[Show abstract][Hide abstract] ABSTRACT: In this paper, we study the connectivity of multihop wireless networks with the log-normal shadowing model by investigating the critical transmission power required by each node for asymptotic vanishing of the isolated nodes, and the precise distribution of the number of isolated nodes. The vanishing of isolated nodes is not only a prerequisite but also a good indication of network connectivity. Most of the known works on network connectivity under such a shadowing model were obtained only based on simulation studies or ignoring the important boundary effect to avoid the challenging technical analysis, and thus hardly applied to practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic shadowing model because the transmission area of each node is an irregular region other than a circular area. Assume the wireless nodes are represented by a Poisson point process with density \(n\) over a unit-area disk. With the boundary effect taken into consideration, we first obtain an explicit formula for the expected number of isolated nodes, we then derive an upper and a lower bounds of the critical transmission power for asymptotic vanishing of the isolated nodes. The tightness of the upper and lower bounds for the critical transmission power are analyzed via numerical analysis by using the software engineering approach. When a wireless network consists of \(n\) nodes distributed independently and uniformly over a unit-area disk, we derive the precise distribution of the number of the isolated nodes under such a realistic shadowing model with the linear power assignment, taking the boundary effect into consideration.
[Show abstract][Hide abstract] ABSTRACT: One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. We study the coverage of a line interval with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor whose length is decided by the power the sensor chooses. The objective is to find a range assignment with the minimum cost. There are two variants of the optimization problem. In the discrete variant, each sensor can only choose from a finite set of powers, whereas in the continuous variant, each sensor can choose power from a given interval. For the discrete variant of the problem, a polynomial-time exact algorithm is designed. For the continuous variant of the problem, NP-hardness of the problem is proved and followed by an ILP formulation. Then, constant-approximation algorithms are designed when the cost for all sensors is proportional to rκfor some constant κ ≥ 1, where r is the covering radius corresponding to the chosen power. Specifically, if κ = 1, we give a 1.25-approximation algorithm and a fully polynomial-time approximation scheme; if κ > 1, we give a 2-approximation algorithm. We also show that the approximation analyses are tight.
[Show abstract][Hide abstract] ABSTRACT: Multiple-input multiple-output (MIMO) technology provides a means of boosting network capacity without requiring additional spectrum. It has received widespread attention over the past decade from both industry and academic researchers, now forming a key component of nearly all emerging wireless standards. Despite the huge promise and considerable attention, a rigorous algorithm-theoretic framework for maximizing network capacity in multihop wireless MIMO\ networks is missing in the state of the art. The existing algorithms and protocols for maximizing network capacity in multihop wireless MIMO networks are purely heuristic without any provable performance guarantees. In this paper we conduct a comprehensive algorithm study for maximizing network capacity in multihop wireless MIMO networks with receiver-side interference suppression, including the full characterization of NP-hardness and APX-hardness, the polynomial time approximation schemes, and the practical approximation algorithms with provable performance guarantees.
[Show abstract][Hide abstract] ABSTRACT: Maximum multiflow and maximum concurrent mul-tiflow in multi-channel multi-radio (MC-MR) wireless networks have been well-studied in the literature. They are NP-hard even in single-channel single-radio (SC-SR) wireless networks when all nodes have uniform (and fixed) interference radii and the positions of all nodes are available. While they admit a polynomial-time approximation scheme (PTAS) when the number of channels is bounded by a constant, such PTAS is quite infeasible practically. Other than the PTAS, all other known approximation algorithms, in both SC-SR wireless networks and MC-MR wireless networks, resorted to solve a polynomial-sized linear program (LP) exactly. The scalability of their running time is fundamentally limited by the general-purposed LP solvers. In this paper, we first introduce the concept of interference costs and prices of a path and explore their relations with the maximum (concurrent) multiflow. Then we develop purely combinatorial approximation algorithms which compute a sequence of least interference-cost routing paths along which the flows are routed. These algorithms are faster and simpler, and achieve nearly the same approximation bounds known in the literature.
