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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
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥10,700,000 (Direct Cost: ¥10,700,000)
Fiscal Year 2000: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1999: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1998: ¥4,500,000 (Direct Cost: ¥4,500,000)
Keywordsgraph / algorithm / edge-coloring / total coloring / cost edge-coloring / 1-vertex-coloring / [g, f]-coloring / 点彩色 / 金彩色 / 部分k-ホ / 辺ランク / ランク付け / 辺ランク付け / 彩色問題
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.

Report

(4 results)
  • 2001 Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (42 results)

All Other

All Publications (42 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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [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
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Mizuki,Z.B.Sui,H.Shizuyu T.Niskizeki: "On the average length of secret key exchange eulerian circuits"IEICE Trans Fund.. E83-A. 662-670 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] X.Zhou,S.Tamura,T.Nishizeki: "Finding edge-disjoint pattis in partial k-trees"Algorithmica. 26. 3-30 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] X.Zhou,K.Fuse,T.Nishizeki: "A linear algorithm for finding [g,f]-colorings of partial k-trees"Algorithmica. 27. 227-243 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] X.Zhou,y.Kanari,T.Nishizeki: "Generalized vertex-colorings of partial k-trees"IEICE Trans.Found.. E83-A. 671-678 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Md.A.Kashem,X.Zhou,T.Nishizeki: "Algorithms for generalized vertex-rankings of partial k-trees"Theoretical Computer Science. 240. 407-427 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] X.Zhou,T.Nishizeki: "Finding independent spanning trees in partial k-trees"Proc.of ISAAC'00,Lect.Notes in computer Sci.. 1969. 168-179 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Xiao Zhon,Takao Nishizeki: "Decompositions to degree-constrained subgraphs are simply reducible to edge-colorings"J.of Combinatorial Theory, Series B. 75. 270-287 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Xiao Zhon,Takao Nishizeki: "Edge-coloring and f-coloring for various classes of graphs"J.of Graph Algorithms and Applications. 3. 1-18 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Shuji Isobe,Xiao Zhon,Takao Nishizeki: "A polynomial-time algorithm for finding total colorings of partial k-trees"International Journal of Foundations of Computer Science. 10. 171-194 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Shuji Isobe,Xiao Zhon,Takao Nishizeki: "Alinearalgorithm 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)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Kusakari,D.Masubichi,T.Nishizeki: "Algorithms for finding noncrossing Steiner forests in plane graphs"Proc.of the 10th International Symposium on Algorithms and Computation,Lect.Notes in Computer Science,Spriger. 1741. 337-346 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Xiao Zhon,Syurei Tamura,Takao Nishizeki: "Finding edge-disjoint paths in partial k-trees"Algorithmica. 26. 3-30 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] X.Zhou, Md,A.Kashem, T.Nishizeki: "Generalized eolge-rankings of trees" IEICE Transaction on Fundamentals of Electronics,Communications and Computer Sciences. E81-A. 310-320 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Isobe, X.Zhon, T.Nishizeki: "A polynomial-time algorithm for finding total colorings of partial k thees" Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science,LNCS,Springer. 1517. 100-113 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] X.Zhen, T.Nishizeki: "The elye-disjoint paths proscem is NP-compietc for partial ktrees" Proceedings of the 9th International Symposium on Algorithns and Compntation,LNCS,Springer. 1533. 417-426 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Md.A.Kashem, X.Zhon, T.Nishizeki: "Algorithms for generalized eolye-rankings of partial k trees with boundecl maximum degree" Proceeding of International Conference on computer and Information Technology,ICCIT'98. 1. 45-51 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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