A recent study characterizing failures in computer networks shows that transient single element (node link) failures are the dominant failures in large communication networks like the Internet. Thus, having the routing paths globally recomputed on a failure does not pay off since the failed element recovers fairly quickly, and the recomputed routing paths need to be discarded. In this paper, we present the first distributed algorithm that computes the alternate paths required by some "proactive recovery schemes" for handling transient failures. Our algorithm computes paths that avoid a failed node, and provides an alternate path to a particular destination from an upstream neighbor of the failed node. With minor modifications, we can have the algorithm compute alternate paths that avoid a failed link as well. To the best of our knowledge all previous algorithms proposed for computing alternate paths are centralized, and need complete information of the network graph as input to the algorithm.
Slosiar and Latin @cite_10 studied the single link failure recovery problem and presented an @math time for computing the link-avoiding alternate paths. A faster algorithm, with a running time of @math for this problem was presented in @cite_2 . The local-rerouting based fast recovery protocol of @cite_5 can use these paths to recover from single link failures as well. Both these algorithms, @cite_2 @cite_10 , are centralized algorithms that work using the information of the entire communication graph.
@cite_5 @cite_10 @cite_2
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We investigate the single link failure recovery problem and its application to the alternate path routing problem for ATM networks, and the k-replacement edges for each edge of a minimum cost spanning tree. Specifically, given a 2-connected graph G, a specified node s, and a shortest paths tree Ts = e1, e2, . . . , eni1 of s, where ei = (xi, yi) and xi = parentTs(yi), find a shortest path from yi to s in the graph G for 1 · i · n i 1. We present an O(m + n log n) time algorithm for this problem and a linear time algorithm for the case when all weights are equal. When the edge weights are integers, we present an algorithm that takes O(m + Tsort(n)) time, where Tsort(n) is the time required to sort n integers. We establish a lower bound of ­(min(m p n, n 2 )) for the directed version of our problem under the path comparison model, where Ts is the shortest paths destination tree of s. We show that any solution to the single link recovery problem can be adapted to solve the alternate path routing problem in ATM networks. Our technique for the single link failure recovery problem is adapted to find the k-replacement edges for the tree edges of a minimum cost spanning tree in O(m + n log n) time. Single node failures represent more than 85 of all node failures in the today's large communication networks such as the Internet. Also, these node failures are usually transient. Consequently, having the routing paths globally recomputed does not pay off since the failed nodes recover fairly quickly, and the recomputed routing paths need to be discarded. Instead, we develop algorithms and protocols for dealing with such transient single node failures by suppressing the failure (instead of advertising it across the network), and routing messages to the destination via alternate paths that do not use the failed node. We compare our solution to that of Ref. [11] wherein the authors have presented a "Failure Insensitive Routing" protocol as a proactive recovery scheme for handling transient node failures. We show that our algorithms are faster by an order of magnitude while our paths are equally good. We show via simulation results that our paths are usually within 15 of the optimal for randomly generated graph with 100-1000 nodes. We consider the setting of data storage across n nodes in a distributed manner. A data collector (DC) should be able to reconstruct the entire data by connecting to any k out of the n nodes and downloading all the data stored in them. When a node fails, it has to be regenerated back using the existing nodes. In a recent paper, have obtained an information theoretic lower bound for the repair bandwidth. Also, there has been additional interest in storing data in systematic form as no post processing is required when DC connects to k systematic nodes. Because of their preferred status there is a need to regenerate back any systematic node quickly and exactly. Replacement of a failed node by an exact replica is termed Exact Regeneration.In this paper, we consider the problem of minimizing the repair bandwidth for exact regeneration of the systematic nodes. The file to be stored is of size B and each node can store alpha = B k units of data. A failed systematic node is regenerated by downloading beta units of data each from d existing nodes. We give a lower bound for the repair bandwidth for exact regeneration of the systematic nodes which matches with the bound given by For d >= 2k-1 we give an explicit code construction which minimizes the repair bandwidth when the existing k-1 systematic nodes participate in the regeneration. We show the existence and construction of codes that achieve the bound for d >= 2k-3. Here we also establish the necessity of interference alignment. We prove that the bound is not achievable for d = 2k-1. Recovery from tracking failure is essential in any simultaneous localization and tracking system. In this context, we explore an efficient keyframe-based relocalization method based on frame encoding using randomized ferns. The method enables automatic discovery of keyframes through online harvesting in tracking mode, and fast retrieval of pose candidates in the case when tracking is lost. Frame encoding is achieved by applying simple binary feature tests which are stored in the nodes of an ensemble of randomized ferns. The concatenation of small block codes generated by each fern yields a global compact representation of camera frames. Based on those representations we define the frame dissimilarity as the block-wise hamming distance (BlockHD). Dissimilarities between an incoming query frame and a large set of keyframes can be efficiently evaluated by simply traversing the nodes of the ferns and counting image co-occurrences in corresponding code tables. In tracking mode, those dissimilarities decide whether a frame pose pair is considered as a novel keyframe. For tracking recovery, poses of the most similar keyframes are retrieved and used for reinitialization of the tracking algorithm. The integration of our relocalization method into a hand-held KinectFusion system allows seamless continuation of mapping even when tracking is frequently lost.