IEEE INFOCOM 2014 - IEEE Conference on Computer Communications; 04/2014
[Show abstract][Hide abstract] ABSTRACT: Finding a maximum-weighted independent set of links is a fundamental problem in wireless networking and has broad applications in various wireless link scheduling problems. Under protocol interference model, it is NP-hard even when all nodes have uniform (and fixed) interference radii and the positions of all nodes are available. On one hand, it admits a polynomial-time approximation scheme (PTAS). In other words, for any fixed ε > 0, it has a polynomial-time (depending on ε) (1 + ε)-approximation algorithm. However, such PTAS is of theoretical interest only and is quite infeasible practically. On the other hand, only with the uniform interference radii is a simple (greedy) constant-approximation algorithm known. For the arbitrary interference radii, fast constant-approximation algorithms are still missing. In this paper, we present a number of fast and simple approximation algorithms under the general protocol interference model. When applied to the plane geometric variants of the protocol interference model, these algorithms produce constant-approximate solutions efficiently.
IEEE INFOCOM 2014 - IEEE Conference on Computer Communications; 04/2014
[Show abstract][Hide abstract] ABSTRACT: We are in an age where people are paying increasing attention to energy conservation around the world. The heating and air-conditioning systems of buildings introduce one of the largest chunks of energy expenses. In this article, we make a key observation that after a meeting or a class ends in a room, the indoor temperature will not immediately increase to the outdoor temperature. We call this phenomenon thermal inertia. Thus, if we arrange subsequent meetings in the same room rather than in a room that has not been used for some time, we can take advantage of such undissipated cool or heated air and conserve energy. Though many existing energy conservation solutions for buildings can intelligently turn off facilities when people are absent, we believe that understanding thermal inertia can lead system designs to go beyond on-and-off-based solutions to a wider realm. We propose a framework for exploring thermal inertia in room management. Our framework contains two components. (1) The energy-temperature correlation model captures the relation between indoor temperature change and energy consumption. (2) The energy-aware scheduling algorithms: given information for the relation between energy and temperature change, energy-aware scheduling algorithms arrange meetings not only based on common restrictions, such as meeting time and room capacity requirement, but also energy consumptions. We identify the interface between these components so further works towards same on direction can make efforts on individual components. We develop a system to verify our framework. First, it has a wireless sensor network to collect indoor, outdoor temperature and electricity expenses of the heating or air-conditioning devices. Second, we build an energy-temperature correlation model for the energy expenses and the corresponding room temperature. Third, we develop room scheduling algorithms. In detail, we first extend the current sensor hardware so that it can record the electricity expenses in re-heating or re-cooling a room. As the sensor network needs to work unattendedly, we develop a hardware board for long-range communications so that the Imote2 can send data to a remote server without a computer relay close by. An efficient two-tiered sensor network is developed with our extended Imote2 and TelosB sensors. We apply laws of thermodynamics and build a correlation model of the energy needed to re-cool a room to a target temperature. Such model requires parameter calibration and uses the data collected from the sensor network for model refinement. Armed with the energy-temperature correlation model, we develop an optimal algorithm for a specified case, and we further develop two fast heuristics for different practical scenarios. Our demo system is validated with real deployment of a sensor network for data collection and thermodynamics model calibration. We conduct a comprehensive evaluation with synthetic room and meeting configurations, as well as real class schedules and classroom topologies of The Hong Kong Polytechnic University, academic calendar year of Spring 2011. We observe 20% energy savings as compared with the current schedules.
[Show abstract][Hide abstract] ABSTRACT: This paper addresses the joint selection and power assignment of a largest number of given links which can communicate successfully at the same time under the physical interference model. For this optimization problem, we present a constant-approximation algorithm with improved performance over existing approximation algorithms. In addition, both the algorithm design and analysis are applicable to arbitrary path-loss exponent and arbitrary dimension of the deployment space.
