## Versatile Access to Parallel Memory Systems

Venue: | Proc. of 1998 Wkshp. on Distributed Data and Structures |

Citations: | 2 - 2 self |

### BibTeX

@INPROCEEDINGS{Scarano_versatileaccess,

author = {Vittorio Scarano},

title = {Versatile Access to Parallel Memory Systems},

booktitle = {Proc. of 1998 Wkshp. on Distributed Data and Structures},

year = {},

publisher = {Press,1998}

}

### OpenURL

### Abstract

In this paper, we present a survey of results about the problem of mapping the N items of a data structure on M memory modules so that items can be accessed in parallel by templates i.e. distinct sets of nodes. In particular, we present some results that allow to access several different templates at once, i.e. we focus on versatile mapping algorithms (for a comprehensive survey of other related results see [14] in this volume). In particular, we present some of the algorithms in literature for accessing arrays (by rows, columns, diagonals and subarrays) and trees (accessed by subtrees, root-to-leaf paths, levels and compositions thereof). 1 Introduction In this paper we present a survey of results related to the problem of mapping a data structure to M memory modules when it is known how the access is required i.e. templates of memory access are known. The problem is to minimize the conflicts on the memory modules, i.e. simultaneous access to the same module to retrieve different dat...

### Citations

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(Show Context)
Citation Context ... not only conflictfree) algorithms, we can notice that the algorithm provides also optimal access to s \Theta dn=se blocks (in the example, all the 3 \Theta 3 blocks have 1 conflict). In 1975, Lawrie =-=[23]-=- proposed a similar algorithm for conflict-free access to lines and major and minor diagonals. The scheme, unfortunately, requires 2n memory modules to access only n items at the time and the number o... |

81 |
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(Show Context)
Citation Context ...determining mapping algorithms that extend the versatility of latin squares by accessing conflict-free also other templates like blocks and diagonals. Linear skewing schemes. In 1971, Budnik and Kuck =-=[6]-=- proposed a first extension to latin squares by proposing to map item (i; j) of the n \Theta n array on memory module i \Delta s + j(mod n) for some shift s. This mapping is often called a linear skew... |

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Citation Context ...ls can have as many nodes as (N +1)=2 while root-to-leaf paths all have the same size, i.e., log(N + 1). Some approaches model the access similarly to the so-called finger updates as in [2] (see also =-=[3, 21, 22, 26]-=-), where a pointer (or finger) to a leader node is given as input to access a template is and, from that node, an S-size instance (for any S) of the template is retrieved. Often the size is fixed to b... |

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24 |
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Citation Context ..., they show that more than one-seventh of the memory modules are idle when any mapping is used that is conflict-free for lines and r \Theta s and s \Theta r subarrays. In 1993, Kim and Prasanna-Kumar =-=[25]-=- propose perfect latin squares that allow also conflict-free access to major and minor diagonals and main squares i.e. p n \Theta p n blocks where the top-left item (i; j) is such that Versatile Acces... |

21 |
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Citation Context ...ls can have as many nodes as (N +1)=2 while root-to-leaf paths all have the same size, i.e., log(N + 1). Some approaches model the access similarly to the so-called finger updates as in [2] (see also =-=[3, 21, 22, 26]-=-), where a pointer (or finger) to a leader node is given as input to access a template is and, from that node, an S-size instance (for any S) of the template is retrieved. Often the size is fixed to b... |

10 |
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Citation Context ...and the latin square, several improvements were made in the versatility of the algorithms, namely in considering conflict-free access for many blocks and for diagonals. In 1992, Colbourn and Heinrich =-=[7] proposed -=-algorithms for conflictfree access to lines and arbitrary subarrays, i.e., for r ? s, r \Theta s and s \Theta r subarrays. They also proposed also an interesting "reverse" question: how larg... |

10 | Optimal and Load Balanced Mapping of Parallel Priority Queues in Hypercubes - Das, Pinotti, et al. - 1996 |

