Comparison of Some Approximate Algorithms Proposed for Traveling Salesmen and Graph Partitioning Problems

Abstract

In computation theory, the complexity class NP-complete is one of the most studied classes of decision problem. We can verify any given solution to such a problem, but the most important characteristic of NP-complete problems is that no fast solution to them is known. Time required to solve the problem using any currently known algorithm increases very quickly as the size of the problem grows. So, NP-complete problems like traveling salesman and graph partitioning have various heuristic algorithms to find the optimal solution of these problems in much lesser time. Out of all the algorithms none of them will provide the exact solution of the problem. In this paper, we have considered two of graph based NP-complete problem (Traveling Salesmen Problem (Single and Multiple Salesman) and Graph Partitioning Problem). In TSP, the aim is to minimize the total distance travelled covering all the cities exactly once. In graph partitioning, the aim to partition the graph into smaller subset with each subset has almost equal number of nodes with minimized number of edges whose vertices are in different sets. To achieve these goals, we have implemented various heuristic algorithms of both of the problems. In addition to these, comparison of various algorithms on basis of cost and time of each problem is performed on a range of data set.