Title: Tight bounds for reconstructing graphs from distance queries
| Speaker: | Carla Groenland |
| Affiliation: | TU Delft |
| Location: | MC 5501 |
Abstract: Suppose you are given the vertex set of a graph and you want to discover the edge set. An oracle can tell you, given two vertices, what the distance is between these vertices in the graph. (For example, in a computer network, this would represent the minimum number of communication links needed to send a message from one computer to another.) Based on the answer, you may select the next query. The (labelled) graph is reconstructed when there is a single edge set compatible with the answers. How many queries are needed, in the worst case? The question becomes interesting for bounded degree graphs. We provide tight bounds for various classes of graphs, improving both the lower and upper bound, in both the randomized and deterministic setting.