You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: 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.

[2]: The increasing proportion of data traffic being carried in public networks is necessitating tractable and scalable algorithms in the design of ATM networks. In particular, the design of routing tables for ATM networks operated under the interim inter-switch signalling protocol (IISP) requires a significant amount of manual work in order to design and implement the underlying static routing tables that enable end-to-end connectivity as the network grows. This paper presents a scalable algorithm that generates IISP routing table entries such that no loops are created and so that connectivity is maintained between all origin destination nodes under single-link failures. The algorithm generates shortest (i.e., lowest-cost) primary and alternate paths for any single-link failure scenario, while also demonstrating that at least one such solution can be found for any network graph devoid of bridges. Note that re-routing for single-link failures is considered adequate when sufficient protection is provided at the lower network layers. The algorithm has been fully implemented in a practical software tool, with execution time being a polynomial function of the network complexity.

[3]: 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.
Slosiar and Latin [2] 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 [3] . The local-rerouting based fast recovery protocol of [1] can use these paths to recover from single link failures as well. Both these algorithms, [3] [2] , are centralized algorithms that work using the information of the entire communication graph.