On the Relationship between the Biconnectivity Augmentation and Traveling Salesman Problems

Abstract A strategy for solving the traveling salesman problem is adapted to the problem of finding a biconnected subgraph of a weighted graph whose cost function satisfies the triangle inequality. An approximation algorithm similar to Christofides' algorithm [5] for the traveling salesman problem is shown to possess the same worst-case bound of 3 2 when applied to the biconnectivity augmentation problem. A tight inequality is derived relating the cost of an optimal traveling salesman tour to the cost of an optimal biconnection.

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