## Linear-Time Algorithms in Memory Hierarchies (1994)

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Citations: | 2 - 1 self |

### BibTeX

@MISC{Regan94linear-timealgorithms,

author = {Kenneth W. Regan},

title = {Linear-Time Algorithms in Memory Hierarchies},

year = {1994}

}

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### Abstract

This paper studies linear-time algorithms on a hierarchical memory model called Block Move (BM), which extends the Block Transfer (BT) model of Aggarwal, Chandra, and Snir, and which is more stringent than a pipelining model studied recently by Luccio and Pagli. Upper and lower bounds are shown for various data-processing primitives, and some interesting open problems are given. 1 Introduction Recent years have seen marked dissatisfaction with the computational realism of the classic machine models, such as Turing machines or the standard integer RAM (see [13, 12]). Many algorithms that theoretically run in linear time on the RAM scale non-linearly when it comes time to implement them. Cook [5, 6] proposed replacing the usual unit-cost RAM measure by the log-cost criterion, by which an operation that reads an integer i stored at address a is charged log i+log a time units. Aggarwal, Alpern, Chandra, and Snir [1] went further by introducing a parameter ¯ : N ! N called a memory access...

### Citations

4134 |
Introduction to Automata Theory, Languages, and Computation
- Hopcroft, Ullman
- 1979
(Show Context)
Citation Context ...uction S, not just copy, can be applied to the data stream in a block move S [a 1 : : : b 1 ] into [a 2 : : : b 2 ]: Formally S is a deterministic generalized sequential machine (DGSM), as defined in =-=[7]-=-. If z is the string formed by the characters in cells a 1 : : : b 1 , then S(z) is written into the block a 2 : : : b 2 beginning at a 2 . The validity condition for the move is that the intervals [a... |

560 | The Input/Output complexity of sorting and related problems - Aggarwal, Vitter - 1988 |

270 |
Vector Models for Data-Parallel Computing
- BLELLOCH
- 1990
(Show Context)
Citation Context ... operations on lists, can be computed in linears1 -time and O(log n) passes. Moreover, there is a straightforward extension to segmented prefix-sum and other "scan" operations. By results of=-= Blelloch [4]-=- on expressing many other operations in terms of prefix-sum and prefix-max, this is enough to prove that the BM efficiently simulates his integer-based scan model, except that each scan operation take... |

133 |
A model for hierarchical memory
- Aggarwal, Alpern, et al.
- 1987
(Show Context)
Citation Context ...ing the usual unit-cost RAM measure by the log-cost criterion, by which an operation that reads an integer i stored at address a is charged log i+log a time units. Aggarwal, Alpern, Chandra, and Snir =-=[1]-=- went further by introducing a parameters: N ! N called a memory access cost function, such that the above operation costs 1 +(a) time units. Note that this still treats register contents i as having ... |

113 |
Hierarchical memory with block transfer
- Aggarwal, Chandra, et al.
- 1987
(Show Context)
Citation Context ... Besides (a) = log a, they studied the parameterssd (a) = a 1=d , which model the asymptotic latency of memory laid out on a d-dimensional grid. 1 To allow for pipelining, Aggarwal, Chandra, and Snir =-=[2]-=- defined the Block Transfer (BT) model with a special instruction copy [a \Gamma m : : : a] into [b \Gamma m : : : b]; which is charged m + maxf(a); (b) g time units. In the BT, every function that de... |

82 |
Reckhow, Time bounded random access machines
- Cook, A
- 1973
(Show Context)
Citation Context ...els, such as Turing machines or the standard integer RAM (see [13, 12]). Many algorithms that theoretically run in linear time on the RAM scale non-linearly when it comes time to implement them. Cook =-=[5, 6]-=- proposed replacing the usual unit-cost RAM measure by the log-cost criterion, by which an operation that reads an integer i stored at address a is charged log i+log a time units. Aggarwal, Alpern, Ch... |

81 |
Emde Boas, Machine models and simulations
- van
- 1990
(Show Context)
Citation Context ...problems are given. 1 Introduction Recent years have seen marked dissatisfaction with the computational realism of the classic machine models, such as Turing machines or the standard integer RAM (see =-=[13, 12]-=-). Many algorithms that theoretically run in linear time on the RAM scale non-linearly when it comes time to implement them. Cook [5, 6] proposed replacing the usual unit-cost RAM measure by the log-c... |

60 | The Computational Complexity of Universal Hashing
- Mansour, Nisan, et al.
- 1990
(Show Context)
Citation Context ...ine BM program computing such a permutation requires time \Theta(N log N) unders1 , and \Theta(N loglog N) undersd . We suspect, eyeing the time-space tradeoff arguments of Mansour, Nisan, and Tiwari =-=[9]-=-, that this should lead to non-linear lower bounds onsd -time for natural functions such as sorting, string convolutions, FFTs, and universal hashing. This may impact on their conjecture that these fu... |

17 |
Linear time simulation of deterministic two-way pushdown automata
- Cook
- 1971
(Show Context)
Citation Context ...els, such as Turing machines or the standard integer RAM (see [13, 12]). Many algorithms that theoretically run in linear time on the RAM scale non-linearly when it comes time to implement them. Cook =-=[5, 6]-=- proposed replacing the usual unit-cost RAM measure by the log-cost criterion, by which an operation that reads an integer i stored at address a is charged log i+log a time units. Aggarwal, Alpern, Ch... |

5 | Machine models and linear time complexity
- Regan
- 1993
(Show Context)
Citation Context ...der a given cost function , the charge for a block move is m+ (c), where m = jzj = jb 1 \Gamma a 1 j + 1, and c = maxf a 1 ; b 1 ; a 2 ; b 2 g. Several particular machine forms of the BM are given in =-=[10, 11]-=-. As shown in [11], the BM is very robust : Under anysd function (ds1 and rational), these forms all simulate each other up to linear time, not just polynomial time. Even machines allowed to violate t... |

5 |
Linear time and memory efficient computation
- Regan
- 1994
(Show Context)
Citation Context ...der a given cost function , the charge for a block move is m+ (c), where m = jzj = jb 1 \Gamma a 1 j + 1, and c = maxf a 1 ; b 1 ; a 2 ; b 2 g. Several particular machine forms of the BM are given in =-=[10, 11]-=-. As shown in [11], the BM is very robust : Under anysd function (ds1 and rational), these forms all simulate each other up to linear time, not just polynomial time. Even machines allowed to violate t... |

3 |
A model of sequential computation with pipelined access to memory
- Luccio, Pagli
- 1993
(Show Context)
Citation Context ...fsand ff in place of 1=d. 1 \Omega\Gamma n loglog n) undersd (for all d ? 1), and\Omega\Gamma n log n) unders1 [2]. Hence virtually no algorithms can be called linear-time on the BT. Luccio and Pagli =-=[8]-=- argued that the benefits of pipelining need not be limited to individual block-transfers. Their LPM model is a RAM with m = n O(1) registers available on inputs of size n, and O(log m) delay for acce... |