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.
Our second greedy routing protocol is based on virtual coordinates which we will define by four landmark nodes denoted by @math , @math , @math , and @math . These four landmark nodes are selected similarly as in VCap (virtual coordinate assignment protocol) from @cite_9 . The first landmark node @math is one of the nodes with maximum @math -distance to an arbitrary node @math . The second landmark node @math is one of the nodes with maximum @math -distance to @math . The third landmark node @math is one of the nodes for which [d^ (C,A)+d^ (C,B)-2 |d^ (C,A)-d^ (C,B)| ] is maximum. And finally, the fourth landmark node @math is one of the nodes for which [d^ (D,C)-|d^ (D,A)-d^ (D,B)| ] is maximum. Since will consider energy efficient routing, we use the @math -distances instead of hop distances @cite_9 for the computation of the virtual addresses.
@cite_9
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We propose an energy efficient routing protocol, VCost, for sensor networks. We assume that nodes are unaware of their geographic location thus, VCost assigns virtual coordinates to nodes as follows. Based on the node hop count distances from a set of landmarks, our method computes a distance metric to obtain the node's virtual coordinates. VCost, then uses these coordinates to route packets from node u to node v, in its neighborhood, such that the ratio of the cost to send a message to v to the progress in the routing task towards the destination is minimized. Compared to existing algorithms that use virtual locations, our simulation shows that VCost improves significantly energy consumption and preserves the small percentage of successful routings. 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. 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. Geographic routing can provide efficient routing at a fixed overhead. However, the performance of geographic routing is impacted by physical voids, and localization errors. Accordingly, virtual coordinate systems (VCS) were proposed as an alternative approach that is resilient to localization errors and that naturally routes around physical voids. However, VCS also faces virtual anomalies. Moreover, there are no effective complementary routing algorithm that can be used to traverse voids. Most existing solutions use variants of flooding or blind searching when a void is encountered. In this paper, we make the observation that increasing the number of dimensions in virtual coordinate systems cannot eliminate all virtual anomalies since some portions of the network may be 1-connected to the rest of the network. As a result, we conjecture that a delivery guaranteed protocol must be one-dimensional and propose a spanning-path virtual coordinate system that has this property. We develop a delivery guaranteed routing algorithm on top of this system that can be used on its own, or as a complementary algorithm to traverse voids. With this approach, and for the first time, we demonstrate a stateless and delivery guaranteed geometric routing algorithm on VCS. When used in conjunction with our previously proposed aligned virtual coordinate system (AVCS), it out-performs not only all geometric routing protocols on VCS, but also geographic routing with accurate location information. In this paper we consider the problem of constructing a coordinate system in a sensor network where location information is not available. To this purpose we introduce the virtual coordinate assignment protocol (VCap) which defines a virtual coordinate system based on hop distances. As compared to other approaches, VCap is simple and have very little requirements in terms of communication and memory overheads. We compare by simulations the performances of greedy routing using our virtual coordinate system with the one using the physical coordinates. Results show that the virtual coordinate system can be used to efficiently support geographic routing. 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. 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. 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). 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 conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance to t decreases monotonically along the path. A consequence of this conjecture would be that in any ad hoc network containing such a graph as a spanning subgraph, two-dimensional virtual coordinates for the nodes can be found for which the method of purely greedy geographic routing is guaranteed to work. We discuss this conjecture and its equivalent forms show that its hypothesis is as weak as possible, and show a result delimiting the applicability of our approach: any 3-connected K3,3-free graph has a planar 3-connected spanning subgraph. We also present two alternative versions of greedy routing on virtual coordinates that provably work. Using Steinitz's theorem we show that any 3-connected planar graph can be embedded in three dimensions so that greedy routing works, albeit with a modified notion of distance; we present experimental evidence that this scheme can be implemented effectively in practice. We also present a simple but provably robust version of greedy routing that works for any graph with a 3-connected planar spanning subgraph. In this paper, we address the problem of energy efficient localized routing in wireless ad hoc networks. Numerous energy aware routing protocols were proposed to seek the power efficiency of routes. Among them, several geographical localized routing protocols were proposed to help making smarter routing decision using only local information and reduce the routing overhead. However, most of the proposed localized routing methods cannot theoretically guarantee the power efficiency of their routes. In this paper, we give the first localized routing algorithm, called localized energy aware restricted neighborhood routing (LEARN), which can guarantee the power efficiency of its route asymptotically almost sure. Given destination node t, an intermediate node v will only select a certain neighbor v such that pi alpha, our LEARN routing protocol will find the route for any pair of nodes asymptotically almost sure. When the transmission range rn = radicbet alnl pin for some beta < pi alpha, the LEARN routing protocol will not be able to find the route for any pair of nodes asymptotically almost sure. We also conducted simulations to study the performance of LEARN and compare it with a typical localized routing protocol (GPSR) and a global ad hoc routing protocol (DSR) Geographic routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these coordinates are used to perform point-to-point routing. Here we resolve a conjecture of Papadimitriou and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Euclidean plane. This immediately implies that all 3-connected graphs that exclude K3.3 as a minor admit a greedy embedding into the Euclidean plane. Additionally, we provide the first non-trivial examples of graphs that admit no such embedding. These structural results provide efficiently verifiable certificates that a graph admits a greedy embedding or that a graph admits no greedy embedding into the Euclidean plane. We show that greedy geometric routing schemes exist for the Euclidean metric in R 2, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(logn) bits, where n is the number of vertices in the graph. 