We introduce and evaluate a very simple landmark-based network partition technique called Hierarchical Bipartition Routing (HBR) to support routing with delivery guarantee in wireless ad hoc sensor networks. It is a simple routing protocol that can easily be combined with any other greedy routing algorithm to obtain delivery guarantee. The efficiency of HBR increases if the network is sparse and contains obstacles. The space necessary to store the additional routing information at a node u is on average not larger than the size necessary to store the IDs of the neighbors of u. The amount of work to setup the complete data structure is on average proportional to flooding the entire network log(n) times, where n is the total number of sensor nodes. We evaluate the performance of HBR in combination with two simple energy-aware geographic greedy routing algorithms based on physical coordinates and virtual coordinates, respectively. Our simulations show that the difference between using HBR and a weighted shortest path to escape a dead-end is only a few percent in typical cases.
Greedy routing algorithms can easily be extended by taking into account power consumption. Power aware greedy routing in most cases tries to minimize the ratio of the energy consumed by a transmission to the progress made. The progress is the distance reduction towards the destination. This cost over progress (COP) power-aware framework is first introduced in @cite_13 . If the cost is equal for all connections, we obtain the simple greedy algorithm as already discussed above @cite_28 . If the cost of a connection is proportional to the distance between the nodes, the resulting routing is similar to compass routing @cite_33 .
@cite_28 @cite_13 @cite_33
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A cost aware metric for wireless networks based on remaining battery power at nodes was proposed for shortest-cost routing algorithms, assuming constant transmission power. Power-aware metrics, where transmission power depends on distance between nodes and corresponding shortest power algorithms were also proposed. We define a power-cost metric based on the combination of both node's lifetime and distance-based power metrics. We investigate some properties of power adjusted transmissions and show that, if additional nodes can be placed at desired locations between two nodes at distance d, the transmission power can be made linear in d as opposed to d sup spl alpha dependence for spl alpha spl ges 2. This provides basis for power, cost, and power-cost localized routing algorithms where nodes make routing decisions solely on the basis, of location of their neighbors and destination. The power-aware routing algorithm attempts to minimize the total power needed to route a message between a source and a destination. The cost-aware routing algorithm is aimed at extending the battery's worst-case lifetime at each node. The combined power-cost localized routing algorithm attempts to minimize the total power needed and to avoid nodes with a short battery's remaining lifetime. We prove that the proposed localized power, cost, and power-cost efficient routing algorithms are loop-free and show their efficiency by experiments. In this article we propose several new progress based, localized, power, and cost aware algorithms for routing in ad hoc wireless networks. These algorithms attempt to minimize the total power and or cost needed to route a message from source to destination. In localized algorithms, each node makes routing decisions solely on the basis of location of itself, its neighbors and destination. The new algorithms are based on the notion of proportional progress. A node currently holding the packet will forward it to a neighbor, closer to destination than itself, which minimizes the ratio of power and or cost to reach that neighbor, and the progress made, measured as the reduction in distance to destination, or projection along the line to destination. First, we propose Power Progress, Iterative Power Progress, Projection Power Progress, and Iterative Projection Power Progress algorithms, where the proportional progress is defined in terms of power measure. The power metrics are then replaced by cost or power-co... We propose a novel localized routing protocol for wireless sensor networks (WSN) that is energy-efficient and guarantees delivery. We prove that it is constant factor of the optimum for dense networks. To forward a packet, a node s in graph G computes the cost of the energy weighted shortest path (SP) between s and each of its neighbors which are closer to the destination than itself. It then selects node x which minimizes the ratio of the cost of the SP to the progress towards the destination. It then sends the message to the first node on the SP from s to x: say node x'. Node x' restarts the same greedy routing process until the destination is reached or the routing fails. To recover from failure, our algorithm invokes face routing that guarantees delivery. This work is the first to optimize energy consumption of face routing. First, we build a connected dominating set from graph G, second we compute its Gabriel graph to obtain the planar graph G'. Face routing is applied on G' only to decide which edges to follow in the recovery process. On each edge, greedy routing is used. This two-phase (greedy-Face) end-to-end routing process (EtE) reiterates until the final destination is reached. Simulation results