메뉴 건너뛰기




Volumn 35, Issue 1, 2006, Pages 247-257

Approximating k-node connected subgraphs via critical graphs

Author keywords

Approximation; Connectivity; Graphs; Network design

Indexed keywords

APPROXIMATION RATIO; CONNECTIVITY; NETWORK DESIGN;

EID: 33644585066     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539703435753     Document Type: Article
Times cited : (48)

References (30)
  • 1
    • 0001977155 scopus 로고    scopus 로고
    • A 2-approximation algorithm for finding an optimum 3-vertex connected spanning subgraph
    • V. AULETTA, Y. DINITZ, Z. NUTOV, AND D. PARENTE, A 2-approximation algorithm for finding an optimum 3-vertex connected spanning subgraph, J. Algorithms, 32 (1999), pp. 21-30.
    • (1999) J. Algorithms , vol.32 , pp. 21-30
    • Auletta, V.1    Dinitz, Y.2    Nutov, Z.3    Parente, D.4
  • 2
    • 0005269528 scopus 로고    scopus 로고
    • On rooted node-connectivity problems
    • J. CHERIYAN, T. JORDÁN, AND Z. NUTOV, On rooted node-connectivity problems, Algorithmica, 30 (2001), pp. 353-375.
    • (2001) Algorithmica , vol.30 , pp. 353-375
    • Cheriyan, J.1    Jordán, T.2    Nutov, Z.3
  • 3
    • 0343337501 scopus 로고    scopus 로고
    • Approximating minimum-size k-connected spanning subgraphs via matching
    • J. CHERIYAN AND R. THURIMELLA, Approximating minimum-size k-connected spanning subgraphs via matching, SIAM J. Comput., 30 (2000), pp. 528-560.
    • (2000) SIAM J. Comput. , vol.30 , pp. 528-560
    • Cheriyan, J.1    Thurimella, R.2
  • 4
    • 0141534108 scopus 로고    scopus 로고
    • An approximation algorithm for the minimum-cost k-vertex connected subgraph
    • J. CHERIYAN, S. VEMPALA, AND A. VETTA, An approximation algorithm for the minimum-cost k-vertex connected subgraph, SIAM J. Comput., 32 (2003), pp. 1050-1055.
    • (2003) SIAM J. Comput. , vol.32 , pp. 1050-1055
    • Cheriyan, J.1    Vempala, S.2    Vetta, A.3
  • 5
    • 0001998507 scopus 로고
    • Connectivity augmentation problems in network design
    • J. R. Birge and K. G. Murty, eds., University of Michigan, Ann Arbor
    • A. FRANK, Connectivity augmentation problems in network design, in Mathematical Programming: State of the Art, J. R. Birge and K. G. Murty, eds., University of Michigan, Ann Arbor, 1994, pp. 34-63.
    • (1994) Mathematical Programming: State of the Art , pp. 34-63
    • Frank, A.1
  • 6
    • 0042156608 scopus 로고    scopus 로고
    • Increasing the rooted connectivity of a digraph by one
    • A. FRANK, Increasing the rooted connectivity of a digraph by one, Math. Programming, 84 (1999), pp. 565-576.
    • (1999) Math. Programming , vol.84 , pp. 565-576
    • Frank, A.1
  • 7
    • 0003017893 scopus 로고
    • Minimal edge-coverings of pairs of sets
    • A. FRANK AND T. JORDÁN, Minimal edge-coverings of pairs of sets, J. Combin. Theory Ser. B, 65 (1995), pp. 73-110.
    • (1995) J. Combin. Theory Ser. B , vol.65 , pp. 73-110
    • Frank, A.1    Jordán, T.2
  • 8
    • 0001186361 scopus 로고
    • An application of submodular flows
    • A. FRANK AND E. TARDOS, An application of submodular flows, Linear Algebra Appl., 114/115 (1989), pp. 329-348.
    • (1989) Linear Algebra Appl. , vol.114-115 , pp. 329-348
    • Frank, A.1    Tardos, E.2
  • 9
    • 0027242496 scopus 로고
