메뉴 건너뛰기




Volumn , Issue , 2006, Pages 514-523

All-pairs shortest paths for unweighted undirected graphs in o(mn) time

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; PROBLEM SOLVING; TIME SERIES ANALYSIS;

EID: 33244486056     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1109557.1109614     Document Type: Conference Paper
Times cited : (46)

References (30)
  • 1
    • 0025417561 scopus 로고
    • Faster algorithms for the shortest path problem
    • R. K. Ahuja, K. Mehlhorn, J. B. Orlin, and R. E. Tarjan. Faster algorithms for the shortest path problem. J. ACM, 37:213-223, 1990.
    • (1990) J. ACM , vol.37 , pp. 213-223
    • Ahuja, R.K.1    Mehlhorn, K.2    Orlin, J.B.3    Tarjan, R.E.4
  • 2
    • 0032657365 scopus 로고    scopus 로고
    • Fast estimation of diameter and shortest paths (without matrix multiplication)
    • D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM J. Comput., 28:1167-1181, 1999.
    • (1999) SIAM J. Comput. , vol.28 , pp. 1167-1181
    • Aingworth, D.1    Chekuri, C.2    Indyk, P.3    Motwani, R.4
  • 3
    • 0031125393 scopus 로고    scopus 로고
    • On the exponent of the all pairs shortest path problem
    • N. Alon, Z. Galil, and O. Margalit. On the exponent of the all pairs shortest path problem. J. Comput. Sys. Sci., 54:255-262, 1997.
    • (1997) J. Comput. Sys. Sci. , vol.54 , pp. 255-262
    • Alon, N.1    Galil, Z.2    Margalit, O.3
  • 4
    • 0001539365 scopus 로고
    • On economical construction of the transitive closure of a directed graph
    • V. L. Arlazarov, E. C. Dinic, M. A. Kronrod, and I. A. Faradzev. On economical construction of the transitive closure of a directed graph. Soviet Math. Dokl., 11:1209-1210, 1970.
    • (1970) Soviet Math. Dokl. , vol.11 , pp. 1209-1210
    • Arlazarov, V.L.1    Dinic, E.C.2    Kronrod, M.A.3    Faradzev, I.A.4
  • 6
    • 85023205150 scopus 로고
    • Matrix multiplication via arithmetic progressions
    • D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. J. Symbolic Comput., 9:251-280, 1990.
    • (1990) J. Symbolic Comput. , vol.9 , pp. 251-280
    • Coppersmith, D.1    Winograd, S.2
  • 7
    • 3242725453 scopus 로고
    • A more efficient algorithm for the min-plus multiplication
    • W. Dobosiewicz. A more efficient algorithm for the min-plus multiplication. Int. J. Computer Math., 32:49-60, 1990.
    • (1990) Int. J. Computer Math. , vol.32 , pp. 49-60
    • Dobosiewicz, W.1
  • 8
    • 0034544711 scopus 로고    scopus 로고
    • All pairs almost shortest paths
    • D. Dor, S. Halperin, and U. Zwick. All pairs almost shortest paths. SIAM J. Comput., 29:1740-1759, 2000.
    • (2000) SIAM J. Comput. , vol.29 , pp. 1740-1759
    • Dor, D.1    Halperin, S.2    Zwick, U.3
  • 9
    • 0029392998 scopus 로고
    • Clique partitions, graph compression and speeding-up algorithms
    • T. Feder and R. Motwani. Clique partitions, graph compression and speeding-up algorithms. J. Comput. Sys. Sci., 51:261-272, 1995.
    • (1995) J. Comput. Sys. Sci. , vol.51 , pp. 261-272
    • Feder, T.1    Motwani, R.2
  • 10
    • 0346444539 scopus 로고
    • New bounds on the complexity of the shortest path problem
    • M. L. Fredman. New bounds on the complexity of the shortest path problem. SIAM J. Comput., 5:49-60, 1976.
    • (1976) SIAM J. Comput. , vol.5 , pp. 49-60
    • Fredman, M.L.1
  • 11
    • 0006712603 scopus 로고    scopus 로고
