ON FINDING SPARSE THREE-EDGE-CONNECTED AND THREE-VERTEX-CONNECTED SPANNING SUBGRAPHS (original) (raw)
2014, International Journal of Foundations of Computer Science
We present algorithms that construct a sparse spanning subgraph of a 3-edge-connected graph that preserves 3-edge connectivity or of a 3-vertex-connected graph that preserves 3-vertex connectivity. Our algorithms are conceptually simple and run in O(|E|) time. These simple algorithms can be used to improve the efficiency of the best-known algorithms for 3-edge and 3-vertex connectivity and their related problems, by preprocessing the input graph so as to trim it down to a sparse graph. Afterwards, the original algorithms run in O(|V |) instead of O(|E|) time. Our algorithms generate an adjacency-lists structure to represent the sparse spanning subgraph, so that when a depth-first search is performed over the subgraph based on this adjacency-lists structure it actually traverses the paths in an ear-decomposition of the subgraph. This is useful because many of the existing algorithms for 3-edge-or 3-vertex connectivity and their related problems are based on an ear-decomposition of the given graph. Using such an adjacency-lists structure to represent the input graph would greatly improve the run-time efficiency of these algorithms.
Sign up for access to the world's latest research.
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.