Graph Reconstruction via Distance Oracles
Claire Mathieu, Hang Zhou

TL;DR
This paper introduces randomized algorithms for reconstructing various classes of graphs using distance oracles, achieving improved query complexities for degree-bounded and outerplanar graphs, and near-optimal results for general graphs.
Contribution
It presents new randomized algorithms for graph reconstruction with optimized query complexities for specific graph classes.
Findings
Reconstruction of degree-bounded graphs with O(n^{3/2}) queries.
Reconstruction of outerplanar graphs with O(n) queries.
Near-optimal approximate reconstruction of general graphs.
Abstract
We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity ; reconstruction of a degree bounded outerplanar graph with query complexity ; and near-optimal approximate reconstruction of a general graph.
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Taxonomy
TopicsDigital Image Processing Techniques · Topological and Geometric Data Analysis · Graph Theory and Algorithms
