메뉴 건너뛰기




Volumn 290, Issue 3, 2003, Pages 1475-1501

An asymptotic theory for recurrence relations based on minimization and maximization

Author keywords

Divide and conquer; Optimal algorithms; Power of two rules; Recurrence relations; Slowly varying functions

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SCIENCE;

EID: 85009192420     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00066-X     Document Type: Article
Times cited : (15)

References (57)
  • 2
    • 0343452157 scopus 로고
    • Multidimensional divide-and-conquer maximin recurrences
    • [2] Alonso, L., Reingold, E.M., Schott, R., Multidimensional divide-and-conquer maximin recurrences. SIAM J. Discrete Math. 8 (1995), 428–447.
    • (1995) SIAM J. Discrete Math. , vol.8 , pp. 428-447
    • Alonso, L.1    Reingold, E.M.2    Schott, R.3
  • 3
    • 0012459770 scopus 로고
    • Some maximal solutions of the generalized subadditive inequality
    • [3] Batty, C.J.K., Rogers, D.G., Some maximal solutions of the generalized subadditive inequality. SIAM J. Algebraic Discrete Methods 3 (1982), 369–378.
    • (1982) SIAM J. Algebraic Discrete Methods , vol.3 , pp. 369-378
    • Batty, C.J.K.1    Rogers, D.G.2
  • 5
    • 22544478951 scopus 로고
    • Some linear and some quadratic recursion formulas. II
    • [5] de Bruijn, N.G., Erdős, P., Some linear and some quadratic recursion formulas. II. Indagationes Mathematicae 14 (1952), 152–163.
    • (1952) Indagationes Mathematicae , vol.14 , pp. 152-163
    • de Bruijn, N.G.1    Erdős, P.2
  • 6
    • 84972561194 scopus 로고
    • A sorting function
    • [6] Carlitz, L., A sorting function. Duke Math. J. 38 (1971), 561–568.
    • (1971) Duke Math. J. , vol.38 , pp. 561-568
    • Carlitz, L.1
  • 8
    • 0012462549 scopus 로고    scopus 로고
    • The cost distribution of queue-mergesort, optimal mergesorts, and power-of-2rules
    • [8] Chen, W.-M., Hwang, H.-K., Chen, G.-H., The cost distribution of queue-mergesort, optimal mergesorts, and power-of-2rules. J. Algorithms 30 (1999), 423–448.
    • (1999) J. Algorithms , vol.30 , pp. 423-448
    • Chen, W.-M.1    Hwang, H.-K.2    Chen, G.-H.3
  • 10
    • 0002341863 scopus 로고
    • Sur la fonction sommatoire de la fonction somme des chiffres
    • [10] Delange, H., Sur la fonction sommatoire de la fonction somme des chiffres. Enseign. Math. 21 (1975), 31–47.
    • (1975) Enseign. Math. , vol.21 , pp. 31-47
    • Delange, H.1
  • 11
    • 0000694634 scopus 로고
    • Moment inequalities for random variables in computational geometry
    • [11] Devroye, L., Moment inequalities for random variables in computational geometry. Computing 30 (1983), 111–119.
    • (1983) Computing , vol.30 , pp. 111-119
    • Devroye, L.1
  • 12
    • 0030304083 scopus 로고    scopus 로고
    • On the distribution of binary search trees under the random permutation model
    • [12] Fill, J.A., On the distribution of binary search trees under the random permutation model. Random Structures and Algorithms 8 (1996), 1–25.
    • (1996) Random Structures and Algorithms , vol.8 , pp. 1-25
    • Fill, J.A.1
  • 13
    • 21844484375 scopus 로고
    • Mellin transforms and asymptotics: the mergesort recurrence
    • [13] Flajolet, P., Golin, M., Mellin transforms and asymptotics: the mergesort recurrence. Acta Inform. 31 (1994), 673–696.
    • (1994) Acta Inform. , vol.31 , pp. 673-696
    • Flajolet, P.1    Golin, M.2
  • 15
    • 0028498498 scopus 로고
    • A calculus for the random generation of labelled combinatorial structures
