ON FINDING EULER TOURS IN PARALLEL

1993 ◽  
Vol 03 (03) ◽  
pp. 223-231 ◽  
Author(s):  
EDSON N. CACERES ◽  
NARSINGH DEO ◽  
SHIVAKUMAR SASTRY ◽  
JAYME L. SZWARCFITER
Keyword(s):  
Parallel Algorithm ◽  
Spanning Tree ◽  
Intermediate Step ◽  
Euler Tour ◽  
Euler Tours

We describe an alternative implementation of Atallah and Vishkin’s parallel algorithm for finding an Euler Tour of a graph. Instead of finding a spanning tree as an intermediate step, this algorithm is based on identifying a strut which is easier to compute. Using the strut, vertices which have more than one circuit passing through them are identified directly. Stitching at such vertices reduces the number of circuits in the Euler Partition.

A New Efficient Parallel Algorithm for Minimum Spanning Tree

2018 ◽  
Author(s):  
Jucele Franca de Alencar Vasconcellos ◽  
Edson Norberto Caceres ◽  
Henrique Mongelli ◽  
Siang Wun Song
Keyword(s):  
Parallel Algorithm ◽  
Spanning Tree ◽  
Minimum Spanning Tree

PARALLEL REAL-TIME OPTIMIZATION: BEYOND SPEEDUP

1999 ◽  
Vol 09 (04) ◽  
pp. 499-509 ◽  
Author(s):  
SELIM G. AKL ◽  
Stefan D. Bruda
Keyword(s):  
Parallel Algorithm ◽  
Real Time ◽  
Spanning Tree ◽  
Optimization Problems ◽  
Minimum Weight ◽  
Parallel Computer ◽  
Worst Case ◽  
Time Optimization ◽  
Minimum Weight Spanning Tree ◽  
Real Time Optimization

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained sequentially to that of the solution computed in parallel can be arbitrarily large.

AN OPTIMAL RANDOMIZED PARALLEL ALGORITHM FOR THE SINGLE FUNCTION COARSEST PARTITION PROBLEM

1996 ◽  
Vol 06 (02) ◽  
pp. 187-193
Author(s):  
JOSEPH JÁJÁ ◽  
KWAN WOO RYU
Keyword(s):  
Parallel Algorithm ◽  
High Probability ◽  
Rooted Tree ◽  
Partition Problem ◽  
Single Function ◽  
Crew Pram ◽  
Euler Tour ◽  
Crcw Pram

We describe a randomized parallel algorithm to solve the single function coarsest partition problem. The algorithm runs in O( log n) time using O(n) operations with high probability on the Priority CRCW PRAM. The previous best known algorithms run in O( log 2 n) time using O(n log 2 n) operations on the CREW PRAM and O( log n) time using O(n log log n) operations on the Arbitrary CRCW PRAM. The technique presented can be used to generate the Euler tour of a rooted tree optimally from the parent representation.

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