. First, we give a brief tutorial on the basic concept of PNC. Second, we survey and discuss recent key results in the three aforementioned areas. Third, we examine a critical issue in PNC: synchronization. It has been a common belief that PNC requires tight synchronization. Our recent results suggest, however, that PNC may actually benefit from asynchrony. Fourth, we propose that PNC is not just for wireless networks; it can also be useful in optical networks. We provide an example showing that the throughput of a passive optical network (PON) could potentially be raised by 100% with PNC.

Physical-Layer Network Coding: Tutorial, Survey, and Beyond

In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NP-completeness proofs in such a model. In particular, we prove two problems to be NP-complete: Scheduling and One-Shot Scheduling. The first problem consists in finding a minimum-length schedule for a given set of links. The second problem receives a weighted set of links as input and consists in finding a maximum-weight subset of links to be scheduled simultaneously in one shot. In addition to the complexity proofs, we devise an approximation algorithm for each problem.

Complexity in geometric SINR

In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are single-hop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on special-case topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the network's topology. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one time-slot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higher-dimensional Euclidean spaces, and to more realistic bounded-distortion spaces, induced by non-isotropic signal distortions. Finally, we show that it is NP-hard to approximate the scheduling problem to within n 1-epsiv factor, for any constant epsiv > 0, in the non-geometric SINR model, in which path-loss is independent of the Euclidean coordinates of the nodes.

/pdf/capacity-of-arbitrary-wireless-networks-1rkmd3t8t9.pdf

Capacity of Arbitrary Wireless Networks

In this work we analyze the complexity of local broadcasting in the physical interference model. We present two distributed randomized algorithms: one that assumes that each node knows how many nodes there are in its geographical proximity, and another, which makes no assumptions about topology knowledge. We show that, if the transmission probability of each node meets certain characteristics, the analysis can be decoupled from the global nature of the physical interference model, and each node performs a successful local broadcast in time proportional to the number of neighbors in its physical proximity. We also provide worst-case optimality guarantees for both algorithms and demonstrate their behavior in average scenarios through simulations.

Local broadcasting in the physical interference model

In this monograph we survey results from a newly emerging line of research that targets algorithm analysis in the physical interference model. In the main part of our monograph we focus on wireless scheduling: given a set of communication requests, arbitrarily distributed in space, how can these requests be scheduled efficiently? We study the difficulty of this problem and we examine algorithms for wireless scheduling with provable performance guarantees. Moreover, we present a few results for related problems and give additional context.

/pdf/efficiency-of-wireless-networks-approximation-algorithms-for-2yn6tkl3fj.pdf

Efficiency of Wireless Networks : Approximation Algorithms for the Physical Interference Model

In this paper, we address two basic questions in wireless communication. First, how long does it take to schedule an arbitrary set of communication requests? Second, given a set of communication requests, how many of them can be scheduled concurrently? Our results are derived in the signal-to-interference-plus-noise ratio (SINR) interference model with geometric path loss and consist of efficient algorithms that find a constant approximation for the second problem and a logarithmic approximation for the first problem. In addition, we show that the interference model is robust to various factors that can influence the signal attenuation. More specifically, we prove that as long as influences on the signal attenuation are constant, they affect the capacity only by a constant factor.

Olga Goussevskaia

Papers

Complexity in geometric SINR

Capacity of Arbitrary Wireless Networks

Local broadcasting in the physical interference model

Efficiency of Wireless Networks : Approximation Algorithms for the Physical Interference Model

Algorithms for wireless capacity