Input sensitive, optimal parallel randomized algorithms for addition and identification. by Paul G. Spirakis

Cover of: Input sensitive, optimal parallel randomized algorithms for addition and identification. | Paul G. Spirakis

Published by Courant Institute of Mathematical Sciences, New York University in New York .

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Pagination15 p.
Number of Pages15
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Open LibraryOL17979362M

Download Input sensitive, optimal parallel randomized algorithms for addition and identification.

Although many sophisticated parallel algorithms now exist, it is not at all clear if any of them is sensitive to properties of the input which can be determined only at run-time.

For example, in the case of parallel addition in shared memory models, we intuitively understand that we should not add those inputs whose value is : P G Spirakis.

OPTIMAL PARALLEL RANDOMIZED ALGORITHMS 2. THE CASE OF PARALLEL ADDITION The Algorithm Let the array M represent the shared memory, Let a > 4 be a positive integer constant. Let each processor P; be equipped with a local variable, TIME;, intended to keep the current parallel step.

Initially, each processor P; (1 Cited by: 6. OPTIMAL PARALLEL RANDOMIZED ALGORITHMS 2. THE CASE OF PARALLEL ADDITION The Algorithm Let the array M represent the shared memory. Let a 2 4 be a positive integer constant.

Let each processor Pi be equipped with a local variable, TIME, intended to keep the current parallel step. Initially, each processor. Optimal parallel randomized algorithms for sparse addition and identification☆. Author links open overlay panel Paul G. Spirakis a b. Show moreCited by: 6.

AbstractAlthough many sophisticated parallel algorithms now exist, most of them are not sensitive to properties of the input which can be determined only at run-time.

For example, in the case of parallel addition in shared memory models, we intuitively understand that we should not add those inputs whose value is by: 6. An Optimal Randomized Parallel Algorithm for Finding Connected Components in a Graph. Related Databases. Web of Science You must be logged in with an active subscription to view this.

() Optimal Randomized EREW PRAM Algorithms for Finding Spanning Forests. Journal of Algorithms Cited by: The previously known output-sensitive work-optimal algorithms for convex hulls have running times Ω(log n) (expected) and Ω(log3 n) in two and three dimensions respectively. • Combining branch and bound algorithms with our scheme to obtain input sensitive, fast in practice, algorithms for any trans-formation, and for point sets in any dimension.

• Showing empirically that there is an optimal size of the base that gives the best runtime, depending on the configuration of the sets. by: arithmetic addition on big-integer numbers are presented. The first algorithm is sequential while the second is parallel.

Both algorithms, unlike existing ones, perform addition on blocks or tokens of 60 bits (18 digits), and thus boosting the execution time by a factor of significance. A fast and efficient parallel algorithm for this problem remains a major goal in the design of parallel graph algorithms.

In this paper, we describe a parallel randomized algorithm for comput-ing single-source shortest paths. Our algorithm achieves a significant speed-up even when only a linear number of processors is available. Randomized Algorithm INPUT OUTPUT ALGORITHM Random Number In addition to the input, the algorithm uses a source of pseudo random numbers.

During execution, it takes random choices depending on those random numbers. The behavior (output) can vary if the algorithm is run multiple times on the same Size: KB. We present deterministic and randomized selection algorithms for parallel disk systems. The algorithms to be presented, in addition to being asymptotically optimal.

CONTENTS vi Approximatenearestneighborsearch Locality-sensitivehashfunctions Constructingan(r1,r 2)-PLEB File Size: 2MB. prehensive introduction to randomized algorithms. PARADIGMSFORRANDOMIZED ALGORITHMS In spite of the multitude of areas in which randomized algorithms find ap-plication, a handful of general the summary in Karp [], we present these principles in the follow-ing.

FoilinganAdversary. Intheclassical. Some randomized algorithms have deterministic time complexity. For example, this implementation of Karger’s algorithm has time complexity as O(E).

Such algorithms are called Monte Carlo Algorithms and are easier to analyse for worst case. On the other hand, time complexity of other randomized algorithms (other than Las Vegas) is dependent on /5.

Optimal randomized parallel algorithms for computing the row maxima of a totally monotone matrix. In Proc. 5th ACM-SIAM Symposium on Discrete Algorithms, pp. –, Google ScholarAuthor: Rajeev Raman. problem, in which lines are only available as input one after another.

It is a randomized algorithm for the EREW PRAM that constructs an arrangement of n lines on-line, so that each insertion is done in optimal O(log n) time using n/ log n processors. Both of our algorithms develop new methods for. Bryson, Joshua T., and Agrawal, Sunil K. "Using Randomized Algorithms to Quantify Uncertainty in the Optimal Design of Cable-Driven Manipulators." Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.

Volume 5A: 39th Mechanisms and Robotics Conference. Boston Author: Joshua T. Bryson, Sunil K. Agrawal. Randomized algorithms for very large matrix problems have received a great deal of attention in recent years.

Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many different research communities. This monograph will provide a detailed overview of recent work on the theory of randomized matrix algorithms as well as Cited by: computer science: randomized algorithms and the probabilistic analysis of algorithms.

Randomized algorithms: Randomized algorithms are algorithms that make random choices during their execution. In practice, a randomized program would use values generated by a random number generator to decide the next step at several branches of its execution.

ForFile Size: KB. Randomized Algorithm INPUT OUTPUT ALGORITHM Random Number Randomized Algorithm In addition to the input, the algorithm uses a source of pseudo random numbers.

During execution, it takes random choices depending on those random numbers. The behavior (output) can vary if the algorithm is run multiple times on the same input. How do we analyze. You may find the text Randomized Algorithms by Motwani and Raghavan to be useful, but it is not required.

