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. 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. Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure-tolerance for a given number of parity nodes. Suppose that an MDS code with @math information nodes and @math parity nodes is used to encode data in a distributed storage system. It is known that if @math out of the @math nodes are inaccessible and @math surviving (helper) nodes are used to recover the lost data, then we need to download at least @math fraction of the data stored in each of the helper nodes (Dimakis et. al., 2010 and , 2013). If this lower bound is achieved for the repair of any @math erased nodes from any @math helper nodes, we say that the MDS code has the @math -optimal repair property. We study high-rate MDS array codes with the optimal repair property. Explicit constructions of such codes in the literature are only available for the cases where there are at most 3 parity nodes, and these existing constructions can only optimally repair a single node failure by accessing all the surviving nodes. In this paper, given any @math and @math , we present two explicit constructions of MDS array codes with the @math -optimal repair property for all @math and @math simultaneously. Codes in the first family can be constructed over any base field @math as long as @math where @math The encoding, decoding, repair of failed nodes, and update procedures of these codes all have low complexity. Codes in the second family have the optimal access property and can be constructed over any base field @math as long as @math Moreover, both code families have the optimal error resilience capability when repairing failed nodes. We also construct several other related families of MDS codes with the optimal repair property. Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure tolerance for a given number of parity nodes. Suppose that an MDS code with @math information nodes and @math parity nodes is used to encode data in a distributed storage system. It is known that if @math out of the @math nodes are inaccessible and @math surviving (helper) nodes are used to recover the lost data, then we need to download at least @math fraction of the data stored in each of the helper nodes ( , 2010 and , 2013). If this lower bound is achieved for the repair of any @math erased nodes from any @math helper nodes, we say that the MDS code has the @math -optimal repair property. We study high-rate MDS array codes with the optimal repair property (also known as minimum storage regenerating codes, or MSR codes). Explicit constructions of such codes in the literature are only available for the cases where there are at most three parity nodes, and these existing constructions can only optimally repair a single node failure by accessing all the surviving nodes. In this paper, given any @math and @math , we present two explicit constructions of MDS array codes with the @math -optimal repair property for all @math and @math simultaneously. Codes in the first family can be constructed over any base field @math as long as @math , where @math . The encoding, decoding, repair of failed nodes, and update procedures of these codes all have low complexity. Codes in the second family have the optimal access property and can be constructed over any base field @math as long as @math . Moreover, both code families have the optimal error resilience capability when repairing failed nodes. We also construct several other related families of MDS codes with the optimal repair property.