Skip to main content
SpringerLink
Log in

Covering a graph by circuits

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1978)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 62))

Included in the following conference series:

Abstract

A circuit cover is a set of circuits which cover all the edges of a graph; its length is the sum of the lengths of the circuits. In analyzing irrigation systems it is sometimes necessary to find a short circuit cover. It is shown that every bridge-free connected undirected graph with n vertices and e edges has a circuit cover the length of which is less than or equal to e+2nlogn. A probabilistic algorithm for finding such a cover is presented; its expected running time is 0(n2), independent of the input graph. This constitutes an example of solving a graph-theoretical problem by a probabilistic algorithm — the class of algorithms introduced by Rabin.

If the graph contains two edge-disjoint spanning trees then there exists a circuit cover of length at most e+n-1.

The relationship of circuit covers to the Chinese postman problem is also discussed. It is proven that there exist graphs for which the shortest circuit cover is longer than any optimal postman tour.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, (1974).

    Google Scholar 

  2. H. Cross, "Analysis of Flow in Networks of Conduits of Conductors", Bull. No. 286, Univ. of Illinois Engineering Experimental Station, Urbana, Ill. (1936).

    Google Scholar 

  3. J. Edmonds and E.L. Johnson, "Matching, Euler Tours and the Chinese Postman", Math. Programming 5 (1973), 88–124.

    Article  Google Scholar 

  4. J. Edmonds, and R.M. Karp, "Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems", J. ACM 19 (1972) 248–264.

    Article  Google Scholar 

  5. T. Kameda, "On Maximally Distant Spanning Trees of a Graph", Computing 17 (1976), 115–119.

    Google Scholar 

  6. C.L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill (1968).

    Google Scholar 

  7. M.O. Rabin, "Probabilistic Algorithms", Proc. Sym. on New Directions and Recent Results in Algorithms and Complexity, Carnegie-Mellon University, Academic Press (April 1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technion, Israel Institute of Technology, Haifa, Israel

    Alon Itai

  2. IBM Israel Scientific Center, Haifa, Israel

    Michael Rodeh

Authors
  1. Alon Itai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Rodeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Giorgio Ausiello Corrado Böhm

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Itai, A., Rodeh, M. (1978). Covering a graph by circuits. In: Ausiello, G., Böhm, C. (eds) Automata, Languages and Programming. ICALP 1978. Lecture Notes in Computer Science, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08860-1_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-08860-1_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08860-8

  • Online ISBN: 978-3-540-35807-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation