메뉴 건너뛰기




Volumn 43, Issue 1, 2004, Pages 1-9

Branch Decompositions and Minor Containment

Author keywords

Branch decomposition; Branchwidth; Dynamic programming; Graph minor; Minor containment; Obstruction set

Indexed keywords

BRANCH DECOMPOSITION; BRANCHWIDTH; GRAPH MINOR; MINOR CONTAINMENT; OBSTRUCTION SET;

EID: 2042546751     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/net.10099     Document Type: Article
Times cited : (22)

References (42)
  • 1
    • 84937405099 scopus 로고    scopus 로고
    • Improved tree decomposition based algorithms for domination-like problems
    • Heidelberg, Germany, Springer-Verlag
    • J. Alber and R. Niedermeier, Improved tree decomposition based algorithms for domination-like problems, Proc 5th Latin American Theoretical Informatics (LATIN 2002), Heidelberg, Germany, Springer-Verlag, 2002, pp. 613-627.
    • (2002) Proc 5th Latin American Theoretical Informatics (LATIN 2002) , pp. 613-627
    • Alber, J.1    Niedermeier, R.2
  • 2
    • 0000504885 scopus 로고
    • Easy problems for tree-decomposable graphs
    • S. Arnborg, J. Lagergren, and D. Seese, Easy problems for tree-decomposable graphs, J Alg 12 (1991), 308-340.
    • (1991) J Alg , vol.12 , pp. 308-340
    • Arnborg, S.1    Lagergren, J.2    Seese, D.3
  • 3
    • 85037918238 scopus 로고
    • A tourist guide through treewidth
    • H. Bodlaender, A tourist guide through treewidth, Acta Cybernet 11 (1993), 1-21.
    • (1993) Acta Cybernet , vol.11 , pp. 1-21
    • Bodlaender, H.1
  • 4
    • 0001294529 scopus 로고    scopus 로고
    • A linear time algorithm for finding tree-decompositions of small treewidth
    • H. Bodlaender, A linear time algorithm for finding tree-decompositions of small treewidth, SIAM J Comput 25 (1996), 1305-1317.
    • (1996) SIAM J Comput , vol.25 , pp. 1305-1317
    • Bodlaender, H.1
  • 6
    • 0002981945 scopus 로고    scopus 로고
    • A partial k-arboretum of graphs with bounded treewidth
    • H. Bodlaender, A partial k-arboretum of graphs with bounded treewidth, Theor Comput Sci 209 (1998), 1-45.
    • (1998) Theor Comput Sci , vol.209 , pp. 1-45
    • Bodlaender, H.1
  • 7
    • 0030356420 scopus 로고    scopus 로고
    • Efficient and constructive algorithms for the pathwidth and treewidth of graphs
    • H. Bodlaender and T. Kloks, Efficient and constructive algorithms for the pathwidth and treewidth of graphs, J Alg 21 (1996), 358-402.
    • (1996) J Alg , vol.21 , pp. 358-402
    • Bodlaender, H.1    Kloks, T.2
  • 9
    • 0038521894 scopus 로고    scopus 로고
    • Graphs with branchwidth at most three
    • H. Bodlaender and D. Thilikos, Graphs with branchwidth at most three, J Alg 32 (1999), 167-194.
    • (1999) J Alg , vol.32 , pp. 167-194
    • Bodlaender, H.1    Thilikos, D.2
  • 10
    • 52449145518 scopus 로고
    • Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families
    • R. Borie, R. Parker, and C. Tovey, Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families, Algorithmica 7 (1992), 555-581.
    • (1992) Algorithmica , vol.7 , pp. 555-581
    • Borie, R.1    Parker, R.2    Tovey, C.3
  • 12
    • 0346019157 scopus 로고
    • An algorithm for the ring-router problem
    • Bellcore
    • W. Cook and P.D. Seymour, An algorithm for the ring-router problem, Tech Report, Bellcore, 1994.
    • (1994) Tech Report
    • Cook, W.1    Seymour, P.D.2
  • 13
    • 2042460404 scopus 로고    scopus 로고
    • Tour merging via branch-decomposition