show that EtE outperforms several existing geographical routing on energy consumption metric. This paper considers the problem of designing power efficient routing with guaranteed delivery for sensor networks with known distances between neighbors but unknown geographic locations. We propose Hector, a hybrid energy efficient tree-based optimized routing protocol, based on two sets of virtual coordinates. One set is based on rooted tree coordinates, and the other is based on hop distances toward several landmarks. In our algorithm, the node currently holding the packet forwards it to its neighbor that optimizes ratio of power cost over distance progress with landmark coordinates, among nodes that reduce landmark coordinates and do not increase tree coordinates. If such a node does not exist then forwarding is made to the neighbor that reduces tree based distance and optimizes power cost over tree distance progress ratio. Our simulations show the superiority of our algorithm over existing alternatives while guaranteeing delivery, and only up to 30 additional power compared to centralized shortest weighted path algorithm. The paper copes with the reduction of network power consumption by the definition of new routing algorithms, able to take into account the energy consumed by the network devices. In particular, based on the power consumption characterization of the network devices obtained using the Energy Profile (EP) concept, the paper presents the analysis of the exact solution of the Energy Aware Routing (EAR) problem solved with a Mixed Integer Programming solver. The analysis is aimed at evaluating the impact on the performance of three relevant aspects of the problem: the approximation of the actual EP, the traffic load and the topology of the network. Furthermore, the paper proposes a heuristic solution of the EAR, denoted as Dijkstra-based Power Aware Routing Algorithm (DPRA), defined in order to cope with the complexity of the exact solution. b this paper we present a case for using new power-aware metn.cs for determining routes in wireless ad hoc networks. We present five erent metriw based on battery power consumption at nodw. We show that using th=e metrics in a shortest-cost routing algorithm reduces the cost packet of routing packets by 5-30 over shortwt-hop routing (this cost reduction is on top of a 40-70 reduction in energy consumption obtained by using PAMAS, our MAC layer prtocol). Furthermore, using these new metrics ensures that the mean time to node failure is increased si cantly. An interesting property of using shortest-cost routing is that packet delays do not increase. Fintiy, we note that our new metrim can be used in most tradition routing protocols for ad hoc networks. In a localized routing algorithm, each node currently holding a message makes forwarding decision solely based on the position information about itself, its neighbors and destination. In a unit graph, two nodes can communicate if and only if the distance between them is no more than the transmission radius, which is the same for each node. This paper proposes localized routing algorithms, aimed at minimizing total power for routing a message or maximizing the total number of routing tasks that a network can perform before a partition. The algorithms are combinations of known greedy power and or cost aware localized routing algorithms and an algorithm that guarantees delivery. A shortcut procedure is introduced in later algorithm to enhance its performance. Another improvement is to restrict the routing to nodes in a dominating set. These improvements require two-hop knowledge at each node. The efficiency of proposed algorithms is verified experimentally by comparing their power savings, and the number of routing tasks a network can perform before a node loses all its energy, with the corresponding shortest weighted path algorithms and localized algorithms that use fixed transmission power at each node. Significant energy savings are obtained, and feasibility of applying power and cost-aware localized schemes is demonstrated. Copyright © 2004 John Wiley & Sons, Ltd. In the interference scheduling problem, one is given a set of n communication requests described by source-destination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color class can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We introduce an instance-based measure of interference, denoted by I, that enables us to improve on previous results for the interference scheduling problem. We prove the upper and lower bounds in terms of I on the number of steps needed for scheduling a set of requests. For general power assignments, we prove a lower bound of @W(I ([email protected])) steps, where @D denotes the aspect ratio of the metric. When restricting to the two-dimensional Euclidean space (as in the previous work) the bound improves to @W(I [email protected]). Alternatively, when restricting to linear power assignments, the lower bound improves even to @W(I). