Skip to main content

Polynomial Algorithms for Some Hard Problems of Finding Connected Spanning Subgraphs of Extreme Total Edge Weight

  • Conference paper
Operations Research Proceedings 2006

Part of the book series: Operations Research Proceedings ((ORP,volume 2006))

Abstract

Several hard optimization problems of finding spanning connected subgraphs with extreme total edge weight are considered. A number of results on constructing polynomial algorithms with performance guarantees for these problems is presented.1

Research was supported by Russian Foundation for Basic Research (project 05-01-00395) and INTAS (grant 04-77-7173).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ageev A., Baburin A, Gimadi E. (2006) Polynomial algorithm with performance guarantee of 3/4 for a problem of finding two edge-disjoint Hamiltonian circuits of maximal total edge weight (in russian). Discrete analysis and oper. research. Ser. 1., V. 13,2:10–20.

    Google Scholar 

  2. Baburin E., Gimadi E. (2002) On asymptotical optimality of algoritm for solving maximum weight Euclidean TSP (in russian). Discrete analysis and operations research. Ser. 1., V. 9,4: 23–32.

    Google Scholar 

  3. Baburin A., Gimadi E., Korkishko N. (2004) Approximation algorithms for finding two edge-disjoint Hamiltonian circuits of minimal total edge weight (in russian). Discrete analysis and oper. research. Ser. 2., V. 11,1:11–25.

    Google Scholar 

  4. Baburin E., Gimadi E. (2005) Approximation algorithms for finding a maximum-weight spanning connected subgraph with given vertex degrees. Oper. Res. Proc. 2004, Intern. Conf. OR 2004, Tilburg. Springer, Berlin, 343–351.

    Google Scholar 

  5. Berman P., Karpinski M. (2006) 8/7-approximation algorithm for (1,2)-TSP. Proc. 17th ACM-SIAM SODA, 641–648.

    Google Scholar 

  6. Croce F.D., Pashos V.Th., Calvo R.W. (2005) Approximating the 2-peripatetic salesman problem. 7th Workshop on Modelling and Algorithms for Planning and Scheduling Problems MAPS 2005. (Siena, Italy, June 6–10). 114–116.

    Google Scholar 

  7. De Kort J.B. J.M. (1991) Lower bounds for symmetric K-peripatetic salesman problems. Optimization. V. 22,1: 113–122.

    Article  Google Scholar 

  8. Edmonds J., Johnson E. L. (1970) Matchings: a well solvable class of integer linear programs. Combinatorial Structures and Their Applications. New York: Gordon and Breach. 89–92.

    Google Scholar 

  9. Gabow H. N. (1983) An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems. Proc. 15th annual ACM symposium on theory of computing, (Boston, April 25–27, 1983). New York: ACM, 448–456.

    Google Scholar 

  10. Gimadi E.Kh., Serdyukov A.I. (2001) Problem of Finding the Maximal Spanning Connected Subgraph with Given Vertex Degrees. Oper. Res. Proceed. 2000 (Eds Fleishman B. at al.) Springer, Berlin, 55–59.

    Google Scholar 

  11. Havel V. (1955) A note to question of existance of finite graphs, Casopis Pest Mat, V. 80, 477–480.

    Google Scholar 

  12. Harary F. (1969) Graph Theory, Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  13. Krarup J. (1975) The peripatetic salesman and some related unsolved problems. Combinatorial programming: methods and applications (Proc. NATO Advanced Study Inst., Versailles, 1974). 173–178.

    Google Scholar 

  14. Papadimitriu C. H., Yannakakis M. (1993) The traveling salesman problem with distance One and Two. Math. Oper. Res. V. 18,1:1–11.

    Article  Google Scholar 

  15. Serdukov A.I. (1987) An Asymptoticaly Optimal Algorithm for Solving Max Euclidean TSP. Metodi Celochislennoi Optimizacii (Upravliaemie Sistemi), Novosibirsk. 27:79–87.

    Google Scholar 

  16. The Traveling Salesman Problem and its Variations. Gutin G., Punnen A.P. (eds). Kluver Academic Publishers, Dordrecht / Boston / London. 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baburin, A., Gimadi, E. (2007). Polynomial Algorithms for Some Hard Problems of Finding Connected Spanning Subgraphs of Extreme Total Edge Weight. In: Waldmann, KH., Stocker, U.M. (eds) Operations Research Proceedings 2006. Operations Research Proceedings, vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69995-8_36

Download citation

Publish with us

Policies and ethics