We present a new polynomial-time heuristic algorithm for finding a solution to the Travelling Salesman Problem (TSP) for any complete and edge-weighted graph K n, with a set of vertices V and a set of edges E w
TSP Problem 无向带权图中,寻找环路遍历每个顶点,使得距离最小,权重w(u,v)满足 w(u,v)≤w(u,x)+w(x,v) algorithm(FINDTOUR) 找到graph的一个最小生成树T 在T上重复每个边两次,得到H 在H上找到一条Eulerian回路C 构建TSP,如果C上遍历一个vertex两次,则跳过这个vertex直接visit下一个vertex 2-Approxima...
G that has at most 1.5 times the weight of an optimal TSP solution of G. Based on this algorithm and a novel use of orientations in graphs, we obtain a (3β/4+3β2/4)-approximation algorithm for TSP with β-relaxed triangle inequality (...
First, we consider the symmetric TSP (STSP) with γ-triangle inequality. For this problem, we present a deterministic polynomial-time algorithm that achieves an approximation ratio of min{1 + γ, (2γ~2)/(2γ~2-2γ+1)} + ε and a randomized approximation algorithm that achieves a ...
1. Approximation ratioCost: the size of the solution, for example, in vertex cover, it’s the size of the cover; in TSP, it’s the total distance.Since the approximation algorithm, the cost we have is always greater than the optimal solution.2. Vertex CoverRunning...
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(1):347-360, 2014) claimed a 5.875-approximation algorithm for allk≥4andn≥6. However, there were both flaws in the construction of the schedule and in the analysis. In this paper, we show that there is a 5-approximation algorithm for allkandn. Furthermore, ifk≥n/2, the ...
摘要: We present a polynomial time approximation algorithm for the asymmetric maximum traveling salesperson problem that achieves performance ratio ja:math . The running time of our algorithm is O ( n 3 ).关键词: Practical, Theoretical or Mathematical/ approximation theory computational complexity ...
A classic example is the initial PTAS forEuclidean TSPdue toSanjeev