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only O(Ilogn) steps. A more sophisticated algorithm computes a schedule using even only O(I+log^2n) steps. For dense instances in the two-dimensional Euclidean space, this gives a constant factor approximation for scheduling under linear power assignments, which shows that the price for using linear (and, hence, energy-efficient) power assignments is bounded by a factor of O([email protected]). In addition, we extend these results for single-hop scheduling to multi-hop scheduling and combined scheduling and routing problems, where our analysis generalizes the previous results towards general metrics and improves on the previous approximation factors. Reducing power consumption and increasing battery life of nodes in an ad-hoc network requires an integrated power control and routing strategy. Power optimal routing selects the multi-hop links that require the minimum total power cost for data transmission under a constraint on the link quality. This paper studies optimal power routing under the constraint of a fixed end-to-end probability of error and compares the power optimal routes obtained with this criterion with those from the more commonly used fixed per hop error rate constraint. The comparison is carried out by looking at the properties of the power optimal graph, formed by the union of all the power optimal routes. The paper also provides algorithms to determine the power optimal routes. The efficiency of routing algorithms in ad-hoc networks is measured by delay, throughput, and energy. Here, we focus on routing algorithms optimizing energy consumption while providing small routing delay. For this, we exploit the sender beamforming gain in the line-of-sight path-loss model, where multiple nodes (each with a single antenna) cooperate for beamforming and the routing algorithms provide distributed self-synchronization. While direct point-to-point communication over distance d in the line-of-sight model needs transmission power Θ(d 2 ), and multi-hop power needs power Θ(d) and delay Θ(d), we can reduce the power to Θ(√d) or Θ(log d) depending on the geometry. We present three algorithms with different trade-offs. The first algorithm is designed for grid nodes in the plane and has a point-to-point delay of Θ(log d) and overall power consumption of Θ(√d). The second algorithm for the same geometry decreases the delay to Θ(1 over e log log d) with power Θ((√d) 1+e ) for e > 0. The third algorithm requires a three-dimensional grid network and achieves a delay of Θ(log d) and reduces the energy needed by all nodes to Θ(log d). Since ad hoc and sensor networks can be composed of a very large number of devices, the scalability of network protocols is a major design concern. Furthermore, network protocols must be designed to prolong the battery lifetime of the devices. However, most existing routing techniques for ad hoc networks are known not to scale well. On the other hand, the so-called geographical routing algorithms are known to be scalable but their energy efficiency has never been extensively and comparatively studied. In a geographical routing algorithm, data packets are forwarded by a node to its neighbor based on their respective positions. The neighborhood of each node is constituted by the nodes that lie within a certain radio range. Thus, from the perspective of a node forwarding a packet, the next hop depends on the width of the neighborhood it perceives. The analytical framework proposed in this paper allows to analyze the relationship between the energy efficiency of the routing tasks and the extension of the range of the topology knowledge for each node. A wider topology knowledge may improve the energy efficiency of the routing tasks but increases the cost of topology information due to signaling packets needed to acquire this information. The problem of determining the optimal topology knowledge range for each node to make energy efficient geographical routing decisions is tackled by integer linear programming. It is shown that the problem is intrinsically localized, i.e., a limited topology knowledge is sufficient to make energy efficient forwarding decisions. The leading forwarding rules for geographical routing are compared in this framework, and the energy efficiency of each of them is studied. Moreover, a new forwarding scheme, partial topology knowledge forwarding (PTKF), is introduced, and shown to outperform other existing schemes in typical application scenarios. A probe-based distributed protocol for knowledge range adjustment (PRADA) is finally introduced that allows each node to efficiently select online its topology knowledge range. PRADA is shown to rapidly converge to a near-optimal solution. Greedy geographic routing is attractive for large multi-hop wireless networks because of its simple and distributed operation. However, it may easily result in dead ends or hotspots when routing in a network with obstacles (regions without sufficient connectivity to forward messages). In this paper, we propose a distributed routing algorithm that combines greedy geographic routing with two non-Euclidian distance metrics, chosen so as to provide load balanced routing around obstacles and hotspots. The first metric, Local Shortest Path, is used to achieve high probability of progress, while the second metric, Weighted Distance Gain, is used to select a desirable node among those that provide progress. The proposed Load Balanced Local Shortest Path (LBLSP) routing algorithm provides loop freedom, guarantees delivery when a path exists, is able to efficiently route around obstacles, and provides good load balancing. This paper considers max-min fair rate allocation and routing in energy harvesting networks where fairness is required among both the nodes and the time slots. Unlike most previous work on fairness, we focus on multihop topologies and consider different routing methods. We assume a