Optimal parallel 3-colouring algorithm for rooted trees and its application

Rajčáni, Peter

doi:10.1007/3-540-53414-8_43

Aspects and Prospects of Theoretical Computer Science

1990

DOI: 10.1007/3-540-53414-8_43

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Optimal parallel 3-colouring algorithm for rooted trees and its application

Peter Rajčáni

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2000

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“…optimal parallel sublogarithmic time algorithm for 3-colouring have been successful only for rooted forests with a constant maximum degree [22], [23]. The algorithm of [22] takes O(log n/log log n) time on a CREW PRAM; the time bound was improved to O(log (k) n) on an Exclusive Read Exclusive Write (EREW) PRAM in [23].…”

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Optimal Sublogarithmic Time Parallel Algorithms on Rooted Forests

Sajith

Saxena

2000

Algorithmica

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The problem of finding a sublogarithmic time optimal parallel algorithm for 3-colouring rooted forests has been open for long. We settle this problem by obtaining an O((log log n) log * (log * n)) time optimal parallel algorithm on a TOLERANT Concurrent Read Concurrent Write (CRCW) Parallel Random Access Machine (PRAM).Furthermore, we show that if f (n) is the running time of the best known algorithm for 3-colouring a rooted forest on a COMMON or TOLERANT CRCW PRAM, a fractional independent set of the rooted forest can be found in O( f (n)) time with the same number of processors, on the same model.Using these results, it is shown that decomposable top-down algebraic computation and, hence, depth computation (ranking), 2-colouring and prefix summation on rooted forests can be done in O(log n) optimal time on a TOLERANT CRCW PRAM.These algorithms have been obtained by proving a result of independent interest, one concerning the self-simulation property of TOLERANT: an N -processor TOLERANT CRCW PRAM that uses an address space of size O(N ) only, can be simulated on an n-processor TOLERANT PRAM in O(N /n) time, with no asymptotic increase in space or cost, when n = O(N/log log N ).

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“…The algorithm of [22] takes O(log n/log log n) time on a CREW PRAM; the time bound was improved to O(log (k) n) on an Exclusive Read Exclusive Write (EREW) PRAM in [23]. In this paper we present an O((log log n) log * (log * n)) time optimal algorithm on the TOLERANT Concurrent Read Concurrent Write (CRCW) PRAM, for 3-colouring general rooted forests.…”

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confidence: 99%

Optimal Sublogarithmic Time Parallel Algorithms on Rooted Forests

Sajith

Saxena

2000

Algorithmica

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Optimal parallel 3-colouring algorithm for rooted trees and its application

Cited by 1 publication

References 11 publications

Optimal Sublogarithmic Time Parallel Algorithms on Rooted Forests

Optimal Sublogarithmic Time Parallel Algorithms on Rooted Forests

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