Reconstructing Cactus Graphs from Shortest Path Information
- Cite this paper as:
- Kranakis E., Krizanc D., Lu Y. (2016) Reconstructing Cactus Graphs from Shortest Path Information. In: Dondi R., Fertin G., Mauri G. (eds) Algorithmic Aspects in Information and Management. AAIM 2016. Lecture Notes in Computer Science, vol 9778. Springer, Cham
Imagine a disaster in which all edges of a network go down simultaneously. Imagine further that the routing tables of the nodes were not destroyed but are still available. Can one “reconstruct” the network from the routing tables? This question was first asked by Kranakis, Krizanc and Urrutia in 1995 as part of an attempt to answer the question of how much information about the network is stored in the node routing tables. In this paper, we answer this question in the affirmative if the underlying network is a cactus graph by providing an algorithm that returns all node-labelled cacti consistent with a given set of routing tables. This is the first such result for a class of non-geodetic graphs.