    • W. Cook and P.D. Seymour, Tour merging via branch-decomposition, INFORMS J Comput 15 (2003), 233-248.
    • (2003) INFORMS J Comput , vol.15 , pp. 233-248
    • Cook, W.1    Seymour, P.D.2
  • 14
    • 0025398865 scopus 로고
    • The monadic second-order logic of graphs 1: Recognizable sets of finite graphs
    • B. Courcelle, The monadic second-order logic of graphs 1: Recognizable sets of finite graphs, Info Comput 85 (1990), 12-75.
    • (1990) Info Comput , vol.85 , pp. 12-75
    • Courcelle, B.1
  • 16
    • 0036211275 scopus 로고    scopus 로고
    • Branch width and well-quasi-ordering in matroids and graphs
    • J. Geelen, A. Gerards, and G. Whittle, Branch width and well-quasi-ordering in matroids and graphs, J Combin Theory B 84 (2002), 270-290.
    • (2002) J Combin Theory B , vol.84 , pp. 270-290
    • Geelen, J.1    Gerards, A.2    Whittle, G.3
  • 18
    • 2042430845 scopus 로고    scopus 로고
    • Branchwidth heuristics
    • to appear
    • I.V. Hicks, Branchwidth heuristics, Cong Num (to appear).
    • Cong Num
    • Hicks, I.V.1
  • 23
    • 2042456276 scopus 로고    scopus 로고
    • Solving frequency assignment problems via tree-decomposition
    • A. Koster, S. van Hoesel, and A. Kolen, Solving frequency assignment problems via tree-decomposition, Elect Notes Discr Math 3 (1999), 1-4.
    • (1999) Elect Notes Discr Math , vol.3 , pp. 1-4
    • Koster, A.1    Van Hoesel, S.2    Kolen, A.3
  • 26
    • 0001962935 scopus 로고    scopus 로고
    • An excluded minor theorem for the the octahedron
    • J. Maharry, An excluded minor theorem for the the octahedron, J Graph Theory 31 (1999), 95-100.
    • (1999) J Graph Theory , vol.31 , pp. 95-100
    • Maharry, J.1
  • 27
    • 0041453672 scopus 로고    scopus 로고
    • The structure and number of obstructions to treewidth
    • S. Ramachandramurthi, The structure and number of obstructions to treewidth, SIAM J Discr Math 10 (1997), 146-157.
    • (1997) SIAM J Discr Math , vol.10 , pp. 146-157
    • Ramachandramurthi, S.1
  • 28
    • 0026979104 scopus 로고
    • Finding approximate separators and computing tree width quickly
    • ACM Press, New York
    • B. Reed, Finding approximate separators and computing tree width quickly, Proc 24th Ann ACM Symp on Theory of Computing, ACM Press, New York, 1992, pp. 221-228.
    • (1992) Proc 24th Ann ACM Symp on Theory of Computing , pp. 221-228
    • Reed, B.1
  • 29
    • 0003164676 scopus 로고    scopus 로고
    • Tree width and tangles: A new connectivity measure and some applications
    • R. Bailey (Editor), Cambridge University Press, Cambridge, UK
    • B. Reed, "Tree width and tangles: A new connectivity measure and some applications," Survey in Combinatorics, R. Bailey (Editor), Cambridge University Press, Cambridge, UK, 1997, pp. 87-162.
    • (1997) Survey in Combinatorics , pp. 87-162
    • Reed, B.1
  • 30
    • 0001977866 scopus 로고
    • Graph minors I: Excluding a forest
    • N. Robertson and P.D. Seymour, Graph minors I: Excluding a forest, J Combin Theory B 35 (1983), 39-61.
    • (1983) J Combin Theory B , vol.35 , pp. 39-61
    • Robertson, N.1    Seymour, P.D.2
  • 31
    • 0001814458 scopus 로고
    • Graph minors: A survey
    • I. Anderson (Editor), Cambridge University Press, Cambridge, UK
    • N. Robertson and P.D. Seymour, "Graph minors: A survey," Surveys in Combinatorics, I. Anderson (Editor), Cambridge University Press, Cambridge, UK, 1985, pp. 153-171.