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. Landmark Routing is a set of algorithms for routing in communications networks of arbitrary size. Landmark Routing is based on a new type of hierarchy, the Landmark Hierarchy. The Landmark Hierarchy exhibits path lengths and routing table sizes similar to those found in the traditional area or cluster hierarchy. The Landmark Hierarchy, however, is easier to dynamically configure using a distributed algorithm. It can therefore be used as the basis for algorithms that dynamically configure the hierarchy on the fly, thus allowing for very large, dynamic networks. This paper describes the Landmark Hierarchy, analyzes it, and compares it with the area hierarchy. We propose an embedding and routing scheme for arbitrary network connectivity graphs, based on greedy routing and utilizing virtual node coordinates. In dynamic multihop packet-switching communication networks, routing elements can join or leave during network operation or exhibit intermittent failures. We present an algorithm for online greedy graph embedding in the hyperbolic plane that enables incremental embedding of network nodes as they join the network, without disturbing the global embedding. Even a single link or node removal may invalidate the greedy routing success guarantees in network embeddings based on an embedded spanning tree subgraph. As an alternative to frequent reembedding of temporally dynamic network graphs in order to retain the greedy embedding property, we propose a simple but robust generalization of greedy distance routing called Gravity-Pressure (GP) routing. Our routing method always succeeds in finding a route to the destination provided that a path exists, even if a significant fraction of links or nodes is removed subsequent to the embedding. GP routing does not require precomputation or maintenance of special spanning subgraphs and, as demonstrated by our numerical evaluation, is particularly suitable for operation in tandem with our proposed algorithm for online graph embedding. Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these coordinates are used to perform point-to-point routing. Here we resolve a conjecture of Papadimitriou and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Euclidean plane. This immediately implies that all 3-connected graphs that exclude K 3,3 as a minor admit a greedy embedding into the Euclidean plane. We also prove a combinatorial condition that guarantees nonembeddability. We use this result to construct graphs that can be greedily embedded into the Euclidean plane, but for which no spanning tree admits such an embedding. Several peer-to-peer networks are based upon randomized graph topologies that permit efficient greedy routing, e. g., randomized hypercubes, randomized Chord, skip-graphs and constructions based upon small-world percolation networks. In each of these networks, a node has out-degree Θ(log n), where n denotes the total number of nodes, and greedy routing is known to take O(log n) hops on average. We establish lower-bounds for greedy routing for these networks, and analyze Neighbor-of-Neighbor (NoN)- greedy routing. The idea behind NoN, as the name suggests, is to take a neighbor's neighbors into account for making better routing decisions.The following picture emerges: Deterministic routing networks like hypercubes and Chord have diameter Θ(log n) and greedy routing is optimal. Randomized routing networks like randomized hypercubes, randomized Chord, and constructions based on small-world percolation networks, have diameter Θ(log n log log n) with high probability. The expected diameter of Skip graphs is also Θ(log n log log n). In all of these networks, greedy routing fails to find short routes, requiring Ω(log n) hops with high probability. Surprisingly, the NoN- greedy routing algorithm is able to diminish route-lengths to Θ(log n log log n) hops, which is asymptotically optimal. We present gradient landmark-based distributed routing (GLIDER), a novel naming addressing scheme and associated routing algorithm, for a network of wireless communicating nodes. We assume that the nodes are fixed (though their geographic locations are not necessarily known), and that each node can communicate wirelessly with some of its geographic neighbors - a common scenario in sensor networks. We develop a protocol which in a preprocessing phase discovers the global topology of the sensor field and, as a byproduct, partitions the nodes into routable tiles - regions where the node placement is sufficiently dense and regular that local greedy methods can work well. Such global topology includes not just connectivity but also higher order topological features, such as the presence of holes. We address each node by the name of the tile containing it and a set of local coordinates derived from connectivity graph distances between the node and certain landmark nodes associated with its own and neighboring tiles. We use the tile adjacency graph for global route planning and the local coordinates for realizing actual inter- and intra-tile routes. We show that efficient load-balanced global routing can be implemented quite simply using such a scheme. In this paper, we study distributed channel assignment in wireless networks with applications to peer discovery in ad hoc wireless networks. We model channel assignment as a coloring problem for spatial point processes in which n nodes are located in a unit cube uniformly at random and each node is assigned one of K colors, where each color represents a channel. The objective is to maximize the spatial separation between nodes of the same color. In general, it is hard to derive the optimal coloring algorithm, and we therefore consider a natural online greedy coloring algorithm first proposed by Ko and Rubenstein in 2005. We prove two key results: 1) with just log n log log n colors, the distance separation achieved by the greedy coloring algorithm asymptotically matches the optimal distance separation that can be achieved by an algorithm which is allowed to optimally place the nodes but is allowed to use only one color; and 2) when K = Ω(log n), the greedy coloring algorithm asymptotically achieves the best distance separation that can be achieved by an algorithm which is allowed to both optimally color and place nodes. The greedy coloring algorithm is also shown to dramatically outperform a simple random coloring algorithm. Moreover, the results continue to hold under node mobility.