In this work, we present a new approach for competitive geometric routing in wireless ad hoc networks. In general, it is well-known that any online routing strategy performs very poor in the worst case. The main difficulty are uncovered regions within the wireless ad hoc network, which we denote as radio holes. Complex shapes of radio holes, for example zig-zag-shapes, make local geometric routing even more difficult, i.e., forwarded messages in direction to the destination might get stuck in a dead end or are routed along very long detours, when there is no knowledge about the ad hoc network. To obtain knowledge about the position and shape of radio holes, we make use of a hybrid network approach. This approach assumes that we can not just make use of the ad hoc network but also of some cellular infrastructure, which is used to gather knowledge about the underlying ad hoc network. Communication via the cellular infrastructure incurs costs as cell phone providers are involved. Therefore, we use the cellular infrastructure only to compute routing paths in the ad hoc network. The actual data transmission takes place in the ad hoc network. In order to find good routing paths we aim at computing an abstraction of the ad hoc network in which radio holes are abstracted by bounding boxes. The advantage of bounding boxes as hole abstraction is that we only have to consider a constant number of nodes per hole. We prove that bounding boxes are a suitable hole abstraction that allows us to find @math -competitive paths in the ad hoc network in case of non-intersecting bounding boxes. In case of intersecting bounding boxes, we show via simulations that our routing strategy significantly outperforms the so far best online routing strategies for wireless ad hoc networks. Finally, we also present a routing strategy that is @math -competitive in case of pairwise intersecting bounding boxes.
The approach we extend in this work makes use of global information as well @cite_2 . The global information is gathered via a Hybrid Communication Network. In a Hybrid Communication Network, nodes can communicate with other nodes in their ad hoc range for free. In addition, they can use long-range links to communicate with any other node of the network. These long-range links, the Cellular Infrastructure, are costly. The solution they propose is to compute an Overlay Network in which holes are represented by their convex hulls. It is assumed that the convex hulls of the holes do not intersect. The storage requirements for some nodes are asymptotically in the size of the sum of all holes. In this work, we aim to reduce the storage requirements for these nodes and investigate also the challenging question of @math -competitive routing through intersections of hole abstractions.
@cite_2
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How much information can one send through a random ad hoc network of n nodes, if overlaid with a cellular architecture of m base stations? This network model is commonly referred to as hybrid wireless networks and our paper analyzes the above question by characterizing its throughput capacity. Although several research efforts related to throughput capacity exist in the area of hybrid wireless networks, most of these solutions under-explore the capacity analysis. Their results particularly indicate that one can realize only a less than log or no gain on capacity, as compared to pure ad hoc networks, when ?? scales slower than some threshold. This unsatisfying capacity gain is due to the fact that the base stations were not properly exploited while formulating the capacity analysis. Moreover, these research efforts also assume an one-hop wireless uplink between a node and its associated base station. Nevertheless, with those power-constrained wireless nodes, this assumption clearly indicates an unrealistic scenario. In this paper, we establish the bounds on capacity and delay by resolving the issues in existing efforts and at the heart of our analysis lies a simple routing policy known as same cell routing policy. Our findings particularly stipulate that whether m = O(n over log n) or Ω(n over log n), each node can realize a throughput that scales, sublinearly or linearly, with m. This is in fact a significant result as opposed to previous efforts which claims that if m grows slower than some threshold, the benefit of augmenting those base stations to the original ad hoc network is insignificant. Our analysis also shows that for a maximum per node throughput Λ(n,m), the average end-to-end delay in a hybrid network can be bounded by Θ(Λ(n,m)n over m), which has an inverse relationship to m. We consider n wireless ad hoc network nodes with one antenna each and equidistantly placed on a line. The transmission power of each node is just large enough to reach its next neighbor. For this setting we show that a message can be broadcasted to all nodes in time O(log n) without increasing each node's transmission power. Our algorithm needs O(log n) messages and consumes a total energy which is only a constant factor larger than the standard approach where nodes sequentially transmit the broadcast message to their next neighbors. We obtain this by synchronizing the nodes on the fly and using MIMO (multiple input multiple output) techniques. To achieve this goal we analyze the communication capacity of multiple antennas positioned on a line and use a communication model which is based on electromagnetic fields in free space. We extend existing communication models which either reflect only the sender