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Volumn 4, Issue 1, 2008, Pages

Randomized minimum spanning tree algorithms using exponentially fewer random bits

Author keywords

Graph algorithms; Minimum spanning trees; Random sampling

Indexed keywords

GRAPH ALGORITHMS; MINIMUM SPANNING TREES; RANDOM SAMPLING;

EID: 42149192061     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/1328911.1328916     Document Type: Article
Times cited : (18)

References (54)
  • 3
    • 0012579094 scopus 로고
    • A linear time approach to the set maxima problem
    • BAR-NOY, A., MOTWANI, R., AND NAOR, J. 1992. A linear time approach to the set maxima problem. SIAM J. Discr. Math. 5, 1, 1-9.
    • (1992) SIAM J. Discr. Math , vol.5 , Issue.1 , pp. 1-9
    • BAR-NOY, A.1    MOTWANI, R.2    NAOR, J.3
  • 7
    • 0012574730 scopus 로고    scopus 로고
    • A minimum spanning tree algorithm with inverse-Ackermann type complexity
    • CHAZELLE, B. 2000a. A minimum spanning tree algorithm with inverse-Ackermann type complexity. J. ACM 47, 6, 1028-1047.
    • (2000) J. ACM , vol.47 , Issue.6 , pp. 1028-1047
    • CHAZELLE, B.1
  • 8
    • 0012608449 scopus 로고    scopus 로고
    • The soft heap: An approximate priority queue with optimal error rate
    • CHAZELLE, B. 2000b. The soft heap: An approximate priority queue with optimal error rate. J. ACM 47, 6, 1012-1027.
    • (2000) J. ACM , vol.47 , Issue.6 , pp. 1012-1027
    • CHAZELLE, B.1
  • 9
    • 0000523923 scopus 로고    scopus 로고
    • Concurrent threads and optimal parallel minimum spanning trees algorithm
    • CHONG, K. W., HAN, Y., AND LAM, T. W. 2001. Concurrent threads and optimal parallel minimum spanning trees algorithm. J. ACM 48, 2, 297-323.
    • (2001) J. ACM , vol.48 , Issue.2 , pp. 297-323
    • CHONG, K.W.1    HAN, Y.2    LAM, T.W.3
  • 11
    • 42149151347 scopus 로고    scopus 로고
    • Personal communication
    • COLE, R. 1999. Personal communication.
    • (1999)
    • COLE, R.1
  • 14
    • 0026155384 scopus 로고
    • Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms
    • COLE, R. AND VISHKIN, U. 1991. Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms. Inf. Comput. 92, 1, 1-47.
    • (1991) Inf. Comput , vol.92 , Issue.1 , pp. 1-47
    • COLE, R.1    VISHKIN, U.2
  • 16
    • 0024641026 scopus 로고
    • Average case selection
    • CUNTO, W., AND MUNRO, J. I. 1989. Average case selection. J. ACM 36, 2, 270-279.
    • (1989) J. ACM , vol.36 , Issue.2 , pp. 270-279
    • CUNTO, W.1    MUNRO, J.I.2
  • 17
    • 34147120474 scopus 로고
    • A note on two problems in connexion with graphs
    • DUKSTRA, E. W. 1959. A note on two problems in connexion with graphs. Numer. Math. 1, 269-271.
    • (1959) Numer. Math , vol.1 , pp. 269-271
    • DUKSTRA, E.W.1
  • 18
    • 0001522013 scopus 로고
    • Verification and sensitivity analysis of minimum. spanning trees in linear time
    • DIXON, B., RAUCH, M., AND TARJAN, R. E. 1992. Verification and sensitivity analysis of minimum. spanning trees in linear time. SIAM J. Comput. 21, 6, 1184-1192.
    • (1992) SIAM J. Comput , vol.21 , Issue.6 , pp. 1184-1192
