On the structure of unique shortest paths in graphs
G Bodwin - Proceedings of the Thirtieth Annual ACM-SIAM …, 2019 - SIAM
This paper develops a structural theory of unique shortest paths in real-weighted graphs.
Our main goal is to characterize exactly which sets of node sequences, which we call path …
Our main goal is to characterize exactly which sets of node sequences, which we call path …
Graph reconstruction and verification
How efficiently can we find an unknown graph using distance or shortest path queries
between its vertices? We assume that the unknown graph G is connected, unweighted, and …
between its vertices? We assume that the unknown graph G is connected, unweighted, and …
Optimal distance query reconstruction for graphs without long induced cycles
Given access to the vertex set $ V $ of a connected graph $ G=(V, E) $ and an oracle that
given two vertices $ u, v\in V $, returns the shortest path distance between $ u $ and $ v …
given two vertices $ u, v\in V $, returns the shortest path distance between $ u $ and $ v …
A simple algorithm for graph reconstruction
C Mathieu, H Zhou - Random Structures & Algorithms, 2023 - Wiley Online Library
How 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 …
We assume that the unknown graph is connected, unweighted, and has bounded degree …
Graph reconstruction via mis queries
C Konrad, C O'Sullivan, V Traistaru - arxiv preprint arxiv:2401.05845, 2024 - arxiv.org
We consider the Graph Reconstruction problem given only query access to the input graph
via a Maximal Independent Set oracle. In this setting, in each round, the player submits a …
via a Maximal Independent Set oracle. In this setting, in each round, the player submits a …
Reconstruction and verification of chordal graphs with a distance oracle
A hidden graph is a graph whose edge set is hidden. A distance oracle of a graph G is a
black-box that receives two vertices of G and outputs the distance between the two vertices …
black-box that receives two vertices of G and outputs the distance between the two vertices …
Finding mnemon: Reviving memories of node embeddings
Previous security research efforts orbiting around graphs have been exclusively focusing on
either (de-) anonymizing the graphs or understanding the security and privacy issues of …
either (de-) anonymizing the graphs or understanding the security and privacy issues of …
Tight query complexity bounds for learning graph partitions
X Liu, S Mukherjee - Conference on Learning Theory, 2022 - proceedings.mlr.press
Given a partition of a graph into connected components, the membership oracle asserts
whether any two vertices of the graph lie in the same component or not. We prove that for …
whether any two vertices of the graph lie in the same component or not. We prove that for …
Learning Hypertrees From Shortest Path Queries
We consider the problem of learning a labeled hypergraph from a given family of
hypergraphs, using shortest path (SP) queries. An SP query specifies two vertices and asks …
hypergraphs, using shortest path (SP) queries. An SP query specifies two vertices and asks …
Exact learning of multitrees and almost-trees using path queries
R Afshar, MT Goodrich - Latin American Symposium on Theoretical …, 2022 - Springer
Given a directed graph, G=(V, E), a path query, path (u, v), returns whether there is a
directed path from u to v in G, for u, v∈ V. Given only V, exactly learning all the edges in G …
directed path from u to v in G, for u, v∈ V. Given only V, exactly learning all the edges in G …