Discrete Applied Mathematics
Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the marginal utility of network topology measurements
IMW '01 Proceedings of the 1st ACM SIGCOMM Workshop on Internet Measurement
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Approximability of the Minimum Test Collection Problem
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
On Metric Generators of Graphs
Mathematics of Operations Research
The power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Learning and Verifying Graphs Using Queries with a Focus on Edge Counting
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Network discovery and verification with distance queries
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
The covert set-cover problem with application to network discovery
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
On the metric dimension of infinite graphs
Discrete Applied Mathematics
Approximate discovery of random graphs
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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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Consider the problem of discovering (or verifying) the edges and non-edges of a network, modeled as a connected undirected graph, using a minimum number of queries. A query at a vertex v discovers (or verifies) all edges and non-edges whose endpoints have different distance from v. In the network discovery problem, the edges and non-edges are initially unknown, and the algorithm must select the next query based only on the results of previous queries. We study the problem using competitive analysis and give a randomized on-line algorithm with competitive ratio $O(\sqrt{nlogn})$ for graphs with n vertices. We also show that no deterministic algorithm can have competitive ratio better than 3. In the network verification problem, the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges. This problem has previously been studied as the problem of placing landmarks in a graph or determining the metric dimension of a graph. We show that there is no approximation algorithm for this problem with ratio o(log n) unless $\mathcal{P} = \mathcal{nP}$.