    • (1985) Surveys in Combinatorics , pp. 153-171
    • Robertson, N.1    Seymour, P.D.2
  • 32
    • 0001227241 scopus 로고
    • Graph minors X: Obstructions to tree-decompositions
    • N. Robertson and P.D. Seymour, Graph minors X: Obstructions to tree-decompositions, J Combin Theory B 52 (1991), 153-190.
    • (1991) J Combin Theory B , vol.52 , pp. 153-190
    • Robertson, N.1    Seymour, P.D.2
  • 33
    • 0002848005 scopus 로고
    • Graph minors XIII: The disjoint paths problem
    • N. Robertson and P.D. Seymour, Graph minors XIII: The disjoint paths problem, J Combin Theory B 63 (1995), 65-110.
    • (1995) J Combin Theory B , vol.63 , pp. 65-110
    • Robertson, N.1    Seymour, P.D.2
  • 34
    • 44949266653 scopus 로고
    • Graph searching and a min-max theorem for tree-width
    • P.D. Seymour and R. Thomas, Graph searching and a min-max theorem for tree-width, J Combin Theory B 58 (1993), 22-33.
    • (1993) J Combin Theory B , vol.58 , pp. 22-33
    • Seymour, P.D.1    Thomas, R.2
  • 35
    • 0038521887 scopus 로고
    • Call routing and the ratcatcher
    • P.D. Seymour and R. Thomas, Call routing and the ratcatcher, Combinatorica 14 (1994), 217-241.
    • (1994) Combinatorica , vol.14 , pp. 217-241
    • Seymour, P.D.1    Thomas, R.2
  • 36
    • 23544481200 scopus 로고    scopus 로고
    • A linear time heuristic for the branch-decomposition of planar graphs
    • Max-Planck-Institut Fur Informatick
    • H. Tamaki, A linear time heuristic for the branch-decomposition of planar graphs, Tech report MPI-I-2003-1-010, Max-Planck-Institut Fur Informatick, 2003.
    • (2003) Tech Report , vol.MPI-I-2003-1-010
    • Tamaki, H.1
  • 37
    • 0000697587 scopus 로고    scopus 로고
    • Algorithms for vertex partitioning problems on partial k-trees
    • J. Telle and A. Proskurowski, Algorithms for vertex partitioning problems on partial k-trees, SIAM J Discr Math 10 (1997), 529-550.
    • (1997) SIAM J Discr Math , vol.10 , pp. 529-550
    • Telle, J.1    Proskurowski, A.2
  • 38
    • 38249020757 scopus 로고
    • A Menger-like property of tree-width: The finite case
    • R. Thomas, A Menger-like property of tree-width: The finite case, J Combin Theory B 48 (1990), 67-76.
    • (1990) J Combin Theory B , vol.48 , pp. 67-76
    • Thomas, R.1
  • 39
    • 0010914970 scopus 로고    scopus 로고
    • Recent excluded minor theorems for graphs
    • J.D. Lamb and D.A. Preece (Editors), Cambridge University Press, Cambridge, UK
    • R. Thomas, "Recent excluded minor theorems for graphs," Surveys in Combinatorics, J.D. Lamb and D.A. Preece (Editors), Cambridge University Press, Cambridge, UK, 1999, pp. 201-222.
    • (1999) Surveys in Combinatorics , pp. 201-222
    • Thomas, R.1
  • 40
    • 0001274390 scopus 로고    scopus 로고
    • A simpler proof of the excluded minor theorem for higher surfaces
    • C. Thomassen, A simpler proof of the excluded minor theorem for higher surfaces, J Combin Theory B 70 (1997), 306-311.
    • (1997) J Combin Theory B , vol.70 , pp. 306-311
    • Thomassen, C.1
  • 41
    • 0008779759 scopus 로고    scopus 로고
    • All structured programs have small tree width and good register allocation
    • M. Thorup, All structured programs have small tree width and good register allocation, Info Comput 142 (1998), 159-181.
    • (1998) Info Comput , vol.142 , pp. 159-181
    • Thorup, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.