Reducing edge connectivity to vertex connectivity
ACM SIGACT News
Graph Algorithms
A Simple 3-Edge-Connected Component Algorithm
Theory of Computing Systems
Yet another optimal algorithm for 3-edge-connectivity
Journal of Discrete Algorithms
Algorithms for Placing Monitors in a Flow Network
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Cactus graphs for genome comparisons
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
The cluster editing problem: implementations and experiments
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Spare capacity allocation using shared backup path protection for dual link failures
Computer Communications
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Graph connectivity is a graph-theoretic concept that is fundamental to the studies of many applications such as network reliability and network decomposition. For the 3-edge-connectivity problem, recently, it has been shown to be useful in a variety of apparently unrelated areas such as solving the G-irreducibility of Feynman diagram in physics and quantum chemistry, editing cluster and aligning genome in bioinformatics, placing monitors on the edges of a network in flow networks, spare capacity allocation and decomposing a social network to study its community structure. A number of linear-time algorithms for 3-edge-connectivity have thus been proposed. Of all these algorithms, the algorithm of Tsin is conceptually the simplest and also runs efficiently in a recent study. In this article, we shall show how to simplify the implementation of a key step in the algorithm making the algorithm much more easier to implement and run more efficiently. The simplification eliminates a rather complicated linked-lists structure and reduces the space requirement of that step from O(|E|) to O(|V|), where V and E are the vertex set and the edge set of the input graph, respectively.