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Volumn 3341, Issue , 2004, Pages 921-932

A slightly improved sub-cubic algorithm for the all pairs shortest paths problem with real edge lengths

Author keywords

[No Author keywords available]

Indexed keywords

ALL PAIRS SHORTEST PATHS; CUBIC ALGORITHM; EDGE LENGTH; SHORTEST PATH PROBLEM; TIME ALGORITHMS;

EID: 35048829333     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-30551-4_78     Document Type: Article
Times cited : (40)

References (31)
  • 4
    • 0001539365 scopus 로고
    • English translation in
    • English translation in Soviet Mathematics Doklady, 11:1209-1210, 1970.
    • (1970) Soviet Mathematics Doklady , vol.11 , pp. 1209-1210
  • 7
    • 34147120474 scopus 로고
    • A note on two problems in connexion with graphs
    • E. W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik, 1:269-271, 1959.
    • (1959) Numerische Mathematik , vol.1 , pp. 269-271
    • Dijkstra, E.W.1
  • 9
    • 84945709831 scopus 로고
    • Algorithm 97: Shortest path
    • R. W. Floyd. Algorithm 97: Shortest path. Communications of the ACM, 5(6):345, 1962.
    • (1962) Communications of the ACM , vol.5 , Issue.6 , pp. 345
    • Floyd, R.W.1
  • 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 Journal on Computing, 5:49-60, 1976.
    • (1976) SIAM Journal on Computing , vol.5 , pp. 49-60
    • Fredman, M.L.1
  • 11
    • 0023384210 scopus 로고
    • Fibonacci heaps and their uses in improved network optimization algorithms
    • M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34:596-615, 1987.
    • (1987) Journal of the ACM , vol.34 , pp. 596-615
    • Fredman, M.L.1    Tarjan, R.E.2
  • 12
    • 0343702441 scopus 로고
    • Application of a method of rapid multiplication of matrices to the problem of finding the transitive closure of a graph
    • M. E. Furman. Application of a method of rapid multiplication of matrices to the problem of finding the transitive closure of a graph. Doklady Akademii Nauk SSSR, 194:524, 1970.
    • (1970) Doklady Akademii Nauk SSSR , vol.194 , pp. 524
    • Furman, M.E.1
  • 13
    • 0343702441 scopus 로고
    • English translation in
    • English translation in Soviet Mathematics Doklady, 11:1252, 1970.
    • (1970) Soviet Mathematics Doklady , vol.11 , pp. 1252
  • 14
    • 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. Information and Computation, 134:103-139, 1997.
    • (1997) Information and Computation , vol.134 , pp. 103-139
    • Galil, Z.1    Margalit, O.2
  • 15
    • 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. Journal of Computer and System Sciences, 54:243-254, 1997.
    • (1997) Journal of Computer and System Sciences , vol.54 , pp. 243-254
    • Galil, Z.1    Margalit, O.2
  • 16
    • 84974533426 scopus 로고    scopus 로고
    • Improved shortest paths on the word RAM
    • T. Hagerup. Improved shortest paths on the word RAM. In Proc. of 27th ICALP, pages 61-72, 2000.
    • (2000) Proc. of 27th ICALP , pp. 61-72
    • Hagerup, T.1
  • 17
    • 84976789814 scopus 로고
    • Efficient algorithms for shortest paths in sparse graphs
    • D. B. Johnson. Efficient algorithms for shortest paths in sparse graphs. Journal of the ACM, 24:1-13, 1977.
    • (1977) Journal of the ACM , vol.24 , pp. 1-13
    • Johnson, D.B.1
  • 18
    • 0002277797 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. of 40th FOCS, pages 81-91, 1999.
    • (1999) Proc. of 40th FOCS , pp. 81-91
    • King, V.1
  • 19
    • 0342653947 scopus 로고
    • Efficient determination of the transitive closure of a directed graph
    • I. Munro. Efficient determination of the transitive closure of a directed graph. Information Processing Letters, 1(2):56-58, 1971.
    • (1971) Information Processing Letters , vol.1 , Issue.2 , pp. 56-58
    • Munro, I.1
  • 20
    • 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. Theoretical Computer Science, 312(1):47-74, 2004.
    • (2004) Theoretical Computer Science , vol.312 , Issue.1 , pp. 47-74
    • Pettie, S.1
  • 21
    • 84968902218 scopus 로고    scopus 로고
    • Computing shortest paths with comparisons and additions
    • S. Pettie and V. Ramachandran. Computing shortest paths with comparisons and additions. In Proc. of 13th SODA, pages 267-276, 2002.
    • (2002) Proc. of 13th SODA , pp. 267-276
    • Pettie, S.1    Ramachandran, V.2
  • 22
    • 0036954330 scopus 로고    scopus 로고
    • Improved dynamic reachability algorithms for directed graphs
    • L. Roditty and U. Zwick. Improved dynamic reachability algorithms for directed graphs. In Proc. of 43rd FOCS, pages 679-688, 2002.
    • (2002) Proc. of 43rd FOCS , pp. 679-688
    • Roditty, L.1    Zwick, U.2
  • 23
    • 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. Journal of Computer and System Sciences, 51:400-403, 1995.
    • (1995) Journal of Computer and System Sciences , vol.51 , pp. 400-403
    • Seidel, R.1
  • 24
    • 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. of 40th FOCS, pages 605-614, 1999.
    • (1999) Proc. of 40th FOCS , pp. 605-614
    • Shoshan, A.1    Zwick, U.2
  • 25
    • 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
  • 26
    • 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. Information Processing Letters, 43:195-199, 1992.
    • (1992) Information Processing Letters , vol.43 , pp. 195-199
    • Takaoka, T.1
  • 27
    • 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. Journal of the ACM, 46:362-394, 1999.
    • (1999) Journal of the ACM , vol.46 , pp. 362-394
    • Thorup, M.1
  • 28
    • 84945708259 scopus 로고
    • A theorem on boolean matrices
    • S. Warshall. A theorem on boolean matrices. Journal of the ACM, 9(1):11-12, 1962.
    • (1962) Journal of the ACM , vol.9 , Issue.1 , pp. 11-12
    • Warshall, S.1
  • 29
    • 0039947721 scopus 로고
    • 2. 81 infinite-precision multiplications
    • 2. 81 infinite-precision multiplications. Information Processing Letters, 4:155-156, 1976.
    • (1976) Information Processing Letters , vol.4 , pp. 155-156
    • Yuval, G.1
  • 30
    • 84943271885 scopus 로고    scopus 로고
    • Exact and approximate distances in graphs - A survey
    • U. Zwick. Exact and approximate distances in graphs - a survey. In Proc. of 9th ESA, pages 33-48, 2001.
    • (2001) Proc. of 9th ESA , pp. 33-48
    • Zwick, U.1
  • 31
    • 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. Journal of the ACM, 49:289-317, 2002.
    • (2002) Journal of the ACM , vol.49 , pp. 289-317
    • Zwick, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.