    • DIXON, B.1    RAUCH, M.2    TARJAN, R.E.3
  • 19
    • 0037537067 scopus 로고    scopus 로고
    • Median selection requires (2 + ε)n comparisons
    • DOR, D., AND ZWICK, U. 2001. Median selection requires (2 + ε)n comparisons. SIAM J. Discr. Math. 14, 3, 312-325.
    • (2001) SIAM J. Discr. Math , vol.14 , Issue.3 , pp. 312-325
    • DOR, D.1    ZWICK, U.2
  • 20
    • 0032614072 scopus 로고    scopus 로고
    • Selecting the median
    • DOR, D., AND ZWICK, U. 1999. Selecting the median. SIAM J. Comput. 28, 5, 1722-1758.
    • (1999) SIAM J. Comput , vol.28 , Issue.5 , pp. 1722-1758
    • DOR, D.1    ZWICK, U.2
  • 21
    • 0016485958 scopus 로고
    • Expected time bounds for selection
    • FLOYD, R., AND RIVEST, R. 1975. Expected time bounds for selection. Commun. ACM 18, 3, 165-172.
    • (1975) Commun. ACM , vol.18 , Issue.3 , pp. 165-172
    • FLOYD, R.1    RIVEST, R.2
  • 22
    • 0024700512 scopus 로고
    • Efficient implementation of graph algorithms using contraction
    • GABOW, H. N., GALIL, Z., AND SPENCER, T. H. 1989. Efficient implementation of graph algorithms using contraction. J. ACM 36, 3, 540-572.
    • (1989) J. ACM , vol.36 , Issue.3 , pp. 540-572
    • GABOW, H.N.1    GALIL, Z.2    SPENCER, T.H.3
  • 23
    • 51249176707 scopus 로고
    • Efficient algorithms for finding minimum spanning trees in undirected and directed graphs
    • GABOW, H. N., GALIL, Z., SPENCER, T. H., AND TARJAN, R. E. 1986. Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica 6, 109-122.
    • (1986) Combinatorica , vol.6 , pp. 109-122
    • GABOW, H.N.1    GALIL, Z.2    SPENCER, T.H.3    TARJAN, R.E.4
  • 24
    • 0026390260 scopus 로고
    • An optimal randomized parallel algorithm for finding connected components in a graph
    • GAZIT, H. 1991. An optimal randomized parallel algorithm for finding connected components in a graph. SIAM J. Comput. 20, 6, 1046-1067.
    • (1991) SIAM J. Comput , vol.20 , Issue.6 , pp. 1046-1067
    • GAZIT, H.1
  • 25
    • 0027578635 scopus 로고
    • Optimal randomized algorithms for local sorting and set-maxima
    • GODDARD, W., KENYON, C., KING, V., AND SCHULMAN, L. 1993. Optimal randomized algorithms for local sorting and set-maxima. SIAM J. Comput. 22, 2, 272-283.
    • (1993) SIAM J. Comput , vol.22 , Issue.2 , pp. 272-283
    • GODDARD, W.1    KENYON, C.2    KING, V.3    SCHULMAN, L.4
  • 26
    • 0002726668 scopus 로고
    • On the history of the minimum spanning tree problem
    • GRAHAM, R. L. AND HELL, P. 1985. On the history of the minimum spanning tree problem.. Ann. Hist. Comput. 7, 1, 43-57.
    • (1985) Ann. Hist. Comput , vol.7 , Issue.1 , pp. 43-57
    • GRAHAM, R.L.1    HELL, P.2
  • 27
    • 84976845937 scopus 로고
    • Information bounds are weak in the shortest distance problem
    • GRAHAM, R. L., YAO, A. C., AND YAO, F. F. 1980. Information bounds are weak in the shortest distance problem. J. ACM 27, 3, 428-444.
    • (1980) J. ACM , vol.27 , Issue.3 , pp. 428-444
    • GRAHAM, R.L.1    YAO, A.C.2    YAO, F.F.3
  • 28
    • 0030393752 scopus 로고    scopus 로고