    • All pairs shortest distances for graphs with small integer length edges
    • Z. Galil and O. Margalit. All pairs shortest distances for graphs with small integer length edges. Inf. Comput., 134:103-139, 1997.
    • (1997) Inf. Comput. , vol.134 , pp. 103-139
    • Galil, Z.1    Margalit, O.2
  • 12
    • 0031122908 scopus 로고    scopus 로고
    • All pairs shortest paths for graphs with small integer length edges
    • Z. Galil and O. Margalit. All pairs shortest paths for graphs with small integer length edges. J. Comput. Sys. Sci., 54:243-254, 1997.
    • (1997) J. Comput. Sys. Sci. , vol.54 , pp. 243-254
    • Galil, Z.1    Margalit, O.2
  • 13
    • 84974533426 scopus 로고    scopus 로고
    • Improved shortest paths on the word RAM
    • Lect. Notes Comput. Sci., Springer-Verlag
    • T. Hagerup. Improved shortest paths on the word RAM. In Proc. 27th Int. Collog. Automata, Languages, and Programming, Lect. Notes Comput. Sci., vol. 1853, Springer-Verlag, pages 61-72, 2000.
    • (2000) Proc. 27th Int. Collog. Automata, Languages, and Programming , vol.1853 , pp. 61-72
    • Hagerup, T.1
  • 14
    • 3242702293 scopus 로고    scopus 로고
    • Improved algorithm for all pairs shortest paths
    • Y. Han. Improved algorithm for all pairs shortest paths. Inform. Process. Lett., 91:245-250, 2004.
    • (2004) Inform. Process. Lett. , vol.91 , pp. 245-250
    • Han, Y.1
  • 15
    • 0032606988 scopus 로고    scopus 로고
    • Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs
    • V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In Proc. 40th IEEE Sympos. Found. Comput. Sci., pages 81-91, 1999.
    • (1999) Proc. 40th IEEE Sympos. Found. Comput. Sci. , pp. 81-91
    • King, V.1
  • 16
    • 0346339721 scopus 로고    scopus 로고
    • A new approach to all-pairs shortest paths on real-weighted graphs
    • S. Pettie. A new approach to all-pairs shortest paths on real-weighted graphs. Theoret. Comput. Sci., 312:47-74, 2004.
    • (2004) Theoret. Comput. Sci. , vol.312 , pp. 47-74
    • Pettie, S.1
  • 17
    • 29344454699 scopus 로고    scopus 로고
    • A shortest path algorithm for real-weighted undirected graphs
    • S. Pettie and V. Ramachandran. A shortest path algorithm for real-weighted undirected graphs. SIAM J. Comput., 34:1398-1431, 2005.
    • (2005) SIAM J. Comput. , vol.34 , pp. 1398-1431
    • Pettie, S.1    Ramachandran, V.2
  • 18
    • 0029509262 scopus 로고
    • On the all-pairs-shortest-path problem in unweighted undirected graphs
    • R. Seidel. On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Sys. Sci., 51:400-403, 1995.
    • (1995) J. Comput. Sys. Sci. , vol.51 , pp. 400-403
    • Seidel, R.1
  • 19
    • 0033309270 scopus 로고    scopus 로고
    • All pairs shortest paths in undirected graphs with integer weights
    • A. Shoshan and U. Zwick. All pairs shortest paths in undirected graphs with integer weights. In Proc. 40th IEEE Sympos. Found. Comput. Sci., pages 605-614, 1999.
    • (1999) Proc. 40th IEEE Sympos. Found. Comput. Sci. , pp. 605-614
    • Shoshan, A.1    Zwick, U.2
  • 21
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • V. Strassen. Gaussian elimination is not optimal. Numerische Mathematik, 13:354-356, 1969.
    • (1969) Numerische Mathematik , vol.13 , pp. 354-356
    • Strassen, V.1
  • 22
    • 0001586202 scopus 로고
    • A new upper bound on the complexity of the all pairs shortest path problem
