Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Reconstructing a Hamiltonian cycle by querying the graph: application to DNA physical mapping
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
On the complexity of distance-based evolutionary tree reconstruction
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
On the longest path algorithm for reconstructing trees from distance matrices
Information Processing Letters
The Journal of Machine Learning Research
Combinatorial search on graphs motivated by bioinformatics applications: a brief survey
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
network discovery and verification
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Optimal query complexity bounds for finding graphs
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Optimally reconstructing weighted graphs using queries
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Toward a deterministic polynomial time algorithm with optimal additive query complexity
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Inferring social networks from outbreaks
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Topology discovery of sparse random graphs with few participants
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Topology discovery of sparse random graphs with few participants
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions
Journal of Computer and System Sciences
On parity check (0, 1)-matrix over Zp
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Graph reconstruction via distance oracles
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We consider the problem of learning and verifying hidden graphs and their properties given query access to the graphs. We analyze various queries (edge detection, edge counting, shortest path), but we focus mainly on edge counting queries. We give an algorithm for learning graph partitions using O(nlogn) edge counting queries. We introduce a problem that has not been considered: verifying graphs with edge counting queries, and give a randomized algorithm with error 茂戮驴for graph verification using O(log(1/茂戮驴)) edge counting queries. We examine the current state of the art and add some original results for edge detection and shortest path queries to give a more complete picture of the relative power of these queries to learn various graph classes. Finally, we relate our work to Freivalds' `fingerprinting technique' --- a probabilistic method for verifying that two matrices are equal by multiplying them by random vectors.