    • A representation for crossing set families with application to submodular flow problems
    • SIAM, Philadelphia
    • H. N. GABOW, A representation for crossing set families with application to submodular flow problems, in Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, 1993, pp. 202-211.
    • (1993) Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) , pp. 202-211
    • Gabow, H.N.1
  • 10
    • 0004145084 scopus 로고
    • L. GRAHAM, M. GRÖTSCHEL, AND L. LOVÁSZ, EDS., Elsevier Science B.V., Amsterdam; MIT Press, Cambridge, MA
    • L. GRAHAM, M. GRÖTSCHEL, AND L. LOVÁSZ, EDS., Handbook of Combinatorics, Vol. 1, Elsevier Science B.V., Amsterdam; MIT Press, Cambridge, MA, 1995.
    • (1995) Handbook of Combinatorics , vol.1
  • 11
    • 0002672799 scopus 로고
    • On the optimal vertex-connectivity augmentation
    • T. JORDÁN, On the optimal vertex-connectivity augmentation, J. Combin. Theory Ser. B, 63 (1995), pp. 8-20.
    • (1995) J. Combin. Theory Ser. B , vol.63 , pp. 8-20
    • Jordán, T.1
  • 12
    • 0013019861 scopus 로고    scopus 로고
    • On the existence of (k,l)-critical graphs
    • T. JORDÁN, On the existence of (k,l)-critical graphs, Discrete Math., 179 (1998), pp. 273-275.
    • (1998) Discrete Math. , vol.179 , pp. 273-275
    • Jordán, T.1
  • 14
    • 0005363324 scopus 로고    scopus 로고
    • A factor 2 approximation algorithm for the generalized Steiner network problem
    • K. JAIN, A factor 2 approximation algorithm for the generalized Steiner network problem, Combinatorica, 21 (2001), pp. 39-60.
    • (2001) Combinatorica , vol.21 , pp. 39-60
    • Jain, K.1
  • 15
    • 3142717683 scopus 로고    scopus 로고
    • Hardness of approximation for vertex-connectivity network design problems
    • G. KORTSARZ, R. KRAUTHGAMER, AND J. LEE, Hardness of approximation for vertex-connectivity network design problems, SIAM J. Comput., 33 (2004), pp. 704-720.
    • (2004) SIAM J. Comput. , vol.33 , pp. 704-720
    • Kortsarz, G.1    Krauthgamer, R.2    Lee, J.3
  • 16
    • 0942290222 scopus 로고    scopus 로고
    • Approximating node connectivity problems via set covers
    • G. KORTSARZ AND Z. NUTOV, Approximating node connectivity problems via set covers, Algorithmica, 37 (2003), pp. 75-92.
    • (2003) Algorithmica , vol.37 , pp. 75-92
    • Kortsarz, G.1    Nutov, Z.2
  • 17
    • 0030367201 scopus 로고    scopus 로고
    • Improved approximation algorithms for uniform connectivity problems
    • S. KHULLER AND B. RAGHAVACHARI, Improved approximation algorithms for uniform connectivity problems, J. Algorithms, 21 (1996), pp. 434-450.
    • (1996) J. Algorithms , vol.21 , pp. 434-450
    • Khuller, S.1    Raghavachari, B.2
  • 18
    • 0036972952 scopus 로고    scopus 로고
    • Upper bounds to the number of vertices in a k-critically n-connected graph
    • M. KRIESELL, Upper bounds to the number of vertices in a k-critically n-connected graph, Graphs Combin., 18 (2002), pp. 133-146.
    • (2002) Graphs Combin. , vol.18 , pp. 133-146
    • Kriesell, M.1
  • 19
    • 0000576654 scopus 로고
    • Ecken vom Grad n in minimalen n-fach zusammenhängenden Graphen
    • W. MADER, Ecken vom Grad n in minimalen n-fach zusammenhängenden Graphen, Arch. Math. (Basel), 23 (1972), pp. 219-224.
