Generating Spanning-Tree Sequences of a Fan Graph in Lexicographic Order and Ranking/Unranking Algorithms

Job shop Scheduling Problem is an NP-hard combinatorial optimization problem. The research on its solving algorithm has been a hot topic, and many achievements have been made. However, due to the complexity of time and variable space in the solving process of job shop scheduling problems, teaching tools of scheduling algorithms are still lacking. To solve the problem, this paper takes a topological sorting algorithm to illustrate the design principle and solving instances of the scheduling algorithm for job shop scheduling problems. Firstly, the method of using a graph to express the correlation between operations is described. Secondly, the idea of the topological sorting algorithm for job shop scheduling is proposed, and the steps of algorithm programming are explained in detail. Thirdly, based on the case, the solving performance of the algorithm is analyzed, and the solving effect of the algorithm is expounded.

Experimental Teaching Platform Development for Topological Sorting Algorithm Education

Subgraphs of a graph can be generated in two ways, either removing edges from the graph or adding valid edges to the isolated vertices. In this paper, we have proposed an algorithm which follows the first method, i.e., starting from a complete graph of a given order and removing possible edges in successive levels; it generates non-isomorphic connected subgraphs of same order but of different sizes. It generates at least one connected subgraph of a particular size and the subgraphs of the same size are non-isomorphic. The set of graphs generated by the proposed algorithm can be utilized to determine the performance of spanning tree generation algorithms, approximation algorithms, graph algorithms, algorithms for modeling and simulation, and so on. 

Generation of Non-isomorphic Connected Graphs by Successive Edge Removals from a Complete Graph

The objective of this paper is to propose an algorithm to generate all possible structures of spanning trees of an undirected complete graph of n vertices. The process starts with a star-tree (T) of the given complete graph and then replacing the edges of T one by one to generate different possible structures like chain, branch, etc. These spanning tree structures repeat themselves as we move from lower to higher values of n. The authors have attempted to find out some generalized expressions for different structures of spanning trees for a complete graph of order n.

Algorithm to Generate All Spanning Tree Structures of a Complete Graph

Random connected graphs are required to determine the performance of approximation algorithms, graph algorithms, algorithm for modeling and simulation, algorithms solving problems regarding database applications. Also, developing algorithms to generate all spanning trees required random connected graphs as input. In this paper, we have proposed an algorithm to generate random simple undirected graph instances that can be utilized to determine the performance and reliability of the above-mentioned algorithms. Our proposed algorithm creates random connected graphs with a given number of vertices and a distinct number of edges. We have been able to formulate the number of such generated graphs. The reliability and the time bound of the algorithm have also been established. We have included the computational results of the algorithm that are greatly encouraging.

Sumit Chakraborty

Papers

Algorithm to Generate All Spanning Tree Structures of a Complete Graph

Generation of Simple Undirected Connected Random Graphs