FLOYD, R. W. Permuting information in idealized two-level storage. In Complexity of Computer Calculations (1972), pp. 105--109. R. Miller and J. Thatcher, Eds. Plenum, New York.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....differs from actual hardware, in which a track on disk is usually divided into multiple blocks, but such considerations are easy to deal with effectively. For simplicity in this paper, we also adopt the block track correspondence. The above model generalized the initial work on I O of Floyd [Flo] and Hong and Kung [HoK] Aggarwal and Vitter proved that the average case and worst case number of (disk) Figure 1: A simple D parallel two level memory model. disks) L Figure 2: Model of parallel disks I Os required for sorting is Theta : 1) Their lower bound is based solely on ....

Robert W. Floyd, "Permuting Information in Idealized Two-Level Storage," in Complexity of Computer Computations, R. Miller and J. Thatcher, ed., Plenum, 1972, 105--109.

....= number of processors, where M N , and 1 DB M=2. All sizes are in units of application data items. The PDM cost measure is the number of I O operations required by an algorithm, where DB items can be transferred between the internal memory and the disk system in a single I O operation. Floyd [21] studied sorting (and matrix transpose) in a single disk single processor model, where B = M=2 = Theta(N c ) for some constant c 0, and provided upper and lower I O bounds. Aggarwal and Vitter [2] generalized Floyd s model and provided matching upper and lower I O bounds for several ....

Floyd, R. W. Permuting information in idealized two-level storage. In Complexity of Computer Calculations (1972), pp. 105--109. R. Miller and J. Thatcher, Eds. Plenum, New York.

....for future work. 2 Related work The I O model assumes that most of the data resides on disk and has to be transferred to main memory to do any processing. Because of the tremendous difference in speeds, it ignores the cost of internal processing and counts only the number of I Os. Floyd [15] originally defined a formal model and proved tight bounds on the number of I Os required to transpose a matrix using two pages of internal memory. Hong and Kung [21] extended this model and studied the I O complexity of FFT when the internal memory size is bounded by M . Aggarwal and Vitter [4] ....

R. Floyd. Permuting information in idealized two-level storage. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 105--109. Plenum Press, New York, NY, 1972.

....anybody B. Gates 1 In this chapter we first consider basic paradigms for designing I O efficient algorithms and then address the question of lower bounds in the I O model. Early work on I O complexity concentrated on sorting and sorting related problems. Initial theoretical work was done by Floyd [59] and by Hong and Kung [72] who studied matrix transposition and fast Fourier transformation in restricted I O models. The general I O model was introduced by Aggarwal and Vitter [5] and the notion of parallel disks was introduced by Vitter and Shriver [133] The latter papers also deal with ....

R. W. Floyd. Permuting information in idealized two-level storage. In Complexity of Computer Calculations, pages 105--109, 1972. R. Miller and J. Thatcher, Eds. Plenum, New York.

....on disk, thus necessitating I O as a fundamental, frequently used operation during sorting. One approach to alleviate the effects of the I O bottleneck is to use parallel disk systems [HGK 94, PGK88, Uni89, GS84, Mag87] Aggarwal and Vitter [AV88] generalizing initial work done by Floyd [Flo72] and Hong and Kung [HK81] laid the foundation for I O algorithms by studying the I O complexity of sorting and related problems. The model they studied [AV88] considers an internal memory of size M and I O reads or writes that each result in a transfer of D blocks, where each block is comprised ....

R. W. Floyd. Permuting information in idealized two-level storage. In R. Miller and J. Thatcher, editors, Complexity of Computer Computations, pages 105-- 109. Plenum, 1972.

....on EM issues, and updates it periodically as new results are published. 1.3.1 A Brief Survey We list here selected research in EM with some relevance to the focus of this thesis. Some of the discussion is repeated in subsequent sections which deal with specific external memory topics. Floyd [49] is credited with some of the earliest work towards optimal EM algorithms. He studied matrix transposition and permutation algorithms in a paged memory, with a limited set of basic operations. Aggarwal and Vitter [4] studied sorting on a model which involved a single disk which could read or ....

R. W. Floyd. Permuting information in idealized two-level storage. In Complexity of Computer Calculations, pages 105--109, 1972. R. Miller and J. Thatcher, Eds. Plenum, New York.

....to the point of being unrealistic. The I O model assumes that most of the data resides on disk and has to be transferred to main memory to do any processing. Because of the tremendous difference in speeds, it ignores the cost of internal processing and counts only the number of I Os. Floyd [15] defined a formal model and proved tight bounds on the number of I Os required to transpose a matrix using two internal memory pages. Hong and Kung [24] extended this model and studied the I O complexity of FFT when the internal memory size is bounded by M . Aggarwal and Vitter [3] further ....

....operation as compared to the cost of internal processing. In a single I O, we can tranfer B elements (M # 2 B ) The goal of designing I O algorithms is to minimize the number of I O operations. The problem of transposing a matrix residing in the external memory was addressed as early as Floyd[15], who designed an optimal algorithm for the case where the main memory holds two pages. This was adapted by Aggarwal and Vitter [3] in the external memory model. What happens if we use the simple program of Section 3.1 to transpose in the I O model If N#M (number of elements in a row column ....

