Universal cycles for combinatorial structures
Discrete Mathematics
On some properties of DNA graphs
Discrete Applied Mathematics
Power-optimal encoding for DRAM address bus (poster session)
ISLPED '00 Proceedings of the 2000 international symposium on Low power electronics and design
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Synchronizing finite automata on Eulerian digraphs
Theoretical Computer Science - Mathematical foundations of computer science
De Bruijn sequences and De Bruijn graphs for a general language
Information Processing Letters
Minimal de bruijn sequence in a language with forbidden substrings
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
On the complexity of the Eulerian closed walk with precedence path constraints problem
Theoretical Computer Science
| Hi-index | 0.00 |
Let G = (V,A) be an Eulerian directed graph with an arc-labeling. In this work we study the problem of finding an Eulerian circuit of lexicographically minimal label among all Eulerian circuits of the graph. We prove that this problem is NP-hard by showing a reduction from the Directed-Hamiltonian-Circuit problem. If the labeling of the arcs is such that arcs going out from the same vertex have different labels, the problem can be solved in polynomial time. We present an algorithm to construct the unique Eulerian circuit of lexicographically minimal label starting at a fixed vertex. Our algorithm is a recursive greedy algorithm which runs in ${\mathcal O}$(|A|) steps. We also show an application of this algorithm to construct the minimal De Bruijn sequence of a language.