Homework policy: There will be a homework assignment every weeks. Collaboration policy: You are encouraged to collaborate on homework.

However, you must write up your own solutions. Randomized Algorithm A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic. The algorithm typically uses uniformly random bits as an auxiliary input to.

rather inefficient parallel algorithms. The design of parallel algorithms and data structures, or even the design of existing algorithms and data structures for par-allelism, require new paradigms and techniques.

These notes attempt to provide a short guided tour of some of the new concepts at a level and scope which make. These factors greatly increase the complexity of algorithm design and challenge traditional ways of thinking about the design of parallel and distributed algorithms.

Here, we review recent work on developing and implementing randomized matrix algorithms in large-scale parallel Cited by: Equivalently, A0 is also optimal.

An algorithm is strongly optimal if it is optimal, and its time T(n) is minimum for all parallel algorithms solving the same problem. For example, assume we have a problem that needs Workseq(n) = O(n) for an optimal single processor algorithm.

If X and Y are two parallel algorithms for this problem and X runs in. A parallel algorithm that is efficient (or optimal) when run using a certain number of processors win remain an efficient (or optimal) parallel algorithm when implemented on a smaller number of processors while running proportionately slower.

A randomized algorithm Ais an algorithm that at each new run receives, in addition to its input i, a new stream/string r of random bits which are then used to specify outcomes of the subsequent random choices (or coin tossing) during the execution of the algorithm. Streams r of random bits are assumed to be independent of the input i for the.

Efficient randomized pattern-matching algorithms by Richard M. Karp Michael 0. Rabin We present randomized algorithms to solve the following string-matching problem and some of its generalizations: Given a string X of length n (the pattern) and a string Y (the text), find theFile Size: 1MB.

Randomized Algorithms A randomized algorithm is an algorithm that incorporates randomness as part of its operation. Often aim for properties like Good average-case behavior.

Getting exact answers with high probability. Getting answers that are close to the right answer. Often find very simple algorithms with dense but clean Size: KB. R.M. Karp 2. Introduction A randomized algorithm is one that receives, in addition to its input data, a stream of random bits that it can use for the purpose of making random choices.

Even for a fixed input, different runs of a randomized algorithm may give different. The randomized incremental approach has been a very useful paradigm for generating simple and efficient algorithms for a variety of problems.

There have been many dozens of papers on the topic (e.g., see the surveys [63, 54]).Much of the early work was in the context of computational geometry, but the approach has also been applied to graph algorithms [20, 24].

such a randomized algorithm is the largest average number of pivots on any problem with the same size. (The maximum is over all problems of this size, and the average is over the internal randomizations performed by the algorithm.) Hence in this approach the algorithm is randomized, and the input.

parallel randomized incremental algorithms can be found in Table 1. Preliminaries We analyze parallel algorithms in the work-depth paradigm [42]. An algorithm proceeds in a sequence of D(depth) rounds, with round idoing w i work in parallel. The total work is therefore W= P D i=1 w i.

We account for the cost of allocating processors and. Cornell University, Spring CS Algorithms Lecture notes on randomized approximation algorithms May 2, 1 Randomized Approximation Algorithms Randomized techniques give rise to some of the simplest and most elegant approximation algo-rithms.

This section gives several examples. A Randomized 2-Approximation for Max-CutFile Size: KB. Unlike the classical algorithms, the scheme of the present paper is a randomized one, and fails with a small proba-bility.

However, one can determine rapidly whether the algorithm has succeeded, using a verification scheme such as that described in Section If the algorithm were to fail, then one could run the algorithm again with an.

RANDOMIZED ALGORITHMS Instructor: Avrim Blum Time: MW Place: Wean A 12 Units, 1 CU Course description: Randomness has proven itself to be a useful resource for developing provably efficient algorithms and protocols.

As a result, the study of randomized algorithms has become a major research topic in recent years. Randomized Algorithms: a randomized algorithm A, input x is fixed, just as usual, from some space I of possible inputs, but the algorithm may draw (and use) random samples y = (y 1, y 2, ) from a given sample space S and probability distribution P any x ∈ I and any y ∈ S, let T(x,y) be the time taken by A on input x when y File Size: 1MB.

Global Min Cuts A cut in a graph G = (V, E) is a way of partitioning V into two sets S and V – denote a cut as the pair (S, V – S).

The size of a cut is the number of edges with one endpoint in S and one endpoint in V – S. These edges are said to cross the cut. A global minimum cut (or just min cut) is a cut with the least total size. Intuitively: removing the edges crossing a min. CMPS Intro. to Algorithms 9 Randomized Algorithm: Insertion Sort • Runtime is independent of input order ([1,2,3,4] may have good or bad runtime, depending on sequence of random numbers) •No assumptions need to be made about input distribution • No one specific input elicits worst-case behaviorFile Size: KB.

A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random bits.

Formally, the algorithm's performance will be a random variable determined by the random bits. Parallel Algorithms UNIT 1 PARALLEL ALGORITHMS Structure Page Nos.

Introduction 5 Objectives 6 The algorithm works for a given input and will terminate in a well defined state. The basic conditions of an algorithm are: input, output, definiteness, effectiveness which have similar upper and lower bounds are known as optimal File Size: KB.Chan T An optimal randomized algorithm for maximum Tukey depth Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, () Hurtado F, Mora M, Ramos P and Seara C () Separability by two lines and by nearly straight polygonal chains, Discrete Applied Mathematics,(), Online publication date: 1.

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