Connectivity guarantees for wireless networks with directional antennas

We study a combinatorial geometric problem related to the design of wireless networks with directional antennas. Specifically, we are interested in necessary and sufficient conditions on such antennas that enable one to build a connected communication network, and in efficient algorithms for building such networks when possible.We formulate the problem by a set P of n points in the plane, indicating the positions of n transceivers. Each point is equipped with an α-degree directional antenna, and one needs to adjust the antennas (represented as wedges), by specifying their directions, so that the resulting (undirected) communication graph G is connected. (Two points p,q∈P are connected by an edge in G, if and only if q lies in p?s wedge and p lies in q?s wedge.) We prove that if α=60°, then it is always possible to adjust the wedges so that G is connected, and that α?60° is sometimes necessary to achieve this. Our proof is constructive and yields an time algorithm for adjusting the wedges, where k is the size of the convex hull of P.Sometimes it is desirable that the communication graph G contain a Hamiltonian path. By a result of Fekete and Woeginger (1997) [8], if α=90°, then it is always possible to adjust the wedges so that G contains a Hamiltonian path. We give an alternative proof to this, which is interesting, since it produces paths of a different nature than those produced by the construction of Fekete and Woeginger. We also show that for any n and ε>0, there exist sets of points such that G cannot contain a Hamiltonian path if α=90°−ε.     

Bounded-hops power assignment in ad hoc wireless networks

Motivated by topology control in ad hoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity). The input consists of a directed complete weighted digraph G=(V,c) (that is, ). The power of a vertex u in a directed spanning subgraph H is given by , and corresponds to the energy consumption required for node u to transmit to all nodes v with uv∈E(H). The power of H is given by . Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint.Min-Power Bounded-Hops Broadcast is a power assignment problem which has as additional input a positive integer d and a r∈V. The output H must be a r-rooted outgoing arborescence of depth at most d. We give an (O(logn),O(logn)) bicriteria approximation algorithm for Min-Power Bounded-Hops Broadcast: that is, our output has depth at most O(dlogn) and power at most O(logn) times the optimum solution.For the Euclidean case, when c(u,v)=c(v,u)=∥u,v∥^κ (here ∥u,v∥ is the Euclidean distance and κ is a constant between 2 and 5), the output of our algorithm can be modified to give a O((logn)^κ) approximation ratio. Previous results for Min-Power Bounded-Hops Broadcast are only exact algorithms based on dynamic programming for the case when the nodes lie on the line and c(u,v)=c(v,u)=∥u,v∥^κ.Our bicriteria results extend to Min-Power Bounded-Hops Strong Connectivity, where H must have a path of at most d edges in between any two nodes. Previous work for Min-Power Bounded-Hops Strong Connectivity consists only of constant or better approximation for special cases of the Euclidean case.     

Improved algorithm for broadcast scheduling of minimal latency in wireless ad hoc networks

A wide range of applications for wireless ad hoc networks are time-critical and impose stringent requirement on the communication latency. One of the key communication operations is to broadcast a message from a source node. This paper studies the minimum latency broadcast scheduling problem in wireless ad hoc networks under collision-free transmission model. The previously best known algorithm for this NP-hard problem produces a broadcast schedule whose latency is at least 648（rmax/rmin）^2 times that of the optimal schedule, where rmax and rmin are the maximum and minimum transmission ranges of nodes in a network, respectively. We significantly improve this result by proposing a new scheduling algorithm whose approximation performance ratio is at most （1 ＋ 2rmax/rmin）^2＋32, Moreover, under the proposed scheduling each node just needs to forward a message at most once.     

A fast local search method for minimum energy broadcast in wireless ad hoc networks

Local search methods are often used to reduce the power consumption of broadcast routing in wireless networks. For a classic method, sweep, the best available time complexity result is O(|V|⁴). We present an O(|V|²)-time method, which exhaustively removes unnecessary transmissions yielding a solution comparable to that of sweep.     

