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Volumn 50, Issue 2, 2008, Pages 236-243

All-pairs shortest paths with real weights in O(n 3/log∈n) time

Author keywords

Graph algorithms; Shortest paths

Indexed keywords

GRAPH ALGORITHMS; SHORTEST PATHS; VERTICES;

EID: 38349014115     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-007-9062-1     Document Type: Conference Paper
Times cited : (59)

References (26)
  • 2
    • 0031125393 scopus 로고    scopus 로고
    • On the exponent of the all pairs shortest path problem
    • Alon, N., Galil, Z., Margalit, O.: 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
  • 3
    • 0001539365 scopus 로고
    • On economical construction of the transitive closure of a directed graph
    • Arlazarov, V.L., Dinic, E.C., Kronrod, M.A., Faradzev, I.A.: On economical construction of the transitive closure of a directed graph. Sov. Math. Dokl. 11, 1209-1210 (1970)
    • (1970) Sov. Math. Dokl. , vol.11 , pp. 1209-1210
    • Arlazarov, V.L.1    Dinic, E.C.2    Kronrod, M.A.3    Faradzev, I.A.4
  • 4
    • 0031631006 scopus 로고    scopus 로고
    • Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators
    • Buchsbaum, A.L., Kaplan, H., Rogers, A., Westbrook, J.R.: Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators. In Proc. 30th ACM Sympos. Theory Comput., pp. 279-288 (1998)
    • (1998) Proc. 30th ACM Sympos. Theory Comput. , pp. 279-288
    • Buchsbaum, A.L.1    Kaplan, H.2    Rogers, A.3    Westbrook, J.R.4
  • 5
    • 33244486056 scopus 로고    scopus 로고
    • All-pairs shortest paths for unweighted undirected graphs in o(mn) time
    • Chan, T.M.: All-pairs shortest paths for unweighted undirected graphs in o(mn) time. In Proc. 17th ACM-SIAM Sympos. Discrete Algorithms, pp. 514-523 (2006)
    • (2006) Proc. 17th ACM-SIAM Sympos. Discrete Algorithms , pp. 514-523
    • Chan, T.M.1
  • 6
    • 85023205150 scopus 로고
    • Matrix multiplication via arithmetic progressions
    • Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9, 251-280 (1990)
    • (1990) J. Symb. Comput. , vol.9 , pp. 251-280
    • Coppersmith, D.1    Winograd, S.2
  • 8
    • 3242725453 scopus 로고
    • A more efficient algorithm for the min-plus multiplication
    • Dobosiewicz, W.: A more efficient algorithm for the min-plus multiplication. Int. J. Comput. Math. 32, 49-60 (1990)
    • (1990) Int. J. Comput. Math. , vol.32 , pp. 49-60
    • Dobosiewicz, W.1
  • 9
    • 1842487303 scopus 로고    scopus 로고
    • Quasiconvex analysis of backtracking algorithms
    • Proc. 15th ACM-SIAM Sympos
    • Eppstein, D.: Quasiconvex analysis of backtracking algorithms. In Proc. 15th ACM-SIAM Sympos. Discrete Algorithms, pp. 788-797 (2004)
    • (2004) Discrete Algorithms , pp. 788-797
    • Eppstein, D.1
  • 10
    • 0029392998 scopus 로고
    • Clique partitions, graph compression and speeding-up algorithms
    • Feder, T., Motwani, R.: Clique partitions, graph compression and speeding-up algorithms. J. Comput. Syst. Sci. 51, 261-272 (1995)
    • (1995) J. Comput. Syst. Sci. , vol.51 , pp. 261-272
    • Feder, T.1    Motwani, R.2
  • 11
    • 0346444539 scopus 로고
    • New bounds on the complexity of the shortest path problem
    • Fredman, M.L.: 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
  • 12
    • 0031122908 scopus 로고    scopus 로고
    • All pairs shortest paths for graphs with small integer length edges
    • Galil, Z., Margalit, O.: All pairs shortest paths for graphs with small integer length edges. J. Comput. Syst. Sci. 54, 243-254 (1997)
