An efficient parallel algorithm for shifting the root of a depth first spanning tree

1986 ◽  
Vol 7 (1) ◽  
pp. 105-119 ◽  
Author(s):  
Prasoon Tiwari
Keyword(s):  
Parallel Algorithm ◽  
Spanning Tree

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.

scholarly journals Listing all spanning trees in Halin graphs — sequential and Parallel view

2018 ◽  
Vol 10 (01) ◽  
pp. 1850005
Author(s):  
K. Krishna Mohan Reddy ◽  
P. Renjith ◽  
N. Sadagopan
Keyword(s):  
Parallel Algorithm ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Combinatorial Problem ◽  
Halin Graph ◽  
Labeled Graph ◽  
Number Of Leaves ◽  
Acyclic Subgraph ◽  
Number Of Spanning Trees ◽  
Halin Graphs

For a connected labeled graph [Formula: see text], a spanning tree [Formula: see text] is a connected and acyclic subgraph that spans all vertices of [Formula: see text]. In this paper, we consider a classical combinatorial problem which is to list all spanning trees of [Formula: see text]. A Halin graph is a graph obtained from a tree with no degree two vertices and by joining all leaves with a cycle. We present a sequential and parallel algorithm to enumerate all spanning trees in Halin graphs. Our approach enumerates without repetitions and we make use of [Formula: see text] processors for parallel algorithmics, where [Formula: see text] and [Formula: see text] are the depth, the number of leaves, respectively, of the Halin graph. We also prove that the number of spanning trees in Halin graphs is [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document