Proceedings of the 8th international conference on Wireless Algorithms, Systems, and Applications; 08/2013
[Show abstract][Hide abstract] ABSTRACT: 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.
Proceedings of the 8th international conference on Wireless Algorithms, Systems, and Applications; 08/2013
[Show abstract][Hide abstract] ABSTRACT: Static greedy link schedulings have much simpler implementation than dynamic greedy link schedulings such as Longest-queue-first (LQF) link scheduling. However, its stability performance in multi-channel multi-radio (MC-MR) wireless networks is largely under-explored. In this paper, we present a stability subregion with closed form of a static greedy link scheduling in MC-MR wireless networks under the 802.11 interference model. By adopting some special static link orderings, the stability subregion is within a constant factor of the stable capacity region of the network. We also obtain constant lower bounds on the throughput efficiency ratios of the static greedy link schedulings in some special static link orderings.
[Show abstract][Hide abstract] ABSTRACT: A wireless node is called isolated if it has no links to other nodes. The number of isolated nodes in a wireless network is an important connectivity index. However, most previous works on analytically determining the number of isolated nodes were not based on practical channel models. In this work, we study this problem using a generic probabilistic channel model that can capture the behaviors of the most widely used channel models, including the disk graph model, the Bernoulli link model, the Gaussian white noise model, the Rayleigh fading model, and the Nakagami fading model. We derive the expected number of isolated nodes and further prove that their distribution asymptotically follows a Poisson distribution. We also conjecture that the nonexistence of isolated nodes asymptotically implies the connectivity of the network, and that the probability of connectivity follows the Gumbel function.
[Show abstract][Hide abstract] ABSTRACT: For wireless link scheduling in multi-channel multi-radio wireless networks aiming at maximizing (concurrent) multi-flow, constant-approximation algorithms have recently been developed in [11]. However, the running time of those algorithms grows quickly with the number of radios per node (at least in the sixth order) and the number of channels (at least in the cubic order). Such poor scalability stems intrinsically from the exploding size of the fine-grained network representation upon which those algorithms are built. In this paper, we introduce a new structure, termed as concise conflict graph, on the node-level links directly. Such structure succinctly captures the essential advantage of multiple radios and multiple channels. By exploring and exploiting the rich structural properties of the concise conflict graphs, we are able to develop fast and scalable link scheduling algorithms for either minimizing the communication latency or maximizing the (concurrent) multi-flow. These algorithms have running time growing linearly in both the number of radios per node and the number of channels, while not sacrificing the approximation bounds.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: Although Min-CDS in general graphs is hard to approximate, the restriction to certain special graph classes admits much better approximation results. Min-CDS in planar graphs remains NP-hard even for planar graphs that are regular of degree 4 [57]. The related problem, Min-DS in planar graphs, is also NP-hard even for planar graphs with maximum vertex degree 3 and planar graphs that are regular of degree 4 [57]. It is well known that Min-DS in planar graphs possesses a polynomial-time approximation scheme (PTAS) based on the shifting strategy [3]: For any constant ε >0, there is a polynomial-time 1+ε-approximation algorithm. Thus, it is immediate to conclude that Min-CDS in planar graphs can be approximated within a factor 3+ε for any ε>0 in polynomial time. However, the degree of the polynomial grows with 1∕ε and hence, the approximation scheme is hardly practical.
Connected Dominating Set: Theory and Applications, 01/2013: pages 183-191;
[Show abstract][Hide abstract] ABSTRACT: A classic type of resource management problem is as follows: Given a certain amount of resource and a set of users, find an assignment of resource to maximize the number of satisfied users. The maximum lifetime coverage is such a classic type of problem in wireless sensor networks.