    • [15] Flajolet, P., Zimmerman, P., Van Cutsem, B., A calculus for the random generation of labelled combinatorial structures. Theoret. Comput. Sci. 132 (1994), 1–35.
    • (1994) Theoret. Comput. Sci. , vol.132 , pp. 1-35
    • Flajolet, P.1    Zimmerman, P.2    Van Cutsem, B.3
  • 16
    • 0016129208 scopus 로고
    • Recurrence relations based on minimization
    • [16] Fredman, M.L., Knuth, D.E., Recurrence relations based on minimization. J. Math. Anal. Appl. 48 (1974), 534–559.
    • (1974) J. Math. Anal. Appl. , vol.48 , pp. 534-559
    • Fredman, M.L.1    Knuth, D.E.2
  • 17
    • 0016351278 scopus 로고
    • A discrete search game
    • [17] Gal, S., A discrete search game. SIAM J. Appl. Math. 27 (1974), 641–648.
    • (1974) SIAM J. Appl. Math. , vol.27 , pp. 641-648
    • Gal, S.1
  • 18
    • 0016993829 scopus 로고
    • On the optimality of Huffman trees
    • [18] Glassey, C.R., Karp, R.M., On the optimality of Huffman trees. SIAM J. Appl. Math. 31 (1976), 368–378.
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 368-378
    • Glassey, C.R.1    Karp, R.M.2
  • 21
    • 84971124131 scopus 로고
    • Generalization of the fundamental theorem on sub-additive functions
    • [21] Hammersley, J.M., Generalization of the fundamental theorem on sub-additive functions. Proc. Cambridge Philos. Soc. 58 (1962), 235–238.
    • (1962) Proc. Cambridge Philos. Soc. , vol.58 , pp. 235-238
    • Hammersley, J.M.1
  • 22
    • 0003201047 scopus 로고
    • Maximal solutions of the generalized subadditive inequality
    • E.F. Harding D.G. Kendall Wiley London
    • [22] Hammersley, J.M., Grimmett, G.R., Maximal solutions of the generalized subadditive inequality. Harding, E.F., Kendall, D.G., (eds.) Stochastic Geometry, 1974, Wiley, London, 270–284.
    • (1974) Stochastic Geometry , pp. 270-284
    • Hammersley, J.M.1    Grimmett, G.R.2
  • 23
    • 0001996348 scopus 로고
    • The probabilities of rooted tree-shapes generated by random bifurcation
    • [23] Harding, E.F., The probabilities of rooted tree-shapes generated by random bifurcation. Adv. Appl. Probab. 3 (1971), 44–77.
    • (1971) Adv. Appl. Probab. , vol.3 , pp. 44-77
    • Harding, E.F.1
  • 24
    • 0000748659 scopus 로고
    • A note on the edges of the n-cube
    • [24] Hart, S., A note on the edges of the n-cube. Discrete Math. 14 (1976), 157–163.
    • (1976) Discrete Math. , vol.14 , pp. 157-163
    • Hart, S.1
  • 25
    • 84909652489 scopus 로고
    • Dichotomous search for random objects on an interval
    • [25] Hassin, R., Henig, M., Dichotomous search for random objects on an interval. Math. Oper. Res. 9 (1984), 301–308.
    • (1984) Math. Oper. Res. , vol.9 , pp. 301-308
    • Hassin, R.1    Henig, M.2
  • 26
    • 0026853667 scopus 로고
    • Asymptotic analysis of dichotomous search with search and travel costs
    • [26] Hassin, R., Rotovely, R., Asymptotic analysis of dichotomous search with search and travel costs. European J. Oper. Res. 58 (1992), 78–89.
    • (1992) European J. Oper. Res. , vol.58 , pp. 78-89
    • Hassin, R.1    Rotovely, R.2
  • 27
    • 84963146750 scopus 로고
    • On dichotomous search with direction-dependent costs for a uniformly hidden object
    • [27] Hinderer, K., On dichotomous search with direction-dependent costs for a uniformly hidden object. Optimization 21 (1990), 215–229.
    • (1990) Optimization , vol.21 , pp. 215-229
    • Hinderer, K.1
  • 31
    • 0041999165 scopus 로고