[Article contains additional citation context not shown here]

R. Floyd. Permuting information in idealized two-level storage. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 105--109. Plenum Press, New York, NY, 1972.

.... into multiple levels of storage with significantly different access times (e.g. registers, cache, memory, disk, tape) In an effort to properly capture this phenomenon, a variety of sequential models of multi level storage (often referred to as memory hierarchy models) have been proposed [1, 2, 3, 4, 12]. For example, one simple model assumes that accessing memory location i costs lg i units of time [1] More elaborate models tend to allow special block operations, or to define discontinuous access functions [2, 4] For each particular model of multi level storage, it is natural to analyze the ....

R. W. Floyd. Permuting information in idealized two-level storage. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 105--109. Plenum Press, New York, 1972.

....anybody B. Gates 1 In this chapter we first consider basic paradigms for designing I O e#cient algorithms and then address the question of lower bounds in the I O model. Early work on I O complexity concentrated on sorting and sorting related problems. Initial theoretical work was done by Floyd [59] and by Hong and Kung [72] who studied matrix transposition and fast Fourier transformation in restricted I O models. The general I O model was introduced by Aggarwal and Vitter [5] and the notion of parallel disks was introduced by Vitter and Shriver [133] The latter papers also deal with ....

R. W. Floyd. Permuting information in idealized two-level storage. In Complexity of Computer Calculations, pages 105--109, 1972. R. Miller and J. Thatcher, Eds. Plenum, New York.

....to the point of being unrealistic. The I O model assumes that most of the data resides on disk and has to be transferred to main memory to do any processing. Because of the tremendous difference in speeds, it ignores the cost of internal processing and counts only the number of I Os. Floyd [15] defined a formal model and proved tight bounds on the number of I Os required to transpose a matrix using two internal memory pages. Hong and Kung [24] extended this model and studied the I O complexity of FFT when the internal memory size is bounded by M . Aggarwal and Vitter [3] further refined ....

....I O operation as compared to the cost of internal processing. In a single I O, we can tranfer B elements (M 2B) The goal of designing I O algorithms is to minimize the number of I O operations. The problem of transposing a matrix residing in the external memory was addressed as early as Floyd[15], who designed an optimal algorithm for the case where the main memory holds two pages. This was adapted by Aggarwal and Vitter [3] in the external memory model. What happens if we use the simple program of Section 3.1 to transpose in the I O model If N M (number of elements in a row column ....

[Article contains additional citation context not shown here]

R. Floyd. Permuting information in idealized two-level storage. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 105--109. Plenum Press, New York, NY, 1972.

....disk subsystem, but the model applies equally well to a fast cache vs. main memory, a disk vs. tape archives, or in VLSI, on chip vs. off chip memory. Floyd considered an idealized two level storage where the slow memory was separated into pages of size p, and looked at the problem of permuting [Flo]. In the two level memory hierarchy, the data elements reside initially in the external memory and the goal of the computation is to write the answer to the problem back into external memory. In order for the algorithm to use any data element, however, it must move it into internal memory, ....

....on developing specialpurpose algorithms that are optimal for the problem and architecture. There is a long history of developing special purpose algorithms with a view towards I O efficiency. As mentioned above, Floyd considered an algorithm for permuting on two level memory hierarchies [Flo]. Knuth has 132 pages devoted to the I O efficiency of sorting, all but 17 of which deal with the problems of using tapes [Knu] Even considered the problem of sorting using parallel tapes with parallel processors [Eve] but his algorithms are hampered a bit by the fact that he assumes that each ....

[Article contains additional citation context not shown here]

Robert W. Floyd, "Permuting Information in Idealized Two-Level Storage," in Complexity of Computer Computations , R. Miller and J. Thatcher, ed., Plenum, 1972, 105--109.

....for future work. 2 Related work The I O model assumes that most of the data resides on disk and has to be transferred to main memory to do any processing. Because of the tremendous difference in speeds, it ignores the cost of internal processing and counts only the number of I Os. Floyd [13] defined a formal model and proved tight bounds on the number of I Os required to transpose a matrix using two internal memory pages. Hong and Kung [19] extended this model and studied the I O complexity of FFT when the internal memory size is bounded by M . Aggarwal and Vitter [4] further ....

R. Floyd. Permuting information in idealized two-level storage. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 105--109. Plenum Press, New York, NY, 1972.

....be stored on disk, thus necessitating I O as a fundamental, frequently used operation during sorting. One way to alleviate the e#ects of the I O bottleneck is to use parallel disk systems [HGK 94, PGK88, Uni89, GS84, Mag87] Aggarwal and Vitter [AV88] generalizing initial work done by Floyd [Flo72] and Hong and Kung [HK81] laid the foundation for I O algorithms by studying the I O complexity of sorting and related problems. The model they studied [AV88] considers an internal memory of size M and I O reads or writes that each result in a transfer of D blocks, where each block is comprised ....

