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European Symposium on Algorithms

ESA 1995: Algorithms — ESA '95 pp 1–16Cite as

On mixed connectivity certificates

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 979))

Abstract

Vertex and edge connectivity are special cases of mixed connectivity, in which all edges and a specified set of vertices play a similar role. Certificates of k-connectivity for a graph are obtained by removing a subset of its edges, while preserving its connectivity up to k.

We unify the previous work on connectivity certificates and extend it to handle mixed connectivity and multigraphs. Our treatment contributes a new insight of the pertinent structures, yielding more general results and simpler proofs. Also, we present a communication-optimal distributed algorithm for finding mixed connectivity certificates.

Part of this research was conducted while visiting the Instituto de Matemáticas, U.N.A.M. Supported by the Fund for the Promotion of Research at the Technion and DGAPA Projects, U.N.A.M.

Supported by the Israeli Council for Higher Education and NSF grant CCR90 15276. Part of this research was conducted in Boston University.

Part of this research was conducted while visiting the MIT Laboratory for Computer Science, and GRL Digital Equipment Corporation. Partly supported by DGAPA Projects, U.N.A.M.

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References

  1. B. Awerbuch and D. Peleg, “Network synchronization with polylogarithmic overhead”, in FOCS, 1990, pp. 514–522.

    Google Scholar 

  2. J. Cheriyan and S. N. Maheshwari, “Finding nonseparating induced cycles and independent spanning trees in 3-connected graphs”, J. Algorithms, 9, 1988, pp. 507–537.

    Article  Google Scholar 

  3. J. Cheriyan, M.-Y. Kao, R. Thurimella, “Scan-first search and sparse certificates: an improved parallel algorithm for k-vertex connectivity”, SIAM J. of Computing, 22(1), 1993, pp. 157–174.

    Article  Google Scholar 

  4. G. B. Dantzig and D. R. Fulkerson, “On the Max-Flow Min-Cut Theorem of networks”, Linear Inequalities and Related Systems, Annals of Math. Study, 38, Princeton University Press, 1956, pp.215–221.

    Google Scholar 

  5. D. Eppstein, Z. Galil, G. F. Italiano, A. Nissenzweig, “Sparsification — a technique for speeding up dynamic algorithms”, FOCS, 1992, pp. 60–69.

    Google Scholar 

  6. A. Frank, T. Ibaraki, H. Nagamochi, “On sparse subgraphs preserving connectivity properties”, J. of Graph Theory, 17(3), 1993, pp. 275–281.

    Google Scholar 

  7. H. Gabow, “A matroid approach to finding edge connectivity and packing arborescences”, STOC, 1991, pp. 112–132.

    Google Scholar 

  8. M. R. Garey and D. S. Johnson, Computers and intractability, a guide to the theory of NP-completeness, Freeman, San Francisco, 1979, p. 198.

    Google Scholar 

  9. A. Itai and M. Rodeh, “The Multi-Tree Approach to Reliability in Distributed Networks”, Information and Computation, 79(1), 1988, pp. 3–59.

    Article  Google Scholar 

  10. W. Mader, “Über minimal n-fach zusammenhängende, unendliche Graphen und ein Extremalproblem,” Arch. Mat., Vol. XXIII, 1972, pp. 553–560.

    Article  Google Scholar 

  11. W. Mader, “Grad und lokaler Zusammenhang in endlichen Graphen,” Math. Ann., Vol. 205, 1973, pp. 9–11.

    Article  Google Scholar 

  12. W. Mader, “Connectivity and edge-connectivity in finite graphs,” in Surveys on Combinatorics, (B. Bollobas, ed.), London Math. Soc. Lecture Note Series, Vol. 38, 1979, pp. 293–309.

    Google Scholar 

  13. H. Nagamochi and T. Ibaraki, “A Linear-time algorithm for finding a sparse k-connected spanning subgraph of a k-conneceted graph,” Algorithmica, 7, 1992, pp. 583–596.

    Article  Google Scholar 

  14. R. Thurimella, “Sub-linear Distributed Algorithms for sparse certificates and Biconnected Components,” to appear in Proc. of the 14th ACM Symposium on Principles of Distributed Computing, August 1995.

    Google Scholar 

  15. A. A. Zykov, Theory of Finite Graphs, (in Russian), Nauka, Novosibirsk, 1969, see pp. 104–105.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Technion, 32000, Haifa, Israel

    Shimon Even & Gene Itkis

  2. Instituto de Matemáticas, U.N.A.M., Ciudad Universitaria, D.F. 04510 México

    Sergio Rajsbaum

Authors
  1. Shimon Even
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  2. Gene Itkis
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  3. Sergio Rajsbaum
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Editor information

Paul Spirakis

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© 1995 Springer-Verlag Berlin Heidelberg

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Even, S., Itkis, G., Rajsbaum, S. (1995). On mixed connectivity certificates. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_130

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  • DOI: https://doi.org/10.1007/3-540-60313-1_130

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60313-9

  • Online ISBN: 978-3-540-44913-3

  • eBook Packages: Springer Book Archive

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