Since wireless channel is vulnerable to eavesdroppers, the secrecy during message delivery is a major concern in many applications such as commercial, governmental, and military networks. This paper investigates information-theoretic secrecy in large-scale networks and studies how capacity is affected by the secrecy constraint where the locations and channel state information (CSI) of eavesdroppers are both unknown. We consider two scenarios: 1) noncolluding case where eavesdroppers can only decode messages individually; and 2) colluding case where eavesdroppers can collude to decode a message. For the noncolluding case, we show that the network secrecy capacity is not affected in order-sense by the presence of eavesdroppers. For the colluding case, the per-node secrecy capacity of $\Theta({1 \over \sqrt{n}})$ can be achieved when the eavesdropper density $\psi_e(n)$ is $O(n^{-\beta})$ , for any constant $\beta > 0$ and decreases monotonously as the density of eavesdroppers increases. The upper bounds on network secrecy capacity are derived for both cases and shown to be achievable by our scheme when $\psi_e(n)=O(n^{-\beta})$ or $\psi_e(n)=\Omega(\log^{\alpha-2 \over \alpha}n)$, where $\alpha$ is the path-loss gain. We show that there is a clear tradeoff between the security constraints and the achievable capacity. Furthermore, we also investigate the impact of secrecy constraint on the capacity of dense network, the impact of active attacks and other traffic patterns, as well as mobility models in the context.

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Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks

Minimizing latency is of primary importance for data aggregation which is an essential application in wireless sensor networks. Many fast data aggregation algorithms under the protocol interference model have been proposed, but the model falls short of being an accurate abstraction of wireless interferences in reality. In contrast, the physical interference model has been shown to be more realistic and has the potential to increase the network capacity when adopted in a design. It is a challenge to derive a distributed solution to latency-minimizing data aggregation under the physical interference model because of the simple fact that global-scale information to compute the cumulative interference is needed at any node. In this paper, we propose a distributed algorithm that aims to minimize aggregation latency under the physical interference model in wireless sensor networks of arbitrary topologies. The algorithm uses O(K) time slots to complete the aggregation task, where K is the logarithm of the ratio between the lengths of the longest and shortest links in the network. The key idea of our distributed algorithm is to partition the network into cells according to the value K, thus obviating the need for global information. We also give a centralized algorithm which can serve as a benchmark for comparison purposes. It constructs the aggregation tree following the nearest-neighbor criterion. The centralized algorithm takes O( logn) and O(log^3n) time slots when coupled with two existing link scheduling strategies, respectively (where n is the total number of nodes), which represents the current best algorithm for the problem in the literature. We prove the correctness and efficiency of our algorithms, and conduct empirical studies under realistic settings to validate our analytical results.

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Latency-minimizing data aggregation in wireless sensor networks under physical interference model

Wireless sensor networks (WSNs) consist of a large number of battery-powered wireless sensor nodes, and one key issue in WSNs is to reduce the energy consumption while maintaining the normal functions of WSNs. Data aggregation, as a typical operation in data gathering applications, can cause a lot of energy wastage since sensor nodes, when not receiving data, may keep in the listen state during the data collection process. To save this energy wastage, sleep scheduling algorithms can be used to turn the nodes to the sleep state when their radios are not in use and wake them up when necessary. In this paper, we identify the contiguous link scheduling problem in WSNs, in which each node is assigned consecutive time slots so that the node can wake up only once in a scheduling period to fulfil its data collection task. The objective of the problem is to find an interference-free link scheduling with the minimum number of time slots used. In virtue of the contiguous link scheduling, the energy consumption caused by nodes' state transitions can be reduced. We prove the contiguous link scheduling problem in WSNs to be NP-complete, and then present efficient centralized and distributed algorithms with theoretical performance bounds in both homogeneous and heterogeneous networks. We also conduct simulation experiments that corroborate the theoretical results and demonstrate the efficiency of our proposed algorithms.

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Contiguous Link Scheduling for Data Aggregation in Wireless Sensor Networks

We consider scheduling problems in wireless networks with respect to flexible data rates. That is, more or less data can be transmitted per time depending on the signal quality, which is determined by the signal-to-interference-plus-noise ratio (SINR). Each wireless link has a utility function mapping SINR values to the respective data rates. We have to decide which transmissions are performed simultaneously and (depending on the problem variant) also which transmission powers are used. 
In the capacity-maximization problem, one strives to maximize the overall network throughput, i.e., the summed utility of all links. For arbitrary utility functions (not necessarily continuous ones), we present an O(log n)-approximation when having n communication requests. This algorithm is built on a constant-factor approximation for the special case of the respective problem where utility functions only consist of a single step. In other words, each link has an individual threshold and we aim at maximizing the number of links whose threshold is satisfied. On the way, this improves the result in [Kesselheim, SODA 2011] by not only extending it to individual thresholds but also showing a constant approximation factor independent of assumptions on the underlying metric space or the network parameters. 
In addition, we consider the latency-minimization problem. Here, each link has a demand, e.g., representing an amount of data. We have to compute a schedule of shortest possible length such that for each link the demand is fulfilled, that is the overall summed utility (or data transferred) is at least as large as its demand. Based on the capacity-maximization algorithm, we show an O(log^2 n)-approximation for this problem.

Approximation Algorithms for Wireless Link Scheduling with Flexible Data Rates

We consider scheduling problems in wireless networks with respect to flexible data rates. That is, more or less data can be transmitted per time depending on the signal quality, which is determined by the signal-to-interference-plus-noise ratio (SINR). Each wireless link has a utility function mapping SINR values to the respective data rates. We have to decide which transmissions are performed simultaneously and (depending on the problem variant) also which transmission powers are used.

In the capacity-maximization problem, one strives to maximize the overall network throughput, i.e., the summed utility of all links. For arbitrary utility functions (not necessarily continuous ones), we present an O(logn)-approximation when having n communication requests. This algorithm is built on a constant-factor approximation for the special case of the respective problem where utility functions only consist of a single step. In other words, each link has an individual threshold and we aim at maximizing the number of links whose threshold is satisfied. On the way, this improves the result in [Kesselheim, SODA 2011] by not only extending it to individual thresholds but also showing a constant approximation factor independent of assumptions on the underlying metric space or the network parameters.

In addition, we consider the latency-minimization problem. Here, each link has a demand, e.g., representing an amount of data. We have to compute a schedule of shortest possible length such that for each link the demand is fulfilled, that is, the overall summed utility (or data transferred) is at least as large as its demand. Based on the capacity-maximization algorithm, we show an O(log2n)-approximation for this problem.

Approximation algorithms for wireless link scheduling with flexible data rates

This paper addresses the join selection and power assignment of a largest set of given links which can communicate successfully at the same time under the physical interference model in the simplex mode. For the special setting in which all nodes have unlimited maximum transmission power, Kesselheim [8] developed an constant approximation algorithm. For the general setting in which all nodes have bounded maximum transmission power, the existence of constant approximation algorithm remains open. In this paper, we resolve this open problem by developing a constant-approximation algorithm for the general setting in which all nodes have bounded maximum transmission power.

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Maximizing capacity with power control under physical interference model in simplex mode

Link scheduling is a fundamental design issue in multihop wireless networks. All existing link scheduling algorithms require the precise information of the positions, and/or communication/interference radii of all nodes. For practical networks, it is not only difficult or expensive to obtain these parameters, but also often impossible to get their precise values. The link scheduling determined by the imprecise values of these parameters may fail to guarantee the same approximation bounds of the link scheduling determined by precise values. Therefore, the existing link scheduling algorithms lack performance robustness. In this paper, we propose a robust link scheduling, which can be easily computed with only the information on whether a given pair of links have conflict or not and therefore is robust. In addition, our link scheduling does not compromise the approximation bound and indeed sometimes can achieve better approximation bound. Particularly, under the 802.11 interference model, its approximation bound is 16 in general and 6 with uniform interference radii, an improvement over the respective best-known approximation bounds 23 and 7.

Weighted wireless link scheduling without information of positions and interference/communication radii

Maximizing the wireless network capacity under physical interference model is notoriously hard due to the nonlocality and the additive nature of the wireless interference under the physical interference model. This problem has been extensively studied recently with the achievable approximation bounds progressively improved from the linear factor to logarithmic factor. It has been a major open problem whether there exists a constant-approximation approximation algorithm for maximizing the wireless network capacity under the physical interference model. In this paper, we improve the status quo for the case of linear transmission power assignment, which is widely adopted due to its advantage of energy conservation. By exploring and exploiting the rich nature of the wireless interference with the linear power assignment, we develop constant-approximation algorithms for maximizing the wireless network capacity with linear transmission power assignment under the physical interference model, in both the unidirectional mode and the bidirectional mode.

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Maximizing wireless network capacity with linear power: Breaking the logarithmic barrier

We study the multicast capacity of a random wireless network consisting of n randomly placed ordinary wireless nodes and m regularly placed base stations in a square region, known as a hybrid network. All ordinary wireless nodes have the uniform transmission range r and uniform interference range R=θ(r) and they can transmit/receive at Wa-bps. Each base station can communicate with adjacent base stations directly with a data rate WB-bps and the data transmission rate between a base station and a wireless node is assumed to be Wc-bps. Assume that there is a random set of ns ordinary wireless nodes that will serve as the source nodes of ns multicast flows (each has randomly selected k-1 receivers). Each flow will have data rate λi bps. We found that the minimum per-flow multicast capacity min ns over i = 1 λi for hybrid networks has three regimes, and for each regime we derive matching asymptotic upper and lower bounds. Thus it closes the gap of previous results in the literature.

Closing the gap in the multicast capacity of hybrid wireless networks

This paper studies the problem of selecting a maximum independent set of links with a fixed monotone and sublinear power assignment under the physical interference model. The best-known approximation bound for this problem is a very large constant. In this paper, we present an approximation algorithm for this problem, which not only has a much smaller approximation bound but also produces an independent set of links with a stronger property, i.e., strong independence.

Chao Ma

Papers

Maximizing capacity with power control under physical interference model in simplex mode

Weighted wireless link scheduling without information of positions and interference/communication radii

Maximizing wireless network capacity with linear power: Breaking the logarithmic barrier

Closing the gap in the multicast capacity of hybrid wireless networks

Maximum independent set of links with a monotone and sublinear power assignment