    • (1997) J. Comput. Syst. Sci. , vol.54 , pp. 243-254
    • Galil, Z.1    Margalit, O.2
  • 13
    • 3242702293 scopus 로고    scopus 로고
    • Improved algorithm for all pairs shortest paths
    • Han, Y.: 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
    • 0346339721 scopus 로고    scopus 로고
    • A new approach to all-pairs shortest paths on real-weighted graphs
    • Pettie, S.: A new approach to all-pairs shortest paths on real-weighted graphs. Theor. Comput. Sci. 312, 47-74 (2004)
    • (2004) Theor. Comput. Sci. , vol.312 , pp. 47-74
    • Pettie, S.1
  • 16
    • 29344454699 scopus 로고    scopus 로고
    • A shortest path algorithm for real-weighted undirected graphs
    • Pettie, S., Ramachandran, V.: 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
    • Seidel, R.: On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Syst. Sci. 51, 400-403 (1995)
    • (1995) J. Comput. Syst. 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
    • Shoshan, A., Zwick, U.: All pairs shortest paths in undirected graphs with integer weights. In Proc. 40th IEEE Sympos. Found. Comput. Sci., pp. 605-614 (1999)
    • (1999) Proc. 40th IEEE Sympos. Found. Comput. Sci. , pp. 605-614
    • Shoshan, A.1    Zwick, U.2
  • 20
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • Strassen, V.: Gaussian elimination is not optimal. Numer. Math. 13, 354-356 (1969)
    • (1969) Numer. Math. , vol.13 , pp. 354-356
    • Strassen, V.1
  • 21
    • 0001586202 scopus 로고
    • A new upper bound on the complexity of the all pairs shortest path problem
    • Takaoka, T.: 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
  • 22
    • 26844521960 scopus 로고    scopus 로고
    • A faster algorithm for the all-pairs shortest path problem and its application
    • Proc. 10th Int. Conf. Comput. Comb. Springer Berlin
    • Takaoka, T.: 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, pp. 278-289. Springer, Berlin (2004)
    • (2004) Lect. Notes Comput. Sci. , vol.3106 , pp. 278-289
    • Takaoka, T.1
  • 23
    • 27144527860 scopus 로고    scopus 로고
    • 3log∈log∈n/log∈n) time algorithm for the all-pairs shortest path problem
    • 3log∈log∈n/log∈n) time algorithm for the all-pairs shortest path problem. Inform. Process. Lett. 96, 155-161 (2005)
    • (2005) Inform. Process. Lett. , vol.96 , pp. 155-161
    • Takaoka, T.1
  • 24
    • 35048828796 scopus 로고    scopus 로고
    • Fast sparse matrix multiplication
    • Proc. 12th European Sympos. Algorithms Springer Berlin
    • Yuster, R., Zwick, U.: Fast sparse matrix multiplication. In: Proc. 12th European Sympos. Algorithms. Lect. Notes Comput. Sci., vol. 3221, pp. 604-615. Springer, Berlin (2004)
    • (2004) Lect. Notes Comput. Sci. , vol.3221 , pp. 604-615
    • Yuster, R.1    Zwick, U.2
  • 25
    • 0012584372 scopus 로고    scopus 로고
    • All-pairs shortest paths using bridging sets and rectangular matrix multiplication
    • Zwick, U.: 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
  • 26
    • 35048829333 scopus 로고    scopus 로고
    • A slightly improved sub-cubic algorithm for the all pairs shortest paths problem with real edge lengths
    • Proc. 15th Int. Sympos. Algorithms and Computation Springer Berlin
    • Zwick, U.: 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, pp. 921-932. Springer, Berlin (2004)
    • (2004) Lect. Notes Comput. Sci. , vol.3341 , pp. 921-932
    • Zwick, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.