Approximating TSP Solution by MST Based Graph Pyramid
نویسندگان
چکیده
The traveling salesperson problem (TSP) is difficult to solve for input instances with large number of cities. Instead of finding the solution of an input with a large number of cities, the problem is approximated into a simpler form containing smaller number of cities, which is then solved optimally. Graph pyramid solution strategies, in a bottom-up manner using Bor̊uvka’s minimum spanning tree, convert a 2D Euclidean TSP problem with a large number of cities into successively smaller problems (graphs) with similar layout and solution, until the number of cities is small enough to seek the optimal solution. Expanding this tour solution in a top-down manner to the lower levels of the pyramid approximates the solution. The new model has an adaptive spatial structure and it simulates visual acuity and visual attention. The model solves the TSP problem sequentially, by moving attention from city to city with the same quality as humans. Graph pyramid data structures and processing strategies are a plausible model for finding near-optimal solutions for computationally hard pattern recognition problems.
منابع مشابه
Approximative graph pyramid solution of the E-TSP
The traveling salesman problem (TSP) is difficult to solve for input instances with large number of cities. Instead of finding the solution for an input with a large number of cities, the problem is transformed into a simpler form containing smaller number of cities, which is then solved optimally. Graph pyramid solution strategies, using Bor̊uvka’s minimum spanning tree step, convert, in a bott...
متن کاملLogarithmic Bounds on an Algorithm for Asymmetric TSP
In 1982 Frieze, Galbiati and Maffioli (Networks 12:23-39) published their famous algorithm for approximating the TSP tour in an asymmetric graph with triangle inequality. They show that the algorithm approximates the TSP tour within a factor of log 2 n. We construct a family of graphs for which the algorithm (with some implementation details specified by us) gives an approximation which is log ...
متن کاملPrize-Collecting Traveling Salesman and Related Problems
The most general version of the Prize Collecting Traveling Salesman Problem (PCTSP) was first introduced by Balas [8]. In this problem, a salesman has to collect a certain amount of prizes (the quota) by visiting cities. A known prize can be collected in every city. Furthermore, by not visiting a city, the salesman incurs a pecuniary penalty. The goal is to minimize the total travel distance pl...
متن کاملThe Gap Property in Doubling Metrics
We introduce the weak gap property as a variant of the gap property. We show that in any metric space of bounded doubling dimension, any directed graph whose vertex set S has size n and which satisfies the weak gap property has total weight O(wt(MST (S)) log n), where wt(MST (S)) denotes the weight of a minimum spanning tree of S. We show that 2-optimal TSP tours and greedy spanners satisfy the...
متن کاملA Multi-MetaHeuristic Combined ACS-TSP System
This paper presents a Multi-MetaHeuristic combined Ant Colony System (ACS)-Travelling Salesman Problem(TSP) algorithm for solving the TSP. We introduce genetic algorithm in ACS-TSP to search solutions space for dealing with the early stagnation problem of the traveling salesman problem. Moreover, we present a new strategy of Minimum Spanning Tree (MST) coupled with Nearest Neighbor(NN) to const...
متن کامل