Two new algorithms for the Min-Power Broadcast problem in static ad hoc networks

In this paper we address the Min-Power Broadcast problem in wireless ad hoc networks. Given a network with an identified source node w, the Min-Power Broadcast (MPB) problem is to assign transmission range to each node such that communication from w to other nodes is possible and the total energy consumption is minimized.

As the problem is NP-Hard we first propose a simulated annealing algorithm for the MPB problem. Utilizing a special node selection mechanism in its neighborhood structure the algorithm is designed in a way enabling an efficient power consumption evaluation and search for neighboring solutions. We then combine the algorithm with a decomposition approach to enhance its performance. This is achieved by decomposing the master problem and performing metropolis chain of the simulated annealing only on the much smaller subproblems resulting from decomposition. Results from a comprehensive computational study indicate the efficiency and effectiveness of the proposed algorithms.     

Location tracking in mobile ad hoc networks using particle filters

Mobile ad hoc networks (MANETs) are dynamic networks formed on-the-fly as mobile nodes move in and out of each others' transmission ranges. In general, the mobile ad hoc networking model makes no assumption that nodes know their own locations. However, recent research shows that location-awareness can be beneficial to fundamental tasks such as routing and energy-conservation. On the other hand, the cost and limited energy resources associated with common, low-cost mobile nodes prohibits them from carrying relatively expensive and power-hungry location-sensing devices such as GPS. This paper proposes a mechanism that allows non-GPS-equipped nodes in the network to derive their approximated locations from a limited number of GPS-equipped nodes. In our method, all nodes periodically broadcast their estimated location, in terms of a compressed particle filter distribution. Non-GPS nodes estimate the distance to their neighbors by measuring the received signal strength of incoming messages. A particle filter is then used to estimate the approximated location, along with a measure of confidence, from the sequence of distance estimates. Simulation studies show that our solution is capable of producing good estimates equal or better than the existing localization methods such as APS-Euclidean for the more difficult scenario when the network connectivity is low.     

On optimizing CSMA for wide area ad hoc networks

The recent deployment of data-rich smart phones has led to a fresh impetus for understanding the performance of wide area ad hoc networks. The most popular medium access mechanism for such ad hoc networks is CSMA/CA with RTS/CTS. In CSMA-like mechanisms, spatial reuse is achieved by implementing energy-based guard zones. We consider the problem of simultaneously scheduling the maximum number of links that can achieve a given signal to interference ratio (SIR). In this paper, using tools from stochastic geometry, we study and maximize the medium access probability of a typical link. Our contributions are two-fold: (i) We show that a simple modification to the RTS/CTS mechanism, viz., changing the receiver yield decision from an energy-level guard zone to an SIR guard zone, leads to performance gains; and (ii) We show that this combined with a simple modification to the transmit power level—setting it inversely proportional to the square root of the link gain—leads to significant improvements in network throughput. Further, this simple power-level choice is no worse than a factor of two away from optimal over the class of all “local” power level selection strategies for fading channels, and further is optimal in the non-fading case. The analysis relies on an extension of the Matérn hard core point process which allows us to quantify both these SIR guard zones and this power control mechanism.     

A biobjective optimization model for routing in mobile ad hoc networks

In this paper, the problem of finding optimal paths in mobile ad hoc networks is addressed. More specifically, a novel bicriteria optimization model, which allows the energy consumption and the link stability of mobile nodes to be taken into account simultaneously, is presented. In order to evaluate the validity of the proposed model, a greedy approach is devised. Some preliminary computational experiments have been carried out, in a simulation environment. The numerical results are very encouraging, showing the correctness of the proposed model. Indeed, the selection of a shorter route leads to a more stable route, but to a greater energy consumption. On the other hand, if longer routes are selected the route fragility is increased, but the average energy consumption is reduced.     