    • (1972) Arch. Math. (Basel) , vol.23 , pp. 219-224
    • Mader, W.1
  • 20
    • 0343038307 scopus 로고
    • Minimal n-fach zusammenhängende digraphen
    • W. MADER, Minimal n-fach zusammenhängende digraphen, J. Combin. Theory Ser. B, 38 (1985), pp. 102-117.
    • (1985) J. Combin. Theory Ser. B , vol.38 , pp. 102-117
    • Mader, W.1
  • 21
    • 0001011005 scopus 로고
    • Endlichkeitsätze für k-kritische graphen
    • W. MADER, Endlichkeitsätze für k-kritische graphen, Math. Ann., 229 (1977), pp. 143-153.
    • (1977) Math. Ann. , vol.229 , pp. 143-153
    • Mader, W.1
  • 22
    • 0036847612 scopus 로고    scopus 로고
    • On k-con-critically n-connected graphs
    • W. MADER, On k-con-critically n-connected graphs, J. Combin. Theory Ser. B, 86 (2002), pp. 296-314.
    • (2002) J. Combin. Theory Ser. B , vol.86 , pp. 296-314
    • Mader, W.1
  • 23
    • 6344278737 scopus 로고    scopus 로고
    • High connectivity keeping sets in n-connected graphs
    • W. MADER, High connectivity keeping sets in n-connected graphs, Combinatorica, 24 (2004), pp. 441-458.
    • (2004) Combinatorica , vol.24 , pp. 441-458
    • Mader, W.1
  • 24
    • 0002183220 scopus 로고
    • Connectivity and edge-connectivity in finite graphs
    • Cambridge University Press, Cambridge, UK
    • W. MADER, Connectivity and edge-connectivity in finite graphs, in Surveys in Combinatorics, London Math. Soc. Lecture Notes Ser. 38, Cambridge University Press, Cambridge, UK, 1979, pp. 66-95.
    • (1979) Surveys in Combinatorics, London Math. Soc. Lecture Notes Ser. , vol.38 , pp. 66-95
    • Mader, W.1
  • 25
    • 0002045578 scopus 로고
    • On k-critically n-connected graphs
    • Academic Press, Toronto, ON
    • W. MADER, On k-critically n-connected graphs, in Progress in Graph Theory, Academic Press, Toronto, ON, 1984, pp. 389-398.
    • (1984) Progress in Graph Theory , pp. 389-398
    • Mader, W.1
  • 26
    • 0013003732 scopus 로고
    • On k-critical, n-connected graphs
    • B. MAURER AND P. SLATER, On k-critical, n-connected graphs, Discrete Math., 20 (1988), pp. 255-262.
    • (1988) Discrete Math. , vol.20 , pp. 255-262
    • Maurer, B.1    Slater, P.2
  • 28
    • 0347669560 scopus 로고    scopus 로고
    • An approximation algorithm for minimum-cost vertex-connectivity problems
    • R. RAVI AND D. P. WILLIAMSON, An approximation algorithm for minimum-cost vertex-connectivity problems, Algorithmica, 18 (1997), pp. 21-43.
    • (1997) Algorithmica , vol.18 , pp. 21-43
    • Ravi, R.1    Williamson, D.P.2
  • 29
    • 0011588974 scopus 로고    scopus 로고
    • Erratum: An approximation algorithm for minimum-cost vertex-connectivity problems
    • R. RAVI AND D. P. WILLIAMSON, Erratum: An approximation algorithm for minimum-cost vertex-connectivity problems, Algorithmica, 34 (2002), pp. 98-107.
    • (2002) Algorithmica , vol.34 , pp. 98-107
    • Ravi, R.1    Williamson, D.P.2
  • 30
    • 4544327352 scopus 로고
    • Proof of Slater's conjecture on k-critical n-connected graphs
    • J. SU, Proof of Slater's conjecture on k-critical n-connected graphs, Kexue Tongbao (English Ed.), 33 (1988), pp. 1675-1678.
    • (1988) Kexue Tongbao (English Ed.) , vol.33 , pp. 1675-1678
    • Su, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.