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Efficient reduction for path problems on circular-arc graphs

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Abstract

An efficient reduction process for path problems on circular-arc graphs is introduced. For the parity path problem, this reduction gives anO(n+m) algorithm for proper circular-arc graphs, and anO(n+m) algorithm for general circular-arc graphs. This reduction also gives anO(n+m) algorithm for the two path problem on circular-arc graphs.

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References

  1. Srinivasa R. Arikati and Uri N. Peled.A linear algorithm for group path problem on chordal graphs. Technical report, RRR No. 29–90, RUTCOR, June 1990.

  2. D. Bienstock.On the complexity of testing for odd holes and induced odd paths. To appear in Discrete Mathematics.

  3. M. A. Bonuccelli.Dominating sets and domatic number of circular-arc graphs. Discrete Appl. Maths., 12: 203–213, 1985.

    Google Scholar 

  4. G. A. Cypher.The k paths problem. PhD thesis, Yale University, 1980.

  5. M. C. Golumbic.Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.

    Google Scholar 

  6. Wen-Lian Hsu.Maximum weight clique algorithms for circular-arc graphs and circle graphs. SIAM Journal on Computing, 14: 224–231, 1985.

    Google Scholar 

  7. Wen-Lian Hsu.Recognizing planar perfect graphs. Journal of the ACM, 34: 255–288, 1987.

    Google Scholar 

  8. J. M. Keil.Finding hamiltonian circuits in interval graphis. Information Processing Letters, 20: 201–206, 1985.

    Google Scholar 

  9. S. V. Krishman, S. Seshadri and C. Pandu Rangan.A new linear algorithm for two path problem on chordal graphs. In Eighth FST and TCS, Pune, India, 1988.

    Google Scholar 

  10. G. K. Manacher, S. R. Arikati and Pandu Rangan C.Chord-free path problems on interval graphs. (submitted).

  11. S. Masuda and K. Nakajima.An optimum algorithm for finding a maximum independent set of a circular-arc graph. SIAM Journal on Computing, 17: 41–52, 1988.

    Google Scholar 

  12. Y. Shiloach.A polynomial solution to the undirected two path problem. Journal of the ACM, 27: 445–456, 1980.

    Google Scholar 

  13. A. Tucker.An efficient test for circular-arc graphs. SIAM Journal on Computing, 9: 1–24, 1980.

    Google Scholar 

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Author notes

  1. Srinivasa R. Arikati

    Present address: Dept. of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Box 4348, 60680, Chicago, IL, USA

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, 600 036, Madras, India

    Srinivasa R. Arikati, C. Pandu Rangan & Glenn K. Manacher

  2. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Box 4348, 60680, Chicago, IL, USA

    Srinivasa R. Arikati, C. Pandu Rangan & Glenn K. Manacher

Authors
  1. Srinivasa R. Arikati
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  2. C. Pandu Rangan
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  3. Glenn K. Manacher
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Arikati, S.R., Pandu Rangan, C. & Manacher, G.K. Efficient reduction for path problems on circular-arc graphs. BIT 31, 181–193 (1991). https://doi.org/10.1007/BF01931279

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  • DOI: https://doi.org/10.1007/BF01931279

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