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Citation Context ...ls can have as many nodes as (N +1)=2 while root-to-leaf paths all have the same size, i.e., log(N + 1). Some approaches model the access similarly to the so-called finger updates as in [2] (see also =-=[3, 21, 22, 26]-=-), where a pointer (or finger) to a leader node is given as input to access a template is and, from that node, an S-size instance (for any S) of the template is retrieved. Often the size is fixed to b... |

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7 |
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Citation Context ...r Trees Mapping tree data structures in parallel memory systems has not received much attention if one compares the wide range and timespan of results about arrays with respect to results about trees =-=[5, 8, 16, 17, 18, 20, 27]-=-. Moreover, given the particular structure of templates (like, e.g., subtrees and levels) the versatility of mapping algorithms is more difficult (in general) to achieve. Lower Bounds. We begin by sho... |

6 | Multiple Template Access of Trees in Parallel Memory Systems
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Citation Context ...eover, given the particular structure of templates (like, e.g., subtrees and levels) the versatility of mapping algorithms is more difficult (in general) to achieve. Lower Bounds. We begin by showing =-=[1]-=- that it is not possible, in general to achieve conflic-free algorithms for subtrees and paths. In a sense, it is p[ossible to prove that the two tempatels are strictly non homogeneous, i.e. that effi... |

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Citation Context ...r Trees Mapping tree data structures in parallel memory systems has not received much attention if one compares the wide range and timespan of results about arrays with respect to results about trees =-=[5, 8, 16, 17, 18, 20, 27]-=-. Moreover, given the particular structure of templates (like, e.g., subtrees and levels) the versatility of mapping algorithms is more difficult (in general) to achieve. Lower Bounds. We begin by sho... |

4 | Towards Universal Mapping Algorithms for Accessing Trees
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(Show Context)
Citation Context .... To wit, levels can have as many nodes as (N +1)=2 while root-to-leaf paths all have the same size, i.e., log(N + 1). Some approaches model the access similarly to the so-called finger updates as in =-=[2]-=- (see also [3, 21, 22, 26]), where a pointer (or finger) to a leader node is given as input to access a template is and, from that node, an S-size instance (for any S) of the template is retrieved. Of... |

4 | Conflict-free Path Access of Trees in Parallel Memory Systems with Application to Distributed Heap Implementation - Das, Pinotti - 1995 |

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2 |
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Citation Context ...r Trees Mapping tree data structures in parallel memory systems has not received much attention if one compares the wide range and timespan of results about arrays with respect to results about trees =-=[5, 8, 16, 17, 18, 20, 27]-=-. Moreover, given the particular structure of templates (like, e.g., subtrees and levels) the versatility of mapping algorithms is more difficult (in general) to achieve. Lower Bounds. We begin by sho... |

1 |
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Citation Context ...s between PEs and the memory modules. They proved that their mapping scheme resulted in a well-known permutation called linear-complement permutation that was realized by a self-routing Benes network =-=[4]-=-. Quasigroups. In 1994, Das and Sarkar [16] proposed a novel approach by studying the multiplication table of a quasi-group (also called groupoids). A quasigroup is a a set S with a binary operation w... |

1 |
Distributed Data Access in Tree-Like Structures and Multidimensional Vector Spaces -- A Survey", this volume
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(Show Context)
Citation Context ...In particular, we present some results that allow to access several different templates at once, i.e. we focus on versatile mapping algorithms (for a comprehensive survey of other related results see =-=[14]-=- in this volume). In particular, we present some of the algorithms in literature for accessing arrays (by rows, columns, diagonals and subarrays) and trees (accessed by subtrees, root-to-leaf paths, l... |

1 |
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Citation Context ...resented also offer costant load. An early start: Latin Squares. Research in this field dates back to more than two centuries 1 since the definition of latin square of order n, given by Euler in 1778 =-=[19]-=-, as an n \Theta n square array of symbols from the set f1; 2; : : :; ng arranged so that each symbol appears exactly once in each row and each column. If integer m is assigned to position i; j in a l... |

1 |
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1 |
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