Eppstein, D., Z. Galil, and R. Giancarlo, Speeding Up Dynamic Programming, Proc. 29th IEEE Symp. on Foundations of Computer Science, 488-296 (1988).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....O by querying only O(n) elements of OUT. Clearly, if both the full DIST and all entries of I are available, then computing an element of OUT is O(1) work. For various solutions to related problems, which also utilize Monge and Total Monotonicity properties, we refer the interested reader to [14] [15], 19] 20] 31] and [33] In order to eciently utilize these properties here, we need to address the following two problems. 1. How to eciently compute DIST and represent it in a format which allows direct access to its entries. This will be done in Section 3.4. 2. SMAWK is intended for a ....

Eppstein, D., Z. Galil, and R. Giancarlo, Speeding Up Dynamic Programming, Proc. 29th IEEE Symp. on Foundations of Computer Science, 488-296 (1988).

....algorithm sketched above, and works by introducing two new arrays for storing distances between prefixes when an insertion or deletion has already been initiated. More complex cost functions for indels can be handled while increasing the time complexity by at most a factor O(log( a b ) cf. [39, 106, 83]. When comparing two DNA sequences each coding for a protein we are faced with a di#cult choice: Should we just compare the DNA sequences or should we compare the two proteins they code for The evolutionary events our model postulates takes place in the DNA sequence but the evolutionary ....

....O( s ) If the stability of an internal loop can be assumed only to depend on the size of the internal loop, Waterman et al. 153] describes how to reduce the time requirement to O( s This is further improved to O( s log s ) for convex free energy functions by Eppstein et.al. [39]. A#ne free energy functions (i.e. of the form a bn, where n is the size of the loop) allows for O( s ) computation time by borrowing a simple method used in sequence alignment [46] Unfortunately the currently used free energy functions for internal loops are not convex, let al..one a#ne. ....

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D. Eppstein, Z. Galil, and R. Giancarlo. Speeding up dynamic programming. In Proceedings of the 29th Annual Symposium on Foundations of

....O(jsj ) If the stability of an internal loop can be assumed only to depend on the size of the internal loop, Waterman et al. 18] describes how to reduce the time requirement to O(jsj . This is further improved to O(jsj log jsj) for convex free energy functions by Eppstein et.al. [1]. Ane free energy functions (i.e. of the form a bn, where n is the size of the loop) allows for O(jsj ) computation time by borrowing a simple method used in sequence alignment [2] Unfortunately the currently used free energy functions for internal loops are not convex, let al..one ane. ....

....of the form a bn, where n is the size of the loop) allows for O(jsj ) computation time by borrowing a simple method used in sequence alignment [2] Unfortunately the currently used free energy functions for internal loops are not convex, let al..one ane. Furthermore, the technique described in [1] hinges on the objective being to nd a structure of maximum stability, and thus does not translate to the calculation of the partition function of [9] where a Boltzmann weighted sum of contributions to the partition function is calculated. In this paper we will describe a method based on a ....

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David Eppstein, Zvi Galil, and Raaele Giancarlo. Speeding up dynamic programming. In Proc. 29th Symp. Foundations of Computer Science, pages 488-496. Assoc. Comput. Mach., October 1988.

....O by querying only O(n) elements of OUT . Clearly, if both the full DIST and all entries of I are available, then computing an element of OUT is O(1) work. For various solutions to related problems, which also utilize Monge and Total Monotonicity properties, we refer the interested reader to [8] [9], 14] 15] 24] and [27] In order to eciently utilize these properties here, we need to address the following two problems. 1. How to eciently compute DIST and represent it in a format which allows direct access to its entries. This will be done in section 3.2.2. 2. SMAWK is intended for a ....

Eppstein, D., Z. Galil, and R. Giancarlo, Speeding Up Dynamic Programming, Proc. 29th IEEE Symp. on Foundations of Computer Science, 488-296 (1988).

....3 ) If the stability of an internal loop can be assumed only to depend on the size of the internal loop, Waterman et al. 18] describes how to reduce the time requirement to O(jsj 3 ) 1 . This is further improved to O(jsj 2 log 2 jsj) for convex free energy functions by Eppstein et.al. [1]. A ne free energy functions (i.e. of the form a bn, where n is the size of the loop) allows for O(jsj 2 ) computation time by borrowing a simple method used in sequence alignment [2] Unfortunately the currently used free energy functions for internal loops are not convex, let al..one a ne. ....

....of the form a bn, where n is the size of the loop) allows for O(jsj 2 ) computation time by borrowing a simple method used in sequence alignment [2] Unfortunately the currently used free energy functions for internal loops are not convex, let al..one a ne. Furthermore, the technique described in [1] hinges on the objective being to nd a structure of maximum stability, and thus does not translate to the calculation of the partition function of [9] where a Boltzmann weighted sum of contributions to the partition function is calculated. In this paper we will describe a method based on a ....

[Article contains additional citation context not shown here]

David Eppstein, Zvi Galil, and Raaele Giancarlo. Speeding up dynamic programming. In Proc. 29th Symp. Foundations of Computer Science, pages 488496. Assoc. Comput. Mach., October 1988.

