O(log*n) algorithms on a Sum-CRCW PRAM

We show that the Largest Empty Rectangle problem can be solved by reducing it, in a natural way, to the All Nearest Smaller Values problem. We provide two classes of algorithms: the first one assumes that the input points are available sorted by x (resp. y) coordinate. Our algorithm corresponding to this case runs in O(log log n) time using [Formula: see text] processors in the Common-CRCW-PRAM model. For unsorted input, we present algorithms that run in [Formula: see text] time using [Formula: see text] processors in the Common-CRCW-PRAM, or in O( log n) time using [Formula: see text] processors in the EREW-PRAM model. No sub-logarithmic time parallel algorithms have been previously reported for this problem.

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Implementing Arbitrary/Common Concurrent Writes of CRCW PRAM

10.1145/3458744.3474041 ◽

2021 ◽

Author(s):

Fady Ghanim ◽

Wael R Elwasif ◽

David E Bernholdt

Keyword(s):

Crcw Pram

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OPTIMAL PARALLEL SUPERPRIMITIVITY TESTING FOR SQUARE ARRAYS

Parallel Processing Letters ◽

10.1142/s0129626496000297 ◽

1996 ◽

Vol 06 (03) ◽

pp. 299-308 ◽

Cited By ~ 4

Author(s):

COSTAS S. ILIOPOULOS ◽

MAUREEN KORDA

Keyword(s):

Time Algorithm ◽

Square Array ◽

Crcw Pram

We present an optimal O( log log n) time algorithm on the CRCW PRAM which tests whether a square array, A, of size n×n, is superprimitive. If A is not superprimitive, the algorithm returns the quasiperiod, i.e., the smallest square array that covers A.

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A SIMPLE PARALLEL ALGORITHM FOR THE SINGLE FUNCTION COARSEST PARTITION PROBLEM

Parallel Processing Letters ◽

10.1142/s0129626494000405 ◽

1994 ◽

Vol 04 (04) ◽

pp. 437-445 ◽

Cited By ~ 1

Author(s):

CLIVE N. GALLEY ◽

COSTAS S. ILIOPOULOS

Keyword(s):

Parallel Algorithm ◽

Parallel Computation ◽

Simple Algorithm ◽

Partition Problem ◽

Pram Model ◽

Single Function ◽

Crcw Pram

This paper shows a simple algorithm for solving the single function coarsest partition problem on the CRCW PRAM model of parallel computation using O(n) processors in O( log n) time with O(n1+ε) space.

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SEQUENTIAL AND PARALLEL ALGORITHMS FOR THE k CLOSEST PAIRS PROBLEM

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195995000167 ◽

1995 ◽

Vol 05 (03) ◽

pp. 273-288 ◽

Cited By ~ 13

Author(s):

HANS-PETER LENHOF ◽

MICHIEL SMID

Keyword(s):

Decision Tree ◽

Parallel Algorithms ◽

Dimensional Space ◽

Decision Tree Model ◽

Sequential Algorithm ◽

Tree Model ◽

Parallel Time ◽

Parallel Version ◽

Pram Model ◽

Crcw Pram

Let S be a set of n points in D-dimensional space, where D is a constant, and let k be an integer between 1 and [Formula: see text]. A new and simpler proof is given of Salowe’s theorem, i.e., a sequential algorithm is given that computes the k closest pairs in the set S in O(n log n+k) time, using O(n+k) space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal. Salowe’s algorithm seems difficult to parallelize. A parallel version of our algorithm is given for the CRCW-PRAM model. This version runs in O((log n)2 log log n) expected parallel time and has an O(n log n log log n+k) time-processor product. Finally, actual running times are given of an implementation of our sequential algorithm.

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ON PARALLEL PREFIX COMPUTATION

Parallel Processing Letters ◽

10.1142/s0129626494000399 ◽

1994 ◽

Vol 04 (04) ◽

pp. 429-436 ◽

Cited By ~ 4

Author(s):

SANJEEV SAXENA ◽

P.C.P. BHATT ◽

V.C. PRASAD

Keyword(s):

Linear Time ◽

Time Algorithm ◽

Optimal Time ◽

Word Size ◽

Parallel Prefix ◽

Parallel Merge ◽

Merge Sort ◽

Sort Algorithm ◽

Crcw Pram ◽

Prefix Sums

We prove that prefix sums of n integers of at most b bits can be found on a COMMON CRCW PRAM in [Formula: see text] time with a linear time-processor product. The algorithm is optimally fast, for any polynomial number of processors. In particular, if [Formula: see text] the time taken is [Formula: see text]. This is a generalisation of previous result. The previous [Formula: see text] time algorithm was valid only for O(log n)-bit numbers. Application of this algorithm to r-way parallel merge sort algorithm is also considered. We also consider a more realistic PRAM variant, in which the word size, m, may be smaller than b (m≥log n). On this model, prefix sums can be found in [Formula: see text] optimal time.

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Achieving optimal CRCW PRAM fault-tolerance

Information Processing Letters ◽

10.1016/0020-0190(91)90156-c ◽

1991 ◽

Vol 39 (2) ◽

pp. 59-66 ◽

Cited By ~ 16

Author(s):

Alex A. Shvartsman

Keyword(s):

Fault Tolerance ◽

Crcw Pram

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Simple and Work-Efficient Parallel Algorithms for the Minimum Spanning Tree Problem

Parallel Processing Letters ◽

10.1142/s012962649700005x ◽

1997 ◽

Vol 07 (01) ◽

pp. 25-37 ◽

Cited By ~ 4

Author(s):

Christos D. Zaroliagis

Keyword(s):

Parallel Algorithms ◽

Spanning Tree ◽

Minimum Spanning Tree ◽

Erew Pram ◽

Minimum Spanning Tree Problem ◽

Crcw Pram

Two Simple and work-efficient parallel algorithms for the minimum spanning tree problem are presented. Both algorithms perform O(m log n) work. The first algorithm runs in O( log 2 n) time on an EREW PRAM, while the second algorithm runs in O( log n) time on a COMMON CRCW PRAM.

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