predictable energy profile and focus on the design of efficient and optimal algorithms that can serve as benchmarks for distributed and approximate algorithms. We first develop an algorithm that obtains a max-min fair rate assignment for any given (time-variable or time-invariable) unsplittable routing or a routing tree. For time-invariable unsplittable routing, we also develop an algorithm that finds routes that maximize the minimum rate assigned to any node in any slot. For fractional routing, we study the joint routing and rate assignment problem. We develop an algorithm for the time-invariable case with constant rates. We show that the time-variable case is at least as hard as the 2-commodity feasible flow problem and design an FPTAS to combat the high running time. Finally, we show that finding a max-min fair unsplittable routing or a routing tree is NP-hard, even for a time horizon of a single slot. Our analysis provides insights into the problem structure and can be applied to other related fairness problems. The inefficiency of energy usage on the Internet has become a critical problem with its rapid growth, as all network devices operate at full capacity in spite of the real traffic load. Existing studies try to develop energy efficient routings by aggregating traffic and switching underutilized devices into sleep mode. However, most existing approaches do not address the problem of routing convergence well. Since traffic changes frequently in a network, routing convergence may be triggered frequently for an energy efficient routing, which may induce routing loops and black holes, resulting in severe packet loss. In this paper, we present a fast rerouting-based (FRR-based) energy efficient routing scheme, namely GreenFRR, which leverages the technique of fast rerouting to reduce the convergence time. We first study typical fast rerouting techniques and address the challenge of guaranteeing loop-free routing. Then, we formalize the FRR-based energy efficient routing problem and prove that the problem is NP-hard. In order to solve this problem, we design heuristic algorithms to maximize the number of sleeping links. In particular, we consider link utilization ratio and path stretch in our algorithms. We evaluate our scheme by simulations on real and synthetic topologies with real and synthetic traffic traces. The results show that the power consumed by line cards achieves a saving of 40 and the convergence time can be reduced by 95 . We consider the optimal online packet scheduling problem in a single-user energy harvesting wireless communication system, where energy is harvested from natural renewable sources, making future energy arrivals instants and amounts random in nature. The most general case of arbitrary energy arrivals is considered where neither the future energy arrival instants or amount, nor their distribution is known. The problem considered is to adaptively change the transmission rate according to the causal energy arrival information, such that the time by which all packets are delivered is minimized. We assume that all bits have arrived and are ready at the source before the transmission begins. For a minimization problem, the utility of an online algorithm is tested by finding its competitive ratio or competitiveness that is defined to be the maximum of the ratio of the gain of the online algorithm with the optimal offline algorithm over all input sequences. We derive a lower and upper bound on the competitive ratio of any online algorithm to minimize the total transmission time in an energy harvesting system. The upper bound is obtained using a lazy' transmission policy that chooses its transmission power to minimize the transmission time assuming that no further energy arrivals are going to occur in future. The lazy transmission policy is shown to be strictly two-competitive. We also derive an adversarial lower bound that shows that competitive ratio of any online algorithm is at least 1.325. A natural generalization of the selfish routing setting arises when some of the users obey a central coordinating authority, while the rest act selfishly. Such behavior can be modeled by dividing the users into an α fraction that are routed according to the central coordinator’s routing strategy (Stackelberg strategy), and the remaining 1−α that determine their strategy selfishly, given the routing of the coordinated users. One seeks to quantify the resulting price of anarchy, i.e., the ratio of the cost of the worst traffic equilibrium to the system optimum, as a function of α. It is well-known that for α=0 and linear latency functions the price of anarchy is at most 4 3 (J. ACM 49, 236–259, 2002). If α tends to 1, the price of anarchy should also tend to 1 for any reasonable algorithm used by the coordinator. We analyze two such algorithms for Stackelberg routing, LLF and SCALE. For general topology networks, multicommodity users, and linear latency functions, we show a price of anarchy bound for SCALE which decreases from 4 3 to 1 as α increases from 0 to 1, and depends only on α. Up to this work, such a tradeoff was known only for the case of two nodes connected with parallel links (SIAM J. Comput. 