Graph traversals, genes, and matroids: An efficient case of the travelling salesman problem
In this paper we consider graph traversal problems that arise from a particular technology for DNA sequencing — sequencing by hybridization (SBH). We first explain the connection of the graph problems to SBH and then focus on the traversal problems. We describe a practical polynomial time solution to the Travelling Salesman Problem in a rich class of directed graphs (including edge weighted binary de Bruijn graphs), and provide a bounded-error approximation algorithm for the maximum weight TSP in a superset of those directed graphs. We also establish the existence of a matroid structure defined on the set of Euler and Hamilton paths in the restricted class of graphs.
KeywordsMinimum Span Tree Travelling Salesman Problem Hamilton Path Binary Number Basic Circle
Unable to display preview. Download preview PDF.
- 1.S. Even. Graph Algorithms. Computer Science Press, Mill Valley, CA., 1979.Google Scholar
- 2.M. Garey and D. Johnson. Computers and intractability. Freeman, San Francisco, 1979.Google Scholar
- 3.S. Golomb. Shift register sequences. Holden-Day, San Francisco, 1967.Google Scholar
- 4.D. Gusfield, L. Wang, and P. Stelling. Graph traversals, genes and matroids: An efficient special case of the travelling salesman problem. Technical Report 96-3, Department of Computer Science, University of California, Davis, January 1996.Google Scholar
- 5.R. Kosaraju, J. Park, and C. Stein. Long tours and short superstrings. In Proceedings of the 35'th Annual Symposium on Foundations of Computer Science, pages 166–177, 1994.Google Scholar
- 7.P. A. Pevzner. Dna physical mapping and alternating eulerian cycles in colored graphs. Algorithmica, 12:77–105, 1994.Google Scholar
- 8.S. Stein. The mathematician as explorer. Scientific American, pages 149–63, May 1961.Google Scholar