On the independence number of random graphs
Discrete Mathematics
On the independence and chromatic numbers of random regular graphs
Journal of Combinatorial Theory Series B
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Maximum matchings in sparse random graphs: Karp-Sipser revisited
Random Structures & Algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimum independent dominating sets of random cubic graphs
Random Structures & Algorithms
On the Approximation Properties of Independent Set Problem in Degree 3 Graphs
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Small Maximal Matchings in Random Graphs
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Improved Approximations of Independent Dominating Set in Bounded Degree Graphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
| Hi-index | 0.00 |
In this paper we introduce a general strategy for approximating the solution to minimisation problems in random regular graphs. We describe how the approach can be applied to the minimum vertex cover (MVC), minimum independent dominating set (MIDS) and minimum edge dominating set (MEDS) problems. In almost all cases we are able to improve the best known results for these problems. Results for the MVC problem translate immediately to results for the maximum independent set problem. We also derive lower bounds on the size of an optimal MIDS.