Abstract
AbstractHow efficiently can we find an unknown graph using distance queries between its vertices? We assume that the unknown graph is connected, unweighted, and has bounded degree. The goal is to find every edge in the graph. This problem admits a reconstruction algorithm based on multi‐phase Voronoi‐cell decomposition and using distance queries. In our work, we analyze a simple reconstruction algorithm. We show that, on random ‐regular graphs, our algorithm uses distance queries. As by‐products, with high probability, we can reconstruct those graphs using queries to an all‐distances oracle or queries to a betweenness oracle, and we bound the metric dimension of those graphs by . Our reconstruction algorithm has a very simple structure, and is highly parallelizable. On general graphs of bounded degree, our reconstruction algorithm has subquadratic query complexity.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