    • An optimal randomised logarithmic time connectivity algorithm for the EREW PRAM
    • HALPERIN, S., AND ZWICK, U. 1996. An optimal randomised logarithmic time connectivity algorithm for the EREW PRAM. J. Comput. Syst. Sci. 53, 3, 395-416.
    • (1996) J. Comput. Syst. Sci , vol.53 , Issue.3 , pp. 395-416
    • HALPERIN, S.1    ZWICK, U.2
  • 29
    • 0012637354 scopus 로고    scopus 로고
    • Optimal randomized EREW PRAM algorithms for finding spanning forests
    • HALPERIN, S., AND ZWICK, U. 2001. Optimal randomized EREW PRAM algorithms for finding spanning forests. J. Algor. 39, 1, 1-46.
    • (2001) J. Algor , vol.39 , Issue.1 , pp. 1-46
    • HALPERIN, S.1    ZWICK, U.2
  • 32
    • 0001542876 scopus 로고
    • On a set of almost deterministic k-independent random variables
    • JOFFE, A. 1974. On a set of almost deterministic k-independent random variables. Ann. Probab. 2, 1, 161-162.
    • (1974) Ann. Probab , vol.2 , Issue.1 , pp. 161-162
    • JOFFE, A.1
  • 34
    • 0029276335 scopus 로고
    • A randomized linear-time algorithm for finding minimum spanning trees
    • KARGER, D. R., KLEIN, P. N., AND TARJAN, R. E. 1995. A randomized linear-time algorithm for finding minimum spanning trees. J. ACM 42, 321-329.
    • (1995) J. ACM , vol.42 , pp. 321-329
    • KARGER, D.R.1    KLEIN, P.N.2    TARJAN, R.E.3
  • 35
    • 0002065879 scopus 로고
    • Parallel algorithms for shared-memory machines
    • MIT Press/Elsevier
    • KARP, R. M., AND RAMACHANDRAN, V. 1990. Parallel algorithms for shared-memory machines. In Handbook of Computer Science. MIT Press/Elsevier, 869-942.
    • (1990) Handbook of Computer Science , pp. 869-942
    • KARP, R.M.1    RAMACHANDRAN, V.2
  • 37
    • 0000626504 scopus 로고    scopus 로고
    • A simpler minimum spanning tree verification algorithm
    • KING, V. 1997. A simpler minimum spanning tree verification algorithm.. Algorithmica 18, 2, 263-270.
    • (1997) Algorithmica , vol.18 , Issue.2 , pp. 263-270
    • KING, V.1
  • 38
    • 0012682946 scopus 로고    scopus 로고
    • An optimal EREW PRAM algorithm for minimum spanning tree verification
    • KING, V., POON, C K., RAMACHANDRAN, V., AND SINHA, S. 1997. An optimal EREW PRAM algorithm for minimum spanning tree verification. Info. Proc. Lett. 62, 3, 153-159.
    • (1997) Info. Proc. Lett , vol.62 , Issue.3 , pp. 153-159
    • KING, V.1    POON, C.K.2    RAMACHANDRAN, V.3    SINHA, S.4
  • 39
    • 51249177436 scopus 로고
    • Linear verification for spanning trees
    • KOMLÓS, J. 1985. Linear verification for spanning trees. Combinatorica 5, 1, 57-65.
    • (1985) Combinatorica , vol.5 , Issue.1 , pp. 57-65
    • KOMLÓS, J.1
  • 40
    • 70350674995 scopus 로고
    • On the shortest spanning subtree of a graph and the traveling salesman problem
    • KRUSKAL, J. B. 1956. On the shortest spanning subtree of a graph and the traveling salesman problem. In Proceedings of the American Mathematical Society, vol. 7, 48-50.
    • (1956) Proceedings of the American Mathematical Society , vol.7 , pp. 48-50
    • KRUSKAL, J.B.1
  • 42
    • 0017217375 scopus 로고
    • Riemann's hypothesis and tests for primality
