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2001 Fiscal Year Final Research Report Summary

A Method for solving scheduling problems by graph algorithms

Research Project

Project/Area Number 10205201
Research Category

Grant-in-Aid for Scientific Research on Priority Areas (B)

Allocation TypeSingle-year Grants
Research InstitutionTohoku University

Principal Investigator

ZHOU Xiao  Tohoku University, Graduate School of Information Sciences, Associate Professor, 情報科学研究科, 助教授 (10272022)

Co-Investigator(Kenkyū-buntansha) MIZUKI Takaaki  Tohoku University, Information Synergy Center, Associate Professor, ネットワーク研究部, 助教授 (90323089)
KUSAKARI Yishiyoki  Akita Prefectural University, Department of Electronics and Information Systems, Lecturer, システム科学技術学部・電子情報システム学科, 講師 (50302203)
Project Period (FY) 1998 – 2000
Keywordsgraph / algorithm / edge-coloring / total coloring / cost edge-coloring / 1-vertex-coloring / [g, f]-coloring
Research Abstract

The scheduling problem was modeled by using the graph in this research. It is well-known that the coloring problem, from which the application to this problem is strongly expected, is NP-hard in general. So it is very unlikely that there exists an efficient algorithm to solve it. However, we showed that the problem can be solved efficiently for some restricted class of graphs. The results achieved for this research are chiefly four of the following.
1. We gave a linear algorithm to solve [g, f]-coloring problem for partial k-trees by a dynamic programming method. This result was published in Algorithmica(1999).
2. We give a linear algorithm to solve the total coloring problem for partial k-trees which is published in ISAAC' 99. Afterwards, we improved it for degenerate graphs which is published in ICALP' 01.
3. We gave a polynomial-time algorithm to solve the 1-vertex-coloring problem for partial k-trees which is published in IEICE Trans. on fundamentals of Electronics, Communication and Computer Science (2000).
4. We give a polynomial-time algorithm to solve the cost edge-coloring problem for trees which is published in COCOON' 01.

  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] X.Zhou, Md.A.Kashem, T.Nishizeki: "Generalized edge-ranking of trees"IEICE Trans.On Fundamentals of Electronics,Communication and Computer Sciences. E81-A. 310-320 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Isobe, X.Zhou, T.Nishizeki: "A polynomial-time algorithm for finding total colorings of partial k-trees"WG'98,LNCS,Springer. 1517. 100-113 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Zhou, T.Nishizeki: "The edge-disjoint paths problem is NP-complete for partial k-trees"ISAAC'98,LNCS,Springer. 1533. 417-425 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Md.A.Kashem, X.Zhou, T.Nishizeki: "Algorithms for generalized edge-rankings of partial k-trees"The first International Conference on Computer and Information Technology. 1. 45-51 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Zhou, T.Nishizeki: "Decompositions to degree-constrained subgraphs are simply reducible to edge-colorings"Journal of Combinatorial Theory,Series B. 75. 270-287 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Zhou, T.Nishizeki: "Edge-coloring and f-colorings for various classes of graphs"Journal of Graph Algorithms and Applications. 3. 1-18 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Isobe, X.Zhou, T.Nishizeki: "A polynomial-time algorithm for finding total colorings of partial k-trees"International Journal of Foundations of Computer Science. 10. 171-194 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Zhou, S.Tamura, T.Nishizeki: "Finding edge-disjoint paths in partial k-trees"Algorithmica. 26. 3-30 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Zhou, K.Fuse, T.Nishizeki: "A linear algorithm for finding[g,f]-colorings of partial k-trees"Algorithmica. 27. 227-243 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nishizeki, J.Vygen, X.Zhou: "The edge-disjoint paths problem is NP-complete for series-parallel graphs"The First Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications. 1. 103-110 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Isobe, X.Zhou, T.Nishizeki: "A linear algorithm for finding total colorings of partial k-trees"ISAAC'99,LNCS,Springer. 1741. 347-356 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X.Zhou, Y.Kanari, T.Nishizeki: "Generalized vertex-coloring of partial k-trees"IEICE Trans on Fundaments of Electronics,Compunication and Computer Science. E83-A. 671-678 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Md.A.Kashem, X.Zhou, T.Nishizeki: "Algorithms for generalized edge-rankings of partial k-trees"Theoretical Computer Science. 240. 212-226 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] X. Zhou, Md. A. Kashem, T. Nishizeki: "Generalized edge-rankings of trees"IEICE Trans. on Fundamentals of Electronics, Communication and Computer Sciences. E81-A. 310-320 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Isobe, X. Zhou, T. Nishizeki: "A polynomial-time algorithm for finding total colorings of partial k-trees"Proc. of the 24th International Workshop, Graph-Theoretic Concepts in Computer Science, WG'98, Lect. Notes in Computer Science, Springer. 1517. 100-113 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X. Zhou, T. Nishizeki: "The edge-disjoint paths problem is NP-complete for partial k-trees"Proc. of the Sixth Annual International Symposium on Algorithms and Computing, ISAAC'98. Lect. Notes in Computer Science, Springer. 1533. 417-425 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Md. A. Kashem, X. Zhou, T. Nishizeki: "Algorithms for generalized edge-rankings of partial k-trees"Proc. of the First International Conference on Computer and Information Technology. 1. 45-51 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X. Zhou, T. Nishizeki: "Decompositions to degree-constrained subgraphs are simply reducible to edge-colorings"Journal of Combinatorial Theory, Series B. 75. 270-287 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X. Zhou, T. Nishizeki: "Edge-coloring and f-colorings for various classes of graphs"Journal of Graph Algorithms and Applications. 3. 1-18 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Isobe, X. Zhou, T. Nishizeki: "A polynomial-time algorithm for finding total colorings of partial k-trees"International Journal of Foundations of Computer Science. 10. 171-194 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X. Zhou, S. Tamura, T. Nishizeki: "Finding edge-disjoint paths in partial k-trees"Algorithmica. 26. 3-30 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X. Zhou, K. Fuse, T. Nishizeki: "A linear algorithm for finding [g, f]-colorings of partial k-trees"Algorithmica. 27. 227-243 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Nishizeki, J. Vygen, X. Zhou: "The edge-disjoint paths problem is NP-complete for series-parallel graphs"Proc. of the First Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications. 103-110 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Isobe, X. Zhou, T. Nishizeki: "A linear algorithm for finding total colorings of partial $k$-trees"Proc. of the 10th International Symposium on Algorithms and Computation, Lect. Notes in Computer Science, Springer. 1741. 347-356 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] X. Zhou, Y. Kanari and T. Nishizeki: "Generalized vertex-coloring of partial k-trees"IEICE Trans. on Fundamentals of Electronics, Communication and Computer Sciences. E83-A. 671-678 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Md. A. Kashem, X. Zhou, d T. Nishizeki: "Algorithms for generalized vertex-rankings of partial k-trees"Theoretical Computer Science. 240. 212-226 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2003-09-17  

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