    • An optimal hierarchical procedure for a modified binomial group-testing problem
    • [31] Hwang, F.K., Pfeifer, C.G., Enis, P., An optimal hierarchical procedure for a modified binomial group-testing problem. J. Amer. Statist. Assoc. 76 (1981), 947–949.
    • (1981) J. Amer. Statist. Assoc. , vol.76 , pp. 947-949
    • Hwang, F.K.1    Pfeifer, C.G.2    Enis, P.3
  • 32
    • 85009209829 scopus 로고    scopus 로고
    • On the number of heaps and the cost of heap construction, Colloquium on Mathematics and Computer Science 2002 (Versailles), accepted.
    • [32] H.-K. Hwang, J.-M. Steyaert, On the number of heaps and the cost of heap construction, Colloquium on Mathematics and Computer Science 2002 (Versailles), accepted.
    • Hwang, H.-K.1    Steyaert, J.-M.2
  • 33
    • 0038248429 scopus 로고
    • New primal and dual matching heuristics
    • [33] Jünger, M., Pulleyblank, W., New primal and dual matching heuristics. Algorithmica 13 (1995), 357–380.
    • (1995) Algorithmica , vol.13 , pp. 357-380
    • Jünger, M.1    Pulleyblank, W.2
  • 34
    • 38549179235 scopus 로고
    • Recurrence relations based on minimization and maximization
    • [34] Kapoor, S., Reingold, E.M., Recurrence relations based on minimization and maximization. J. Math. Anal. Appl. 109 (1985), 591–604.
    • (1985) J. Math. Anal. Appl. , vol.109 , pp. 591-604
    • Kapoor, S.1    Reingold, E.M.2
  • 38
    • 0022663791 scopus 로고
    • Binary trees and uniform distribution of traffic cutback
    • [38] Li, S.Y.R., Binary trees and uniform distribution of traffic cutback. J. Comput. System Sci. 32 (1986), 1–14.
    • (1986) J. Comput. System Sci. , vol.32 , pp. 1-14
    • Li, S.Y.R.1
  • 39
    • 0024899157 scopus 로고
    • Solution of a divide-and-conquer maximin recurrence
    • [39] Li, Z., Reingold, E.M., Solution of a divide-and-conquer maximin recurrence. SIAM J. Comput. 18 (1989), 1188–1200.
    • (1989) SIAM J. Comput. , vol.18 , pp. 1188-1200
    • Li, Z.1    Reingold, E.M.2
  • 40
    • 0039083100 scopus 로고
    • The number of 1's in binary integers: bounds and extremal properties
    • [40] McIlroy, M.D., The number of 1's in binary integers: bounds and extremal properties. SIAM J. Comput. 3 (1974), 255–261.
    • (1974) SIAM J. Comput. , vol.3 , pp. 255-261
    • McIlroy, M.D.1
  • 41
    • 0345747889 scopus 로고
    • Some theorems on sorting
    • [41] Morris, R., Some theorems on sorting. SIAM J. Appl. Math. 17 (1969), 1–6.
    • (1969) SIAM J. Appl. Math. , vol.17 , pp. 1-6
    • Morris, R.1
  • 42
    • 0011524783 scopus 로고
    • A dichotomous search
    • [42] Murakami, S., A dichotomous search. J. Oper. Res. Soc. Japan 14 (1971), 127–142.
    • (1971) J. Oper. Res. Soc. Japan , vol.14 , pp. 127-142
    • Murakami, S.1
  • 44
    • 0040730303 scopus 로고
    • Bottom-up mergesort—a detailed analysis
    • [44] Panny, W., Prodinger, H., Bottom-up mergesort—a detailed analysis. Algorithmica 14 (1995), 340–354.
    • (1995) Algorithmica , vol.14 , pp. 340-354
    • Panny, W.1    Prodinger, H.2
  • 45
    • 85009163316 scopus 로고    scopus 로고
    • A problem in the design of electrical circuits, a generalized subadditive inequality and the recurrence relation j(n,m)=j ([n/2], m)+j ([n+1/2], m)+(j n, m−1), Lecture Notes in Mathematics, Vol. 622, Springer, Berlin, New York, 1977, pp. 153–169.
    • [45] M.J. Pelling, D.G. Rogers, A problem in the design of electrical circuits, a generalized subadditive inequality and the recurrence relation j(n,m)=j ([n/2], m)+j ([n+1/2], m)+(j n, m−1), Lecture Notes in Mathematics, Vol. 622, Springer, Berlin, New York, 1977, pp. 153–169.
