## Optimal Routing of Parentheses on the Hypercube (1994)

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Venue: | IN PROCEEDINGS OF THE SYMPOSIUM ON PARALLEL ARCHITECTURES AND ALGORITHMS |

Citations: | 14 - 6 self |

### BibTeX

@INPROCEEDINGS{Mayr94optimalrouting,

author = {Ernst W. Mayr and Ralph Werchner},

title = {Optimal Routing of Parentheses on the Hypercube},

booktitle = {IN PROCEEDINGS OF THE SYMPOSIUM ON PARALLEL ARCHITECTURES AND ALGORITHMS},

year = {1994},

pages = {109--117},

publisher = {}

}

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### Abstract

We consider a new class of routing requests or partial permutations for which we give optimal on-line routing algorithms on the hypercube and shuffle-exchange network. For well-formed words of parentheses our algorithm establishes communication between all matching pairs in logarithmic time. It can be applied to the membership problem for Dyck languages and a number of problems for algebraic expressions.

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Citation Context ...s the problem of routing data between specified processors. For some constant degree networks with special expansion properties, the problem of routing a permutation can be solved in logarithmic time =-=[AKS83]-=- and [L85],[U89]. For the more feasible networks such as the hypercube, shuffle-exchange or cube-connected-cycle networks, it is also possible to route every single permutation in logarithmic time (gi... |

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Citation Context ...r there is a deterministic algorithm for routing an arbitrary permutation in logarithmic time, given for each item its destination address. The best known deterministic routing algorithm is Sharesort =-=[CP90]-=- with a running time of O(log p(log log p) 2 ). A possible practical solution for the routing problem are randomized routing algorithms [ALMN90],[HLN89],[LP90],[RV83],[VB81] achieving logarithmic runn... |

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Citation Context ...e best known deterministic routing algorithm is Sharesort [CP90] with a running time of O(log p(log log p) 2 ). A possible practical solution for the routing problem are randomized routing algorithms =-=[ALMN90]-=-,[HLN89],[LP90],[RV83],[VB81] achieving logarithmic running time with high propability. In some cases, the required routings are known to belong to a special class of routings that can be performed mo... |

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Citation Context .... It is also known how an algebraic expression containing the operands +; \Gamma; \Delta; = given in tree form can be evaluated work-optimally in logarithmic time on an EREW PRAM [GMT88]. As noted in =-=[GR86]-=-, this dynamic expression evaluation problem can be used to solve the recognition problem for bracket and input-driven languages. These are the most complicated subclasses of DCFL known to be recogniz... |

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Citation Context ... technique of parentheses matching, it is also possible to efficiently compute a tree representation from a partially parenthesized expression containing different operators (with a precedence order) =-=[BV85]-=-. The tree representation essentially is the expression with all the parentheses resulting from the precedence order and right or left associativity of operators inserted. The importance of this repre... |

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Citation Context ...he precedence order and right or left associativity of operators inserted. The importance of this representation as well as its postfix and prefix form for parsing and compiling has been discussed in =-=[DS83]-=-. It is also known how an algebraic expression containing the operands +; \Gamma; \Delta; = given in tree form can be evaluated work-optimally in logarithmic time on an EREW PRAM [GMT88]. As noted in ... |

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Citation Context ...n discussed in [DS83]. It is also known how an algebraic expression containing the operands +; \Gamma; \Delta; = given in tree form can be evaluated work-optimally in logarithmic time on an EREW PRAM =-=[GMT88]-=-. As noted in [GR86], this dynamic expression evaluation problem can be used to solve the recognition problem for bracket and input-driven languages. These are the most complicated subclasses of DCFL ... |

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1 | On the recognition of context free languages - Rytter |