R. W. Floyd. Permuting information in idealized two-level storage. In R. Miller and J. Thatcher, editors, Complexity of Computer Computations, pages 105-- 109. Plenum, 1972.

....improves the bandwidth between secondary memory and main memory, ffl exploiting locality of reference via organization of the data and processing sequence, ffl overlapping I O with computation, e.g. using prefetching. Some of the earliest work in external memory algorithms was done by Floyd [13] and Hong and Kong [16] who studied matrix operations and fast Fourier transforms. Lower bounds for a number of problems related to sorting were presented by Aggarwal and Vitter [1] The classical I O model was introduced by Vitter and Shriver [28] The uniprocessor, single disk version of this ....

R. W. Floyd. Permuting information in idealized two-level storage. In Complexity of Computer Calculations, pages 105--109, 1972. R. Miller and J. Thatcher, Eds. Plenum, New York.

....inputing the entire additional external memory. A natural assumption about the additional external memory is that it can only be used to store duplicate entries of the original matrix. For example, this assumption has been used either explicitly or implicitly for I O complexity lower bounds in [Flo72], AV88] CGG 95] and others. Using this assumption, we give the following easy lower bound for this problem. Let M (n) be the set of entries of the matrix that are stored in the additional external memory. There must exist some column of the matrix for which less than T n entries are in M ....

R. Floyd. Permuting Information in Idealized Two-Level Storage. In Complexity of Computer Calculations, R. Miller and J. Thatcher, ed., Plenum, pp. 105 - 109, 1972.

....used only once) so models (such as the Red Blue pebble game [HK81] that ignore the spatial structure of memory don t provide any insight. However, a two level model becomes relevant when there is an added restriction that only contiguous blocks of data can be moved between the two levels. Floyd [F72] shows that if the small memory can hold only two blocks, each of size B elements, and B min(N 1 ; N 2 ) then transposing a N 1 ThetaN 2 array requires exactly 2(N=B) lg(B) block moves between the two level, where N = N 1 N 2 . Aggarwal and Vitter [AV88] extend this result to show that if the ....

Floyd, R. W., "Permuting Information in Idealized Two-Level Storage," Complexity of Computer Computations, Plenum Press, New York, 1972, pp. 105-109.

....be stored on disk, thus necessitating I O as a fundamental, frequently used operation during sorting. One way to alleviate the effects of the I O bottleneck is to use parallel disk systems [HGK 94, PGK88, Uni89, GS84, Mag87] Aggarwal and Vitter [AV88] generalizing initial work done by Floyd [Flo72] and Hong and Kung [HK81] laid the foundation for I O algorithms by studying the I O complexity of sorting and related problems. The model they studied [AV88] considers an internal memory of size M and I O reads or writes that each result in a transfer of D blocks, where each block is comprised ....

R. W. Floyd. Permuting information in idealized two-level storage. In R. Miller and J. Thatcher, editors, Complexity of Computer Computations, pages 105-- 109. Plenum, 1972.

....fraction of its data references within whatever portion of the cpu cache is available to the running process. A theory of computational reordering is emerging: there is a body of previous work on ordering matrix multiplications, Fourier transformations and sorting algorithms for locality [14, 18, 2, 3, 4, 6, 29, 30]. However, no one has previously studied iterations over three way partitions of sets. Such partitions are encountered in other forms of dynamic programming, so our recursive control structure may well be useful in other combinatorial problems. Someday, perhaps, the problem of ordering a set of ....

R. W. Floyd. Permuting information in idealized two-level storage. In R. Miller and J. Thatcher, editors, Complexity of Computer Calculations, pages 105--109. Plenum, 1972.

No context found.

FLOYD, R. W. Permuting information in idealized two-level storage. In Complexity of Computer Calculations (1972), pp. 105--109. R. Miller and J. Thatcher, Eds. Plenum, New York.

No context found.

FLOYD, R. W. Permuting information in idealized two-level storage. In Complexity of Computer Calculations (1972), pp. 105--109. R. Miller and J. Thatcher, Eds. Plenum, New York.

No context found.

FLOYD, R. W. Permuting information in idealized two-level storage. In Complexity of Computer Calculations (1972), pp. 105--109. R. Miller and J. Thatcher, Eds. Plenum, New York.

No context found.

R. W. Floyd. Permuting information in idealized two-level storage. In Complexity of Computer Calculations, pages 105--109 (R. Miller and J. Thatcher, Eds.). Plenum, New York, 1972.

No context found.

FLOYD, R. W. Permuting information in idealized two-level storage. In Complexity of Computer Calculations (1972), pp. 105--109. R. Miller and J. Thatcher, Eds. Plenum, New York.

No context found.

R. Floyd. Permuting information in idealized two-level storage. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 105--109. Plenum Press, New York, NY, 1972.

No context found.

FLOYD, R. W. Permuting information in idealized two-level storage. In Complexity of Computer Calculations (1972), pp. 105--109. R. Miller and J. Thatcher, Eds. Plenum, New York.

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