THREE TECHNIQUES FOR PARALLEL MAINTENANCE OF A MINIMUM SPANNING TREE UNDER BATCH OF UPDATES

1996 ◽  
Vol 06 (02) ◽  
pp. 213-222 ◽  
Author(s):  
PAOLO FERRAGINA ◽  
FABRIZIO LUCCIO
Keyword(s):  
Data Structure ◽  
Parallel Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Undirected Graph ◽  
Batch Size ◽  
Insertions And Deletions ◽  
Erew Pram ◽  
Pram Model ◽  
Proper Values

In this paper we provide three simple techniques to maintain in parallel the minimum spanning tree of an undirected graph under single or batch of edge updates (i.e., insertions and deletions). Our results extend the use of the sparsification data structure to the EREW PRAM model. For proper values of the batch size, our algorithms require less time and work than the best known dynamic parallel algorithms.

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

1997 ◽  
Vol 07 (01) ◽  
pp. 25-37 ◽  
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.

AN EREW PARM ALGORITHM FOR UPDATING MINIMUM SPANNING TREES

1999 ◽  
Vol 09 (01) ◽  
pp. 111-122 ◽  
Author(s):  
SAJAL K. DAS ◽  
PAOLO FERRAGINA
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Undirected Graph ◽  
Substantial Improvement ◽  
Minimum Spanning Trees ◽  
Single Edge ◽  
Sequential Approach ◽  
Work Complexity

We propose a parallel algorithm for the EREW PRAW model that maintains a minimum spanning tree (MST) of an undirected graph under single edge insertions and deletions. For a graph of n nodes and m edges, each update requires O( log n) time and O(m 2/3 log n) work. This is a substantial improvement over the known bounds on the work complexity. Our algorithm uses a partition of the MST, similar to the sequential approach due to Frederickson [6], and also employs a novel data structure for efficiently managing edge insertions in parallel.

SUB-LOGARITHMIC ALGORITHMS FOR THE LARGEST EMPTY RECTANGLE PROBLEM

1993 ◽  
Vol 03 (01) ◽  
pp. 79-85
Author(s):  
STEPHAN OLARIU ◽  
WENHUI SHEN ◽  
LARRY WILSON
Keyword(s):  
Parallel Algorithms ◽  
Erew Pram ◽  
Pram Model ◽  
The Common ◽  
Crcw Pram ◽  
Natural Way

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.

An optimal EREW PRAM algorithm for minimum spanning tree verification

1997 ◽  
Vol 62 (3) ◽  
pp. 153-159 ◽  
Author(s):  
Valerie King ◽  
Chung Keung Poon ◽  
Vijaya Ramachandran ◽  
Santanu Sinha
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Erew Pram ◽  
Minimum Spanning Tree Verification

ON FINDING A HAMILTONIAN PATH IN A TOURNAMENT USING SEMI-HEAP

2000 ◽  
Vol 10 (04) ◽  
pp. 279-294
Author(s):  
JIE WU
Keyword(s):  
Data Structure ◽  
Parallel Algorithm ◽  
Ordered Set ◽  
Hamiltonian Path ◽  
Linear Ordering ◽  
Sorting Algorithm ◽  
Ranking System ◽  
Special Linear ◽  
Erew Pram ◽  
Pram Model

The problem of sorting an intransitive total ordered set, a generalization of regular sorting, is considered. This generalized sorting is based on the fact that there exists a special linear ordering (also called a generalized sorted sequence) for any intransitive total ordered set, or equivalently, the existence of a Hamiltonian path in a tournament. A new data structure called semi-heap is proposed to construct an optimal Θ(n log n) sorting algorithm. We also provide a cost-optimal parallel algorithm using semi-heap. The run time of this algorithm is Θ(n) with Θ( log n) processors under the EREW PRAM model. The use of a Hamiltonian path (generalized sorting sequence) as an approximation of a ranking system in a tournament is also discussed.

Board Game Supporting Learning Prim’s Algorithm and Dijkstra’s Algorithm

2012 ◽  
pp. 256-270
Author(s):  
Wen-Chih Chang ◽  
Te-Hua Wang ◽  
Yan-Da Chiu
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Experimental Results ◽  
Dijkstra’S Algorithm ◽  
Board Game ◽  
Tree Algorithm ◽  
Dijkstra's Algorithm ◽  
Tree Algorithms

The concept of minimum spanning tree algorithms in data structure is difficult for students to learn and to imagine without practice. Usually, learners need to diagram the spanning trees with pen to realize how the minimum spanning tree algorithm works. In this paper, the authors introduce a competitive board game to motivate students to learn the concept of minimum spanning tree algorithms. They discuss the reasons why it is beneficial to combine graph theories and board game for the Dijkstra and Prim minimum spanning tree theories. In the experimental results, this paper demonstrates the board game and examines the learning feedback for the mentioned two graph theories. Advantages summarizing the benefits of combining the graph theories with board game are discussed.

Parallel Algorithms for Recognizing P5-free and ${\bar P}_5$-free Weakly Chordal Graphs

2004 ◽  
Vol 14 (01) ◽  
pp. 119-129
Author(s):  
Stavros D. Nikolopoulos ◽  
Leonidas Palios
Keyword(s):  
Parallel Algorithms ◽  
Chordal Graphs ◽  
Input Graph ◽  
Model Of Computation ◽  
Erew Pram ◽  
Recognition Algorithms ◽  
Pram Model

We prove algorithmic characterizations of weakly chordal graphs, which lead to efficient parallel algorithms for recognizing P5-free and [Formula: see text]-free weakly chordal graphs. For an input graph on n vertices and m edges, our algorithms run in O( log 2n) time and require O(m2/ log n) processors on the EREW PRAM model of computation. The proposed recognition algorithms efficiently detect P5 s and [Formula: see text] in weakly chordal graphs in O( log n) time with O(m2/ log n) processors on the EREW PRAM. Additionally, we show how the algorithms can be augmented to provide a certificate for the existence of a P5 (or a [Formula: see text]) in case the input graph is not P5-free (respectively, [Formula: see text]-free) weakly chordal.

FAST AND EFFICIENT OPERATIONS ON PARALLEL PRIORITY QUEUES

1996 ◽  
Vol 06 (04) ◽  
pp. 451-467
Author(s):  
DANNY Z. CHEN ◽  
XIAOBO SHARON HU
Keyword(s):  
Data Structure ◽  
Parallel Algorithms ◽  
Computational Model ◽  
Data Structures ◽  
Priority Queue ◽  
Minimal Path ◽  
Erew Pram ◽  
New Ideas ◽  
The Right ◽  
Path Partition

The Parallel Priority Queue (PPQ) data structure supports parallel operations for manipulating data items with keys, such as inserting n new items, deleting n items with the first n smallest keys, creating a new PPQ that contains a set of items, and melding two PPQ’s into one. In this paper, we present fast and efficient parallel algorithms for performing operations on the PPQ’s that maintain data items with real-valued keys. The data structures that we use for implementing the PPQ’s are the unmeldable and meldable parallel heaps. Our algorithms have considerably less time and/or work bounds than the previously best known algorithms, and use a less powerful parallel computational model (EREW PRAM). The new ideas that make our improvement possible are two partition schemes dynamically maintained on the parallel heap structures: the minimal- path partition and the right-path partition. These partition schemes could be of interest in their own right. Our results also lead to optimal parallel algorithms for implementing sequential operations on several commonly-used heap structures.

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