scholarly journals Non-perfect maze generation using Kruskal algorithm

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
MAHYUS IHSAN ◽  
DEDI SUHAIMI ◽  
MARWAN RAMLI ◽  
SYARIFAH MEURAH YUNI ◽  
IKHSAN MAULIDI
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Vertical Wall ◽  
Process Time ◽  
Grid Graph ◽  
Isolated Cell

A non-perfect maze is a maze that contains loop or cycle and has no isolated cell. A non-perfect maze is an alternative to obtain a maze that cannot be satisfied by perfect maze. This paper discusses non-perfect maze generation with two kind of biases, that is, horizontal and vertical wall bias and cycle bias. In this research, a maze is modeled as a graph in order to generate non-perfect maze using Kruskal algorithm modifications. The modified Kruskal algorithm used Fisher Yates algorithm to obtain a random edge sequence and disjoint set data structure to reduce process time of the algorithm. The modification mentioned above are adding edges randomly while taking account of the edge’s orientation, and by adding additional edges after spanning tree is formed. The algorithm designed in this research constructs an  non-perfect maze with complexity of  where  and  denote vertex and edge set of an  grid graph, respectively. Several biased non-perfect mazes were shown in this research by varying its dimension, wall bias and cycle bias.

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.

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.

Practical innovation about the Minimum Spanning Tree (MST) in data structure teaching

2015 ◽  
pp. 113-117
Author(s):  
Jing Yi ◽  
Sheng'en Li ◽  
Xiaobing Tang ◽  
Xiaofei Niu
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Minimum Spanning Tree

SAMPLING IN DYNAMIC DATA STREAMS AND APPLICATIONS

2008 ◽  
Vol 18 (01n02) ◽  
pp. 3-28 ◽  
Author(s):  
GEREON FRAHLING ◽  
PIOTR INDYK ◽  
CHRISTIAN SOHLER
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Finite Range ◽  
Vc Dimension ◽  
Range Space ◽  
Dimension Formula ◽  
Geometric Space ◽  
Point Set ◽  
Current Point

A dynamic geometric data stream is a sequence of m ADD/REMOVE operations of points from a discrete geometric space {1,…, Δ} d ?. ADD (p) inserts a point p from {1,…, Δ} d into the current point set P , REMOVE(p) deletes p from P . We develop low-storage data structures to (i) maintain ε-nets and ε-approximations of range spaces of P with small VC-dimension and (ii) maintain a (1 + ε)-approximation of the weight of the Euclidean minimum spanning tree of P . Our data structure for ε-nets uses [Formula: see text] bits of memory and returns with probability 1 – δ a set of [Formula: see text] points that is an e-net for an arbitrary fixed finite range space with VC-dimension [Formula: see text]. Our data structure for ε-approximations uses [Formula: see text] bits of memory and returns with probability 1 – δ a set of [Formula: see text] points that is an ε-approximation for an arbitrary fixed finite range space with VC-dimension [Formula: see text]. The data structure for the approximation of the weight of a Euclidean minimum spanning tree uses O ( log (1/δ)( log Δ/ε) O ( d )) space and is correct with probability at least 1 – δ. Our results are based on a new data structure that maintains a set of elements chosen (almost) uniformly at random from P .

Fully Retroactive Minimum Spanning Tree Problem

2020 ◽  
Author(s):  
José Wagner de Andrade Júnior ◽  
Rodrigo Duarte Seabra
Keyword(s):  
Data Structure ◽  
Empirical Analysis ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Square Root ◽  
Minimum Spanning Tree Problem

Abstract This article describes an algorithm that solves a fully dynamic variant of the minimum spanning tree (MST) problem. The fully retroactive MST allows adding an edge to time $t$, or to obtain the current MST at time $t$. By using the square root technique and a data structure link-cut tree, it was possible to obtain an algorithm that runs each query in $O(\sqrt{m} \lg{|V(G)|})$ amortized, in which $|V(G)|$ is the number of nodes in graph $G$ and $m$ is the size of the timeline. We use a different approach to solve the MST problem instead of the standard algorithms, such as Prim or Kruskal, and this allows using the square root technique to improve the final complexity of the algorithm. Our empirical analysis shows that the proposed algorithm runs faster than re-executing the standard algorithms, and this difference only increases when the number of nodes in these graphs is larger.

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

2010 ◽  
Vol 1 (4) ◽  
pp. 16-30
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.

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.

Ultrastructure and Morphology of the Neurospora Crassa Cell Wall Mutants, Slime And Slime X, Using Tem and Sem

1976 ◽  
Vol 34 ◽  
pp. 54-55
Author(s):  
Karen S. Howard ◽  
H. D. Braymer ◽  
M. D. Socolofsky ◽  
S. A. Milligan
Keyword(s):  
Cell Wall ◽  
Neurospora Crassa ◽  
Wild Type ◽  
Morphological Comparison ◽  
Small Areas ◽  
Solid Media ◽  
Thin Sectioning ◽  
X Cells ◽  
Mutant Cells ◽  
Isolated Cell

The recently isolated cell wall mutant slime X of Neurospora crassa was prepared for ultrastructural and morphological comparison with the cell wall mutant slime. The purpose of this article is to discuss the methods of preparation for TEM and SEM observations, as well as to make a preliminary comparison of the two mutants.TEM: Cells of the slime mutant were prepared for thin sectioning by the method of Bigger, et al. Slime X cells were prepared in the same manner with the following two exceptions: the cells were embedded in 3% agar prior to fixation and the buffered solutions contained 5% sucrose throughout the procedure.SEM: Two methods were used to prepare mutant and wild type Neurospora for the SEM. First, single colonies of mutant cells and small areas of wild type hyphae were cut from solid media and fixed with OSO4 vapors similar to the procedure used by Harris, et al. with one alteration. The cell-containing agar blocks were dehydrated by immersion in 2,2-dimethoxypropane (DMP).

Sign in / Sign up

Export Citation Format

Share Document