Connected Dominating Set: Theory and Applications, 01/2013: pages 105-118;
[Show abstract][Hide abstract] ABSTRACT: Consider a multihop wireless network in which all network nodes V lie in plane and have a unit communication radius. Its communication topology G is the unit disk graph (UDG) of V. Under the protocol interference model, every node has a communication radius normalized to one, and an interference radius ρ for some parameter ρ ≥ 1 (see Fig. 11.1). A node v can receive the message successfully from a transmitting node u if v is within the transmission range of u but is outside the interference range of any other node transmitting simultaneously.
Connected Dominating Set: Theory and Applications, 01/2013: pages 169-182;
[Show abstract][Hide abstract] ABSTRACT: Consider a finite set V of nodes in the plane and a radius function \(r : V \rightarrow {\rm IR}^{+}\). The disk-intersection graph (DIG) of V with the radius function r, denoted by \({G}_{r}\left (V \right )\), is the undirected graph on V in which u and v are adjacent if and only if the disk centered at u of radius \(r\left (u\right )\) and the disk centered at v of radius \(r\left (v\right )\) intersect, or equivalently, $$\left \Vert uv\right \Vert \leq r\left (u\right ) + r\left (v\right ).$$ If \(r\left (v\right ) = 1/2\) for all v ∈ V, then \({G}_{r}\left (V \right )\) is exactly the unit disk graph (UDG) of V.
Connected Dominating Set: Theory and Applications, 01/2013: pages 151-159;
[Show abstract][Hide abstract] ABSTRACT: This paper presents a theoretical analysis of the maximum throughput of a wireless mesh backhaul network that is achievable over a practical carrier sense multiple access with collision avoidance (CSMA/CA) medium access control (MAC) protocol. We resort to the multicommodity flow (MCF) formulation augmented with the conflict-graph constraints, whereas we use a novel approach to take into account the collision overhead in the distributed CSMA/CA MAC. Such overhead due to random access has been ignored by existing MCF-based capacity studies, which assume impractical centralized scheduling and result in aggressive capacity planning, which is unachievable over the CSMA/CA MAC. This paper makes the following three main contributions: 1) we develop a generic method of integrating the CSMA/CA MAC analysis with the MCF formulation for optimal network capacity analysis, which readily generates an upper bound of the network throughput; 2) we define a new concept of CSMA/CA clique and theoretically study its relationship to a CSMA/CA area in terms of throughput; and 3) using the CSMA/CA clique as a tool, we derive a lower bound of the network throughput achievable over the CSMA/CA MAC by clique-based MCF formulation. NS-2 simulation results are presented to demonstrate the tightness of the upper and lower bounds that are newly developed, compared to those based on the MCF formulation assuming a slotted system and centralized scheduling.
[Show abstract][Hide abstract] ABSTRACT: A wide range of next generation wireless networks are based on the multiradio multichannel (MR-MC) network model. A full exploration of the MR-MC wireless network capacity incurs challenging cooperative networking issues including transmission cooperation, resource allocation cooperation, and cross-layer protocol cooperation. In this article, rather than focus on protocol designs for specific cooperative networking issues, we present a generic theoretical framework that could guide the protocol or algorithm development to approach the maximum network capacity. Based on our multidimensional conflict graph (MDCG) tool, we could achieve a cross-layer linear programming framework to study the optimal cooperative networking in two complementary aspects: optimal network dimensioning and throughputoptimal control. While certain NP-hard computing issues hindered the MR-MC network optimization for a long time, the MDCG-based framework can readily generate simple polynomial and distributed algorithms with guaranteed capacity region.
[Show abstract][Hide abstract] ABSTRACT: Data aggregation, as a primitive communication task in wireless networks, can reduce the communication complexity. However, in-network aggregation usually brings an unavoidable security defect. Some malicious nodes may control a large percentage of the whole network data and compel the network misbehave in an arbitrary manner. Thus, locating the malicious nodes to prevent them from further disaster is a practical challenge for data aggregation schemes. Based on the grouping and localization techniques, we propose a novel integrated protocol to locate malicious nodes. The proposed protocol does not rely on any special hardware and requests only incomplete information of the network from the security schemes. We also conduct simulation study to evaluate the proposed protocol.