....The most time consuming part of these algorithms is the evaluation of internal loops which in general requires time O(jsj 4 ) where jsj is the length of the RNA sequence for which we want to nd the structures of minimum free energy. This problem has previously been addressed, e.g. in [12] and [1]. These solutions unfortunately do not allow for the complexity of the functions currently used for estimating the stability of internal loops, and therefore a heuristic limiting the size of internal loops evaluated to some cuto size (e.g. 30 as suggested in [4] is usually invoked. In this paper ....

David Eppstein, Zvi Galil, and Raaele Giancarlo. Speeding up dynamic programming. In Proc. 29th Symp. Foundations of Computer Science, pages 488496. Assoc. Comput. Mach., October 1988.

....complexity to O(n 3 ) If the stability of an internal loop can be assumed only to depend on the size of the internal loop (Waterman Smith, 1986) describes how to reduce the time requirement to O(n 3 ) 1 . This is further improved to O(n 2 log 2 n) for convex free energy functions in (Eppstein et al. 1988). Ane free energy functions (i.e. of the form a bN , where N is the size of the loop) allows for O(n 2 ) computation time by borrowing a simple method used in sequence alignment by (Gotoh, 1982) Unfortunately the currently used free energy functions for internal loops are not convex, let ....

....a bN , where N is the size of the loop) allows for O(n 2 ) computation time by borrowing a simple method used in sequence alignment by (Gotoh, 1982) Unfortunately the currently used free energy functions for internal loops are not convex, let al..one ane. Furthermore the technique described in (Eppstein et al. 1988) hinges on the objective being to nd a structure of maximum stability, and thus does not translate to the calculation of the partition function of (McCaskill, 1990) where a Boltzmann weighted sum of contributions to the partition function is calculated. In this paper we will describe a method ....

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Eppstein, D., Galil, Z., & Giancarlo, R. (1988). Speeding up dynamic programming. In: Proc. 29th Symp. Foundations of Computer Science pp. 488-496, Assoc. Comput. Mach.

....the Hanan grid. Near the boundary of the grid, one might be able to assert the existence of more than the four Winograd edges in a minimal Steiner tree. Another possible avenue for algorithmic improvements is suggested by the research of Eppstein et al. into the structure of dynamic programming [13]. We see no direct application of the Eppstein Galil Giancarlo ideas to the Dreyfus Wagner recurrences, but of course this does not prove that such an application does not exist. 4 Data Compression Data compression on our temporary files afforded us notable savings in space and time. Our ....

David Eppstein, Zvi Galil, and Raffaele Giancarlo. Speeding up dynamic programming. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science, October 1988.

....classify most DP formulations as serial monadic, serialpolyadic, nonserial monadic, and nonserial polyadic. This classification, first proposed by Li and Wah [91] is important because it helps in designing parallel formulations for these algorithms. Different formulations of DP have been presented [77, 61, 91, 37, 4, 156, 28]. 2 General Algorithmic Issues in Parallel Formulations This section discusses some of the general aspects related to parallel formulations of an algorithm. Various terms used in subsequent sections are also defined here. Sequential Runtime : The sequential runtime T s is defined as the time ....

....do not fall in any of these classes. Furthermore, this categorization is not strong enough to allow development of generic parallel algorithms for each category. A number of new DP algorithms have been proposed which make use of such problem characteristics as sparsity, convexity and concavity [14, 37, 4, 156, 28]. Parallel formulations of many of these need to be investigated. A number of programming environments have been developed for implementing parallel search. These include DIB [33] Chare Kernel [139] MANIP [151] and PICOS [133] Continued work on these programming environments is of prime ....

D. Eppstein, Z. Ghalil, and R. Giancarlo. Speeding up dynamic programming. In Proceedings of 29th IEEE Symposium on Foundations of Computer Science, pages 488--496, 1988.

....from O(n 3 ) to O(n 2 ) In fact the time for solving the recurrence 13 can also be reduced, to O(n 3 ) as was shown by Waterman and Smith [65] In this paper, the authors also conjectured that the given algorithm runs in O(n 2 ) time for convex (and concave) functions. Eppstein et al. [10] have shown how to compute single loop RNA secondary structure, for convex or concave energy costs, in time O(n 2 log 2 n) For many simple cost functions, such as logarithms and square roots, they show how to improve this time bound to O(n 2 log n log log n) The algorithm obtained by [10] ....

.... [10] have shown how to compute single loop RNA secondary structure, for convex or concave energy costs, in time O(n 2 log 2 n) For many simple cost functions, such as logarithms and square roots, they show how to improve this time bound to O(n 2 log n log log n) The algorithm obtained by [10] is based on a new and fast method for the computation of internal loops for convex or concave energy costs. These results have recently been improved by Aggarwal and Park [2] who gave an O(n 2 log n) algorithm, and further by Larmore and Schieber [33] who gave an O(n 2 ) algorithm for the ....

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David Eppstein, Zvi Galil, and Ra#aele Giancarlo, Speeding Up Dynamic Programming, 29th IEEE Symp. Found. Comput. Sci., 1988, pp. 488--496.

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Eppstein, D., Galil, Z., and Giancarlo, R. Speeding up dynamic programming. Proc. 29th IEEE Symp. Found. Computer Science (1988), 488--496.

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