Discrete Applied Mathematics
On inferring autonomous system relationships in the internet
IEEE/ACM Transactions on Networking (TON)
On the marginal utility of network topology measurements
IMW '01 Proceedings of the 1st ACM SIGCOMM Workshop on Internet Measurement
Regular Article: The Diameter of Sparse Random Graphs
Advances in Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Analysis of Internet Inter-Domain Topology and Route Stability
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
On Metric Generators of Graphs
Mathematics of Operations Research
On the bias of traceroute sampling: or, power-law degree distributions in regular graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Exploring networks with traceroute-like probes: theory and simulations
Theoretical Computer Science - Complex networks
Computing the types of the relationships between autonomous systems
IEEE/ACM Transactions on Networking (TON)
On the Metric Dimension of Cartesian Products of Graphs
SIAM Journal on Discrete Mathematics
Network discovery and verification with distance queries
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
network discovery and verification
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Network Discovery and Verification
IEEE Journal on Selected Areas in Communications
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
Network verification via routing table queries
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
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In the layered-graph query model of network discovery, a query at a node v of an undirected graph G discovers all edges and non-edges whose endpoints have different distance from v. We study the number of queries at randomly selected nodes that are needed for approximate network discovery in Erdos-Rényi random graphs Gn,p. We show that a constant number of queries is sufficient if p is a constant, while Ω(nα) queries are needed if p = nε/n, for arbitrarily small choices of ε = 3/(6 ċ i + 5) with i ∈ N. Note that α 0 is a constant depending only on ε. Our proof of the latter result yields also a somewhat surprising result on pairwise distances in random graphs which may be of independent interest: We show that for a random graph Gn,p with p = nε/n, for arbitrarily small choices of ε 0 as above, in any constant cardinality subset of the nodes the pairwise distances are all identical with high probability.