An efficient approximation for minimum energy broadcast in multi-channel multi-hop wireless network with directional antennas

In this paper, We discuss the minimum energy broadcast problem (MEB) in multi-channel multi-hop wireless networks with directional antennas (MEB-MB). This problem is NP-hard since its special version, MEB in single-channel network with directional antennas (MEB-SB) is proved to be NP-hard. We design an efficient approximation for MEB-MB problem, analyze its approximation ratio, and evaluate its performance via numerical experiments.     

Improving time-efficiency in blocking expanding ring search for mobile ad hoc networks

We propose a new strategy for reducing the amount of latency and energy consumption in Blocking Expanding Ring Search (BERS) and enhanced Blocking Expanding Ring Search (BERS*) for mobile ad hoc networks (MANETs). BERS and BERS* are respectively energy and energy–time efficient route discovery protocols for MANETs as compared to conventional Expanding Ring Search (ERS). In this study, we identify unnecessary waiting time caused by a STOP/END instruction in BERS/BERS* and explore the potential of further improvement of their time efficiency. This leads to tBERS and tBERS*, the improved BERS and BERS* respectively. In tBERS/tBERS*, a route node may also issue the STOP/END instruction to terminate flooding. We implement this idea in algorithms, conduct analysis, and achieve further latency reduction in both tBERS and tBERS* as well as the energy saving in tBERS*.     

Location-aided routing with uncertainty in mobile ad hoc networks: A stochastic semidefinite programming approach

We study location-aided routing under mobility in wireless ad hoc networks. Due to node mobility, the network topology changes continuously, and clearly there exists an intricate tradeoff between the message passing overhead and the latency in the route discovery process. Aiming to obtain a clear understanding of this tradeoff, we use stochastic semidefinite programming (SSDP), a newly developed optimization model, to deal with the location uncertainty associated with node mobility. In particular, we model both the speed and the direction of node movement by random variables and construct random ellipses accordingly to better capture the location uncertainty and the heterogeneity across different nodes. Based on SSDP, we propose a stochastic location-aided routing (SLAR) strategy to optimize the tradeoff between the message passing overhead and the latency. Our results reveal that in general SLAR can significantly reduce the overall overhead than existing deterministic algorithms, simply because the location uncertainty in the routing problem is better captured by the SSDP model.     

Minimum power multicasting problem in wireless networks

In this paper we deal with the minimum power multicasting (MPM) problem in wireless ad-hoc networks. By using an appropriate choice of the decision variables and by exploiting the topological properties of the problem, we are able to define an original formulation based on a Set Covering model. Moreover, we propose for its solution two exact procedures that include a preprocessing technique that reduces the huge number of the model’s constraints. We also report some experimental results carried out on a set of randomly generated test problems.     

Approximation for a scheduling problem with application in wireless networks

A network of many sensors and a base station that are deployed over a region is considered. Each sensor has a transmission range, an interference range and a carrier sensing range, which are r, αr and βr, respectively. In this paper, we study the minimum latency conflict-aware many-to-one data aggregation scheduling problem: Given locations of sensors along with a base station, a subset of all sensors, and parameters r, α and β, to find a schedule in which the data of each sensor in the subset can be transmitted to the base station with no conflicts, such that the latency is minimized. We designe an algorithm based on maximal independent sets, which has a latency bound of (a + 19b)R + Δb ? a + 5 time slots, where a and b are two constant integers relying on α and β, Δ is the maximum degree of network topology, and R is the trivial lower bound of latency. Here Δ contributes to an additive factor instead of a multiplicative one, thus our algorithm is nearly a constant (a + 19b)-ratio.     