    • T. Takaoka. A new upper bound on the complexity of the all pairs shortest path problem. Inform. Process. Lett., 43:195-199, 1992.
    • (1992) Inform. Process. Lett. , vol.43 , pp. 195-199
    • Takaoka, T.1
  • 23
    • 0042113503 scopus 로고    scopus 로고
    • Subcubic cost algorithms for the all pairs shortest path problem
    • T. Takaoka. Subcubic cost algorithms for the all pairs shortest path problem. Algorithmica, 20:309-318, 1998.
    • (1998) Algorithmica , vol.20 , pp. 309-318
    • Takaoka, T.1
  • 24
    • 26844521960 scopus 로고    scopus 로고
    • A faster algorithm for the all-pairs shortest path problem and its application
    • Springer-Verlag
    • T. Takaoka. A faster algorithm for the all-pairs shortest path problem and its application. In Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, Springer-Verlag, pages 278-289, 2004.
    • (2004) Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci. , vol.3106 , pp. 278-289
    • Takaoka, T.1
  • 25
    • 0000778521 scopus 로고    scopus 로고
    • Undirected single-source shortest paths with positive integer weights in linear time
    • M. Thorup. Undirected single-source shortest paths with positive integer weights in linear time. J. ACM, 46:362-394, 1999.
    • (1999) J. ACM , vol.46 , pp. 362-394
    • Thorup, M.1
  • 26
    • 4544284899 scopus 로고    scopus 로고
    • Integer priority queues with decrease key in constant time and the single source shortest paths problem
    • M. Thorup. Integer priority queues with decrease key in constant time and the single source shortest paths problem. J. Comput. Sys. Sci., 69:330-353, 2004.
    • (2004) J. Comput. Sys. Sci. , vol.69 , pp. 330-353
    • Thorup, M.1
  • 27
    • 0026102973 scopus 로고
    • High-probability parallel transitive-closure algorithms
    • J. D. Ullman and M. Yannakakis. High-probability parallel transitive-closure algorithms. SIAM J. Comput., 20:100-125, 1991.
    • (1991) SIAM J. Comput. , vol.20 , pp. 100-125
    • Ullman, J.D.1    Yannakakis, M.2
  • 28
    • 35048828796 scopus 로고    scopus 로고
    • Fast sparse matrix multiplication
    • Lect. Notes Comput. Sci., Springer-Verlag
    • R. Yuster and U. Zwick. Fast sparse matrix multiplication. In Proc. 12th European Sympos. Algorithms, Lect. Notes Comput. Sci., vol. 3221, Springer-Verlag, pages 604-615, 2004.
    • (2004) Proc. 12th European Sympos. Algorithms , vol.3221 , pp. 604-615
    • Yuster, R.1    Zwick, U.2
  • 29
    • 0012584372 scopus 로고    scopus 로고
    • All-pairs shortest paths using bridging sets and rectangular matrix multiplication
    • U. Zwick. All-pairs shortest paths using bridging sets and rectangular matrix multiplication. J. ACM, 49:289-317, 2002.
    • (2002) J. ACM , vol.49 , pp. 289-317
    • Zwick, U.1
  • 30
    • 35048829333 scopus 로고    scopus 로고
    • A slightly improved sub-cubic algorithm for the all pairs shortest paths problem with real edge lengths
    • Lect. Notes Comput. Sci., Springer-Verlag
    • U. Zwick. A slightly improved sub-cubic algorithm for the all pairs shortest paths problem with real edge lengths. In Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, Springer-Verlag, pages 921-932, 2004.
    • (2004) Proc. 15th Int. Sympos. Algorithms and Computation , vol.3341 , pp. 921-932
    • Zwick, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.