    • Pelling, M.J.1    Rogers, D.G.2
  • 46
    • 85009172524 scopus 로고
    • A combinatorial problem in the design of electrical circuits
    • [46] Pelling, M.J., Rogers, D.G., A combinatorial problem in the design of electrical circuits. Southeast Asian Bull. Math. 4 (1980), 29–33.
    • (1980) Southeast Asian Bull. Math. , vol.4 , pp. 29-33
    • Pelling, M.J.1    Rogers, D.G.2
  • 47
    • 21144467330 scopus 로고
    • An elementary approach to some analytic asymptotics
    • [47] Pippenger, N., An elementary approach to some analytic asymptotics. SIAM J. Math. Anal. 24 (1993), 1361–1377.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 1361-1377
    • Pippenger, N.1
  • 48
    • 84976789411 scopus 로고
    • A sorting problem and its complexity
    • [48] Pohl, I., A sorting problem and its complexity. Comm. ACM 15 (1972), 462–464.
    • (1972) Comm. ACM , vol.15 , pp. 462-464
    • Pohl, I.1
  • 49
    • 0038304871 scopus 로고
    • On a greedy heuristic for complete matching
    • [49] Reingold, E.M., Tarjan, R.E., On a greedy heuristic for complete matching. SIAM J. Comput. 10 (1981), 676–681.
    • (1981) SIAM J. Comput. , vol.10 , pp. 676-681
    • Reingold, E.M.1    Tarjan, R.E.2
  • 51
    • 0009749612 scopus 로고    scopus 로고
    • Improved master theorems for divide-and-conquer recurrences
    • [51] Roura, S., Improved master theorems for divide-and-conquer recurrences. J. Assoc. Comput. Math. 48 (2001), 170–205.
    • (2001) J. Assoc. Comput. Math. , vol.48 , pp. 170-205
    • Roura, S.1
  • 52
    • 0022488582 scopus 로고
    • Exact balancing is not always good
    • [52] Snir, M., Exact balancing is not always good. Inform. Process. Lett. 22 (1986), 97–102.
    • (1986) Inform. Process. Lett. , vol.22 , pp. 97-102
    • Snir, M.1
  • 53
    • 85009214657 scopus 로고    scopus 로고
    • Probability theory and combinatorial optimization, CBMS-NSF Regional Conf., Series in Applied Mathematics, Vol. 69, SIAM, PA, 1997.
    • [53] J.M. Steele, Probability theory and combinatorial optimization, CBMS-NSF Regional Conf., Series in Applied Mathematics, Vol. 69, SIAM, PA, 1997.
    • Steele, J.M.1
  • 54
    • 0021517679 scopus 로고
    • How evenly should one divide to conquer quickly?
    • [54] Walsh, T.R., How evenly should one divide to conquer quickly?. Inform. Process. Lett. 19 (1984), 203–208.
    • (1984) Inform. Process. Lett. , vol.19 , pp. 203-208
    • Walsh, T.R.1
  • 55
    • 0343887989 scopus 로고    scopus 로고
    • Tighter bounds on the solution of a divide-and-conquer maximin recurrence
    • [55] Wang, B.-F., Tighter bounds on the solution of a divide-and-conquer maximin recurrence. J. Algorithms 23 (1997), 329–344.
    • (1997) J. Algorithms , vol.23 , pp. 329-344
    • Wang, B.-F.1
  • 56
    • 0346379068 scopus 로고
    • A linear search problem
    • [56] Wong, E., A linear search problem. SIAM Rev. 6 (1964), 168–174.
    • (1964) SIAM Rev. , vol.6 , pp. 168-174
    • Wong, E.1
  • 57
    • 85009163307 scopus 로고    scopus 로고
    • Probability theory of classical Euclidean optimization problems, Lecture Notes in Mathematics, Vol. 1675, Springer, Berlin, 1998.
    • [57] J.E. Yukich, Probability theory of classical Euclidean optimization problems, Lecture Notes in Mathematics, Vol. 1675, Springer, Berlin, 1998.
    • Yukich, J.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.