Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Approximating layout problems on random geometric graphs
Journal of Algorithms
Short Vertex Disjoint Paths and Multiconnectivity in Random Graphs: Reliable Network Computing
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Random Geometric Problems on [0, 1]²
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
On Random Intersection Graphs: The Subgraph Problem
Combinatorics, Probability and Computing
On the Cover Time for Random Walks on Random Graphs
Combinatorics, Probability and Computing
The vertex degree distribution of random intersection graphs
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
The cover time of sparse random graphs
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
The second eigenvalue of random walks on symmetric random intersection graphs
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
On the cover time of random geometric graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the existence of hamiltonian cycles in random intersection graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Simple and efficient greedy algorithms for hamilton cycles in random intersection graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Large independent sets in general random intersection graphs
Theoretical Computer Science
Expander properties and the cover time of random intersection graphs
Theoretical Computer Science
Sharp thresholds for Hamiltonicity in random intersection graphs
Theoretical Computer Science
On the independence number and Hamiltonicity of uniform random intersection graphs
Theoretical Computer Science
Selected combinatorial properties of random intersection graphs
Algebraic Foundations in Computer Science
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We investigate important combinatorial and algorithmic properties of Gn,m,p random intersection graphs. In particular, we prove that with high probability (a) random intersection graphs are expanders, (b) random walks on such graphs are "rapidly mixing" (in particular they mix in logarithmic time) and (c) the cover time of random walks on such graphs is optimal (i.e. it is Θ(n log n)). All results are proved for p very close to the connectivity threshold and for the interesting, non-trivial range where random intersection graphs differ from classical Gn,p random graphs.