A Simple PrimalDual Approximation Algorithm for 2EdgeConnected Spanning Subgraphs
Abstract
We propose a simple and natural approximation algorithm for the problem of finding a 2edgeconnected spanning subgraph of minimum total edge cost in a graph. The algorithm maintains a spanning forest starting with an empty edge set. In each iteration, a new edge incident to a leaf is selected in a natural greedy manner and added to the forest. If this produces a cycle, this cycle is contracted. This growing phase ends when the graph has been contracted into a single node and a subsequent cleanup step removes redundant edges in reverse order. We analyze the algorithm using the primaldual method showing that its solution value is at most 3 times the optimum. Although this only matches the ratio of existing primaldual algorithms, we require only a single growing phase, thereby addressing a question by Williamson. Also, we consider our algorithm to be not only conceptually simpler than the known approximation algorithms but also easier to implement in its entirety. For n and m being the number of nodes and edges, respectively, it runs in O(min{nm, m + n^2 log n}) time and O(m) space without data structures more sophisticated than binary heaps and graphs, and without graph algorithms beyond depthfirst search.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.04651
 Bibcode:
 2018arXiv180804651B
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 14 pages, 2 figures