33, 332–350, 2004), while for general networks it was not clear whether such a result could be achieved, even in the single-commodity case. We show a weaker bound for LLF and also some extensions to general latency functions. The existence of a central coordinator is a rather strong requirement for a network. We show that we can do away with such a coordinator, as long as we are allowed to impose taxes (tolls) on the edges in order to steer the selfish users towards an improved system cost. As long as there is at least a fraction α of users that pay their taxes, we show the existence of taxes that lead to the simulation of SCALE by the tax-payers. The extension of the results mentioned above quantifies the improvement on the system cost as the number of tax-evaders decreases. Compact routing addresses the tradeoff between table sizes and stretch, which is the worst-case ratio between the length of the path a packet is routed through by the scheme and the length of an actual shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwick [2001] to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by [2000]. Our result is the first analytical bound coupled to the parameter of the power-law graph model for a compact routing scheme. Let n denote the number of nodes in the network. We provide a labeled routing scheme that, after a stretch--5 handshaking step (similar to DNS lookup in TCP IP), routes messages along stretch--3 paths. We prove that, instead of routing tables with O(n1 2) bits (O suppresses factors logarithmic in n) as in the general scheme by Thorup and Zwick, expected sizes of O(nγ log n) bits are sufficient, and that all the routing tables can be constructed at once in expected time O(n1+γ log n), with γ = τ-22 τ-3 + e, where τ∈(2,3) is the power-law exponent and e 0 (which implies e With the same techniques as for the compact routing scheme, we also adapt the approximate distance oracle by Thorup and Zwick [2001, 2005] for stretch-3 and we obtain a new upper bound of expected O(n1+γ) for space and preprocessing for random power-law graphs. Our distance oracle is the first one optimized for power-law graphs. Furthermore, we provide a linear-space data structure that can answer 5--approximate distance queries in time at most O(n1 4+e) (similar to γ, the exponent actually depends on τ and lies between e and 1 4 + e). We propose a scalable and reliable point-to-point routing algorithm for ad hoc wireless networks and sensor-nets. Our algorithm assigns to each node of the network a virtual coordinate in the hyperbolic plane, and performs greedy geographic routing with respect to these virtual coordinates. Unlike other proposed greedy routing algorithms based on virtual coordinates, our embedding guarantees that the greedy algorithm is always successful in finding a route to the destination, if such a route exists. We describe a distributed algorithm for computing each node's virtual coordinates in the hyperbolic plane, and for greedily routing packets to a destination point in the hyperbolic plane. (This destination may be the address of another node of the network, or it may be an address associated to a piece of content in a Distributed Hash Table. In the latter case we prove that the greedy routing strategy makes a consistent choice of the node responsible for the address, irrespective of the source address of the request.) We evaluate the resulting algorithm in terms of both path stretch and node congestion. A routing problem in static wireless ad hoc networks is considered as it arises in a rapidly deployed, sensor based, monitoring system known as the wireless sensor network. Information obtained by the monitoring nodes needs to be routed to a set of designated gateway nodes. In these networks, every node is capable of sensing, data processing, and communication, and operates on its limited amount of battery energy consumed mostly in transmission and reception at its radio transceiver. If we assume that the transmitter power level can be adjusted to use the minimum energy required to reach the intended next hop receiver then the energy consumption rate per unit information transmission depends on the choice of the next hop node, i.e., the routing decision. We formulate the routing problem as a linear programming problem, where the objective is to maximize the network lifetime, which is equivalent to the time until the network partition due to battery outage. Two different models are considered for the information-generation processes. One assumes constant rates and the other assumes an arbitrary process. A shortest cost path routing algorithm is proposed which uses link costs that reflect both the communication energy consumption rates and the residual energy levels at the two end nodes. The algorithm is amenable to distributed implementation. Simulation results with both information-generation process models show that the proposed algorithm can achieve network lifetime that is very close to the optimal network lifetime obtained by solving the linear programming problem. The energy-efficiency usage is relative to each layer of wireless sensor networks. In order to improve the ZigBee mesh routing protocol for energy-efficiency usage, we propose a routing algorithm combining AODVjr with the node residual energy. To reduce the energy consumption of bottleneck nodes and extend network lifetime, the improved routing algorithm aims to build a new balancing method between the energy-aware routing metric and the shortest path. Based on the energy model of CC2430 RF transceiver, the implemented routing protocol is simulated using NS2 (Network Simulator version 2). Simulation result shows that this improved protocol can extend the network lifetime very efficiently.