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Volumn , Issue , 2009, Pages 179-188

The Euclidean degree-4 minimum spanning tree problem is NP-hard

Author keywords

Bounded degree graphs; Degree constricted graphs; Degree restricted graphs; Geometric graphs; Geometric optimization; NP complete; Reduction; Spanning trees

Indexed keywords

BOUNDED DEGREE GRAPHS; GEOMETRIC GRAPHS; GEOMETRIC OPTIMIZATION; NP COMPLETE; SPANNING TREE;

EID: 70849124897     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1542362.1542399     Document Type: Conference Paper
Times cited : (17)

References (18)
  • 1
    • 0030413554 scopus 로고    scopus 로고
    • Polynomial time approximation schemes for Euclidean TSP and other geometric problems
    • S. Arora. Polynomial time approximation schemes for Euclidean TSP and other geometric problems. In Proc. 37th Annu. IEEE Sympos. Found. Comput. Sci., pages 2-11, 1996.
    • (1996) Proc. 37th Annu. IEEE Sympos. Found. Comput. Sci. , pp. 2-11
    • Arora, S.1
  • 2
    • 0032156828 scopus 로고    scopus 로고
    • Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
    • S. Arora. Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM, 45(5):753-782, 1998.
    • (1998) J. ACM , vol.45 , Issue.5 , pp. 753-782
    • Arora, S.1
  • 3
    • 21044440128 scopus 로고    scopus 로고
    • Approximation schemes for degree-restricted MST and red-blue separation problems
    • S. Arora and K. Chang. Approximation schemes for degree-restricted MST and red-blue separation problems. Algorithmica, 40(3):189-210, 2004.
    • (2004) Algorithmica , vol.40 , Issue.3 , pp. 189-210
    • Arora, S.1    Chang, K.2
  • 4
    • 4344634500 scopus 로고    scopus 로고
    • Euclidean bounded-degree spanning tree ratios
    • T. M. Chan. Euclidean bounded-degree spanning tree ratios. Discrete Comput. Geom., 32(2):177-194, 2004.
    • (2004) Discrete Comput. Geom. , vol.32 , Issue.2 , pp. 177-194
    • Chan, T.M.1
  • 7
    • 0038192551 scopus 로고    scopus 로고
    • A network-flow technique for finding low-weight bounded-degree spanning trees
    • S. P. Fekete, S. Khuller, M. Klemmstein, B. Raghavachari, and N. Young. A network-flow technique for finding low-weight bounded-degree spanning trees. J. Algorithms, 24(2):310-324, 1997.
    • (1997) J. Algorithms , vol.24 , Issue.2 , pp. 310-324
    • Fekete, S.P.1    Khuller, S.2    Klemmstein, M.3    Raghavachari, B.4    Young, N.5
  • 8
    • 0000727336 scopus 로고
    • The rectilinear Steiner tree problem is NP-complete
    • M. R. Garey and D. S. Johnson. The rectilinear Steiner tree problem is NP-complete. SIAM J. Appl. Math., 32:826-834, 1977.
    • (1977) SIAM J. Appl. Math. , vol.32 , pp. 826-834
    • Garey, M.R.1    Johnson, D.S.2
  • 10
    • 60649110437 scopus 로고    scopus 로고
    • Degree-bounded minimum spanning trees
    • R. Jothi and B. Raghavachari. Degree-bounded minimum spanning trees. Discrete Appl. Math., 157(5):960-970, 2009.
    • (2009) Discrete Appl. Math. , vol.157 , Issue.5 , pp. 960-970
    • Jothi, R.1    Raghavachari, B.2
  • 11
    • 0030128523 scopus 로고    scopus 로고
    • Low-degree spanning trees of small weight
    • S. Khuller, B. Raghavachari, and N. Young. Low-degree spanning trees of small weight. SIAM J. Comput., 25(2):355-368, 1996.
    • (1996) SIAM J. Comput. , vol.25 , Issue.2 , pp. 355-368
    • Khuller, S.1    Raghavachari, B.2    Young, N.3
  • 12
    • 0032667193 scopus 로고    scopus 로고
    • Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems
    • J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput., 28:1298-1309, 1999.
    • (1999) SIAM J. Comput. , vol.28 , pp. 1298-1309
    • Mitchell, J.S.B.1
  • 13
    • 21144470704 scopus 로고
    • Transitions in geometric minimum spanning trees
    • C. Monma and S. Suri. Transitions in geometric minimum spanning trees. Discrete Comput. Geom., 8(3):265-293, 1992.
    • (1992) Discrete Comput. Geom. , vol.8 , Issue.3 , pp. 265-293
    • Monma, C.1    Suri, S.2
  • 14
    • 19044391501 scopus 로고
    • The Euclidean traveling salesman problem is NP-complete
    • C. H. Papadimitriou. The Euclidean traveling salesman problem is NP-complete. Theoret. Comput. Sci., 4:237-244, 1977.
    • (1977) Theoret. Comput. Sci. , vol.4 , pp. 237-244
    • Papadimitriou, C.H.1
  • 15
    • 0037854822 scopus 로고
    • On two geometric problems related to the travelling salesman problem
    • C. H. Papadimitriou and U. V. Vazirani. On two geometric problems related to the travelling salesman problem. J. Algorithms, 5:231-246, 1984.
    • (1984) J. Algorithms , vol.5 , pp. 231-246
    • Papadimitriou, C.H.1    Vazirani, U.V.2
  • 16
    • 0039346903 scopus 로고    scopus 로고
    • Algorithms for area-efficient orthogonal drawings
    • A. Papakostas and I. G. Tollis. Algorithms for area-efficient orthogonal drawings. Comput. Geom. Theory Appl., 9(1-2):83-110, 1998.
    • (1998) Comput. Geom. Theory Appl. , vol.9 , Issue.1-2 , pp. 83-110
    • Papakostas, A.1    Tollis, I.G.2
  • 17
    • 5244350263 scopus 로고
    • Low-degree minimum spanning trees
    • G. Robins and J. S. Salowe. Low-degree minimum spanning trees. Discrete Comput. Geom., 14(2):151-165, 1995.
    • (1995) Discrete Comput. Geom. , vol.14 , Issue.2 , pp. 151-165
    • Robins, G.1    Salowe, J.S.2
  • 18
    • 0024735684 scopus 로고
    • Planar grid embedding in linear time
    • R. Tamassia and I. G. Tollis. Planar grid embedding in linear time. IEEE Trans. Circuits Syst., CAS-36(9):1230-1234, 1989.
    • (1989) IEEE Trans. Circuits Syst. , vol.36 , Issue.9 , pp. 1230-1234
    • Tamassia, R.1    Tollis, I.G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.