Orienting graphs to optimize reachability
Information Processing Letters
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Computing minimal triangulations in time O(nα log n) = o(n2.376)
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs
SIAM Journal on Computing
Minimal proper interval completions
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Minimal interval completion through graph exploration
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Minimal split completions of graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Minimal interval completion through graph exploration
Theoretical Computer Science
Characterizing and computing minimal cograph completions
Discrete Applied Mathematics
Improving scratchpad allocation with demand-driven data tiling
CASES '10 Proceedings of the 2010 international conference on Compilers, architectures and synthesis for embedded systems
An O(n2)-time algorithm for the minimal interval completion problem
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
An O( n2)-time algorithm for the minimal interval completion problem
Theoretical Computer Science
| Hi-index | 0.05 |
A transitive orientation of an undirected graph is an assignment of directions to its edges so that these directed edges represent a transitive relation between the vertices of the graph. Not every graph has a transitive orientation, but every graph can be turned into a graph that has a transitive orientation, by adding edges. We study the problem of adding an inclusion minimal set of edges to an arbitrary graph so that the resulting graph is transitively orientable. We show that this problem can be solved in polynomial time, and we give a surprisingly simple algorithm for it. We use a vertex incremental approach in this algorithm, and we also give a more general result that describes graph classes @P for which @P completion of arbitrary graphs can be achieved through such a vertex incremental approach.