power or neglect the locations by concentrating only on the channel matrix. Here, we compute the scalar channel matrix from the locations of the antennas and thereby only consider line-of-sight-communication without obstacles, reflections, diffractions or scattering. First, we show that this communication model reduces to the SINR power model if the antennas are uncoordinated. We show that n coordinated antennas can send a signal which is n times more powerful than the sum of their transmission powers. Alternatively, the power can be reduced to an arbitrarily small polynomial with respect to the distance. For coordinated antennas we show how the well-known power gain for MISO (multiple input single output) and SIMO (single input multiple output) can be described in this model. Furthermore, we analyze the channel matrix and prove that in the free space model no diversity gain can be expected for MIMO. Finally, we present the logarithmic time broadcast algorithm which takes advantage of the MISO power gain by self-coordinating wireless nodes. Compared to single-hop networks such as WiFi, multihop infrastructure wireless mesh networks (WMNs) can potentially embrace the broadcast benefits of a wireless medium in a more flexible manner. Rather than being point-to-point, links in the WMNs may originate from a single node and reach more than one other node. Nodes located farther than a one-hop distance and overhearing such transmissions may opportunistically help relay packets for previous hops. This phenomenon is called opportunistic overhearing listening. With multiple radios, a node can also improve its capacity by transmitting over multiple radios simultaneously using orthogonal channels. Capitalizing on these potential advantages requires effective routing and efficient mapping of channels to radios (channel assignment (CA)). While efficient channel assignment can greatly reduce interference from nearby transmitters, effective routing can potentially relieve congestion on paths to the infrastructure. Routing, however, requires that only packets pertaining to a particular connection be routed on a predetermined route. Random network coding (RNC) breaks this constraint by allowing nodes to randomly mix packets overheard so far before forwarding. A relay node thus only needs to know how many packets, and not which packets, it should send. We mathematically formulate the joint problem of random network coding, channel assignment, and broadcast link scheduling, taking into account opportunistic overhearing, the interference constraints, the coding constraints, the number of orthogonal channels, the number of radios per node, and fairness among unicast connections. Based on this formulation, we develop a suboptimal, auction-based solution for overall network throughput optimization. Performance evaluation results show that our algorithm can effectively exploit multiple radios and channels and can cope with fairness issues arising from auctions. Our algorithm also shows promising gains over traditional routing solutions in which various channel assignment strategies are used. In practical military or first responder deployment scenarios, information flows need to adhere to specified policies regardless of the physical connectivity of nodes. Nodes in such networks are associated with various levels in a command-and-control hierarchy, and therefore typically form a logical hierarchical tree network that is used to route both command and data traffic. Associated with this logical hierarchical network is a communication network that represents the connectivity of these nodes in the deployed scenario. Such composite networks introduce constraints that can result in information flows having to traverse much longer paths in the underlying communication network. In this paper, we look at the problem of adding edges to a logical hierarchical network (or any other social network) so as to minimize the number of hops required to route data traffic in the underlying communication network from a node to other specified nodes. The edges added are a subset of all possible edges in the complementary logical hierarchical graph and have to satisfy specified hierarchical constraints. First, we consider the general problem of minimizing the eccentricity of a source node 's' (where eccentricity of 's' is the maximum of the shortest paths from 's' to all other nodes) in a metric graph on adding upto 'B' unequal cost metric edges from the set of all edges in the complementary graph. We develop an efficient constant factor approximation algorithm for this case that outperforms existing constant factor algorithms for eccentricity minimization. Here the added edge metric cost as well as the graph edge metric cost correspond to the number of hops in the shortest path required to route traffic in the actual deployed topology (i.e., underlying communication network). Next, we consider the case where the set of possible added edges is a specified subset of the edges in the complementary graph and the set of destinations is a subset of the graph nodes. For this case, we develop heuristic algorithms based on the previous eccentricity minimizing algorithm that show good performance. We validate our algorithms using two realistic military deployment scenarios. We find that adding even a low number of hierarchically constrained edges (of the order of 10) can cause a significant decrease (around 50 ) in the eccentricity of a node in the logical hierarchical network and thus can reduce the number of hops required for data traffic traversal.