    • MILLER, G. L. 1976. Riemann's hypothesis and tests for primality. J. Comput. Syst. Sci. 13, 3, 300-317.
    • (1976) J. Comput. Syst. Sci , vol.13 , Issue.3 , pp. 300-317
    • MILLER, G.L.1
  • 46
    • 29344451797 scopus 로고    scopus 로고
    • On the shortest path and minimum spanning tree-problems. Ph.D. thesis, The University of Texas at Austin
    • TR-03-35, Department of Computer Sciences
    • PETTIE, S. 2003. On the shortest path and minimum spanning tree-problems. Ph.D. thesis, The University of Texas at Austin. Also Tech. Rep. TR-03-35, Department of Computer Sciences. http://www.cs.utexas.edu/ftp/pub/ tech.reports/tr03-35.ps.gz.
    • (2003) Also Tech. Rep
    • PETTIE, S.1
  • 47
    • 42149119305 scopus 로고    scopus 로고
    • Finding minimum, spanning trees in time. Tech. Rep. CS-TR-99-23, University of Texas, Austin
    • PETTIE, S. 1999. Finding minimum, spanning trees in O(mα(m, n)) time. Tech. Rep. CS-TR-99-23, University of Texas, Austin.
    • (1999) O(mα(m, n))
    • PETTIE, S.1
  • 49
    • 0002621234 scopus 로고    scopus 로고
    • An optimal minimum spanning tree algorithm
    • PETTIE, S., AND RAMACHANDRAN, V. 2002b. An optimal minimum spanning tree algorithm. J. ACM 49, 1, 16-34.
    • (2002) J. ACM , vol.49 , Issue.1 , pp. 16-34
    • PETTIE, S.1    RAMACHANDRAN, V.2
  • 50
    • 0036767167 scopus 로고    scopus 로고
    • A randomized time-work optimal parallel algorithm for finding a minimum spanning forest
    • PETTIE, S., AND RAMACHANDRAN, V. 2002C. A randomized time-work optimal parallel algorithm for finding a minimum spanning forest. SIAM J. Comput. 31, 6, 1879-1895.
    • (2002) SIAM J. Comput , vol.31 , Issue.6 , pp. 1879-1895
    • PETTIE, S.1    RAMACHANDRAN, V.2
  • 51
    • 84911584312 scopus 로고
    • Shortest connection networks and some generalizations
    • PRIM, R. C. 1957. Shortest connection networks and some generalizations. Bell Syst. Tech. J., 1389-1401.
    • (1957) Bell Syst. Tech. J , pp. 1389-1401
    • PRIM, R.C.1
  • 52
    • 33845432604 scopus 로고
    • Probabilistic algorithm for testing primality
    • RABIN, M. O. 1980. Probabilistic algorithm for testing primality. J. Number Theory 12,1, 128-138.
    • (1980) J. Number Theory , vol.12 , Issue.1 , pp. 128-138
    • RABIN, M.O.1
  • 53
    • 0001595705 scopus 로고
    • Chernoff-Hoeffding bounds for applications with limited independence
    • SCHMIDT, J. P., SIEGEL, A., AND SRINIVASAN, A. 1995. Chernoff-Hoeffding bounds for applications with limited independence. SIAM J. Discr. Math. 8, 2, 223-250.
    • (1995) SIAM J. Discr. Math , vol.8 , Issue.2 , pp. 223-250
    • SCHMIDT, J.P.1    SIEGEL, A.2    SRINIVASAN, A.3
  • 54
    • 0002579339 scopus 로고    scopus 로고
    • TARJAN, R. E. 1982. Sensitivity analysis of minimum spanning trees and shortest path problems. Inf. Proc. Lett. 14, 1, 30-33. See Corrigendum, IPL 23, 4, 219.
    • TARJAN, R. E. 1982. Sensitivity analysis of minimum spanning trees and shortest path problems. Inf. Proc. Lett. 14, 1, 30-33. See Corrigendum, IPL 23, 4, 219.


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