Optimal routing of parentheses on the hypercube

  title={Optimal routing of parentheses on the hypercube},
  author={Ernst W. Mayr and Ralph Werchner},
  journal={J. Parallel Distributed Comput.},
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 certain subclasses of deterministic context-free languages, such as Dyck languages, and to a number of problems dealing with algebraic expressions. 

Figures from this paper

Optimal Tree Contraction on the Hypercube and Related Networks

An optimal tree contraction algorithm for the boolean hypercube and the constant degree hypercubic networks, such as the shuffle exchange or the butterfly network, is presented and the resulting speed-up is optimal due to logarithmic communication overhead.

Optimal Tree Contraction and Term Matching on the Hypercube and Related Networks

The algorithm is based on novel routing techniques and, for certain small subtrees, simulates optimal PRAM algorithms and can be used to solve the term matching problem, one of the fundamental problems in logic programming.

Optimal expression evaluation and term matching on the Boolean hypercube and on hypercubic networks

  • E. MayrRalph Werchner
  • Computer Science
    1994 Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences
  • 1994
An optimal tree contraction algorithm for the Boolean hypercube and constant degree hypercubic networks, such as the shuffle exchange or the butterfly network, is presented and can be shown to be optimal on the hypercube by a corresponding lower bound.

Optimal Implementation of General Divide-and-Conquer on the Hypercube and Related Networks

It is shown how to implement divide- and-conquer algorithms without undue overhead on a wide class of networks, including the shuffle-exchange and the cube-connected-cycles network, and variations of this generic algorithm work for the butterfly network and for the class of hypercubic networks.

Divide-and-Conquer Algorithms on the Hypercube

A new parallel algorithm for the parentheses-matching problem

  • L. BergogneC. Cérin
  • Computer Science
    Proceedings of IEEE International Symposium on Parallel Algorithms Architecture Synthesis
  • 1997
A new parallel algorithm is introduced in this paper to solve the parentheses-matching problem optimally (in O(log/sub 2/ n) parallel time with O(n/log/ sub 2/n) processors) on an EREW-PRAM model.

Optimal Parallel Algorithms for Two Processor Scheduling with Tree Precedence Constraints

Two work optimal parallel algorithms are presented that produce greedy optimal schedules for intrees and outtrees that run in O(log n) time using n/( log n) processors of an EREW PRAM.

Efficient EREW PRAM Algorithms for Parentheses-Matching

Four polylog-time parallel algorithms for matching parentheses on an exclusive-read and exclusive-write (EREW) parallel random-access machine (PRAM) model are presented and provide new insights into the parentheses-matching problem.

An optimal hypercube algorithm for the all nearest smaller values problem

  • D. KravetsC. G. Plaxton
  • Computer Science, Mathematics
    Proceedings of 1994 6th IEEE Symposium on Parallel and Distributed Processing
  • 1994
The authors' ANSV algorithm is used to give the first O(lg n)-time n-processor normal hypercube algorithms for triangulating a monotone polygon and for constructing a Cartesian tree.

All Nearest Smaller Values on the Hypercube

The first normal hypercube ANSV algorithm that is optimal for all values of n and p is presented, and this algorithm is used to give the first O(lg n)-time n-processor normal hyper cube algorithms for triangulating a monotone polygon and for constructing a Cartesian tree.



Fast algorithms for bit-serial routing on a hypercube

The algorithm is adaptive and it is shown that this is necessary to achieve the logarithmic speedup, and generalize the Borodin-Hopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithic degree network requires at least Ω(log2N/log logN) bit steps with high probability for almost all permutations.

A Self-Routing Benes Network and Parallel Permutation Algorithms

A Benes permutation network capable of setting its own switches dynamically and leading to efficient O(log N) parallel algorithms to perform the same class of permutations on cube connected and perfect shuffle computers.

An O(log N) deterministic packet-routing scheme

A deterministic O(log N)-time algorithm for the problem of routing an aribitrary permutation on an N-processor bounded-degree network with bounded buffers is presented and does not use the sorting network of Ajtai, et al.

Deterministic sorting in nearly logarithmic time on the hypercube and related computers

A deterministic sorting algorithm, called Sharesort, is presented that sorts n records on an n -processor hypercube, shuffle-exchange, or cube-connected cycles in O (log n (log log n ) 2 ) time in the worst case.

Divide-and-Conquer Algorithms on the Hypercube

On Self-Routing in Benes and Shuffle-Exchange Networks

The authors present self-routing algorithms for realizing the class of linear permutations in various multistage networks such as Benes and 2n-stage shuffle-exchange and it is shown that the comparison operations can be implemented in bit-serial networks without loss of time.

Universal schemes for parallel communication

This paper shows that there exists an N-processor computer that can simulate arbitrary N- processor parallel computations with only a factor of O(log N) loss of runtime efficiency, and isolates a combinatorial problem that lies at the heart of this question.

Optimal Parallel Recognition of Bracket Languages on Hypercubes

This work investigates the parallel recognition and analysis of bracket languages as a first step towards a parallelly working compiler and designs an appropriate algorithm, which can be executed on hypercubes as well as on related networks with bounded degree.

A logarithmic time sort for linear size networks

A randomized algorithm that sorts on an N node network with constant valence in 0(log N) time and terminates within k within log N time with probability at least 1−N−&agr;.

On the computational equivalence of hypercube-derived networks

It is shown that any computation which can be performed on a butterfly-type network in T steps can be performing on a shuffletype network with the same number of nodes in O(T) steps, and vice versa, which implies that all such hypercube-derived networks are computationally equivalent up to constant factors.