Topology control in the mobile ad hoc networks in order to intensify energy conservation

Although studied for years, due to their dynamic nature, research in the field of mobile ad hoc networks (MANETs) has remained a vast area of interest. Since once distributed, there will be less to no plausibility of recharge, energy conservation has become one of the pressing concerns regarding this particular type of network. In fact, one of the main obligations of designers is to make efficient use of these scarce resources. There has been tremendous work done in different layers of protocol stack in order to intensify energy conservation. To date, numerous topology control algorithms have been proposed, however, only a few have used meta-heuristics such as genetic algorithms, neural networks and/or learning automata to overcome this issue. On the other hand, since nodes are mobile and thus in a different spatial position, as time varies, we can expect that by regulating time intervals between topology controls, one may prolong the network’s lifetime. The main initiative of this paper is to intensify energy conservation in a mobile ad hoc network by using weighted and learning automata based algorithms. The learning automata, regulates time intervals between which the topology controls are done. The represented learning automata based algorithm uses its learning ability to find appropriate time-intervals so that the nodes would regulate the energy needed in order to exchange the information to their neighbors, accordingly. Moreover, at first we have represented two weighted based algorithms which extend two prominent protocols, namely K-Neigh and LMST. Then these algorithms are combined with a learning based algorithm which regulates time intervals between which the topology controls are done. In comparison with approaches that are based on periodic topology controls, proposed approach shows enhanced results. On the other hand, considering the learning ability of the learning automata based algorithms, composition of the aforementioned algorithms has been proven to be enhanced, in the respect of energy consumed per data transmitted, over those compared with.     

Some simple optimization techniques for self-organized public key management in mobile ad hoc networks

We consider some graph theoretical problems arising from security requirements in some communication networks. Basically one has to associate to each node of a directed graph G=(V,E) a partial subgraph of G. A solution consists hence of a collection of |V| subgraphs, subject to some packing constraints or connectivity requirements. We first describe the usual graph theoretical model and we review a known construction procedure for which we point out some basic properties. We then study in more details the case of complete graphs and show the existence of a solution with a guaranteed quality. Next, we study the performance of the construction procedure and we propose an additional construction. We attempt to characterize the cases in which either construction is preferable. In the last section, a tabu search approach is proposed and tested on a sample of numerical examples.     

A fluid system with coupled input and output,and its application to bottlenecks in ad hoc networks

This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c/(n+1), where the remaining c/(n+1) is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can be regarded as a system with Markov fluid input. The rationale behind studying this queue lies in ad hoc networks: bottleneck links have roughly this type of sharing policy. We consider four performance metrics: (i) the stationary workload of the queue, (ii) the queueing delay, i.e., the delay of a ‘packet’ (a fluid particle) that arrives at the queue at an arbitrary point in time, (iii) the flow transfer delay, i.e., the time elapsed between arrival of a flow and the epoch that all its traffic has been put into the queue, and (iv) the sojourn time, i.e., the flow transfer time increased by the time it takes before the last fluid particle of the flow is served. For each of these random variables we compute the Laplace transform. The corresponding tail probabilities decay exponentially, as is shown by a large-deviations analysis. F. Roijers’ work has been carried out partly in the SENTER-NOVEM funded project Easy Wireless.     

网络最小覆盖流问题

网络流理论中最基本的模型是最大流及最小费用流问题. 为研 究堵塞现象, 文献中出现了最小饱和流问题, 但它是NP-难的. 研究类似的最小覆盖流问题, 即求一流, 使每一条弧的流量达到一定的额定量, 而流的值为最小. 主要结果是给出多项式时间算法, 并应用于最小饱和流问题.     

Maximum flow problem on dynamic generative network flows with time-varying bounds

This paper considers a new class of network flows, called dynamic generative network flows in which, the flow commodity is dynamically generated at a source node and dynamically consumed at a sink node and the arc-flow bounds are time dependent. Then the maximum dynamic flow problem in such networks for a pre-specified time horizon T is defined and mathematically formulated in both arc flow and path flow presentations. By exploiting the special structure of the problem, an efficient algorithm is developed to solve the general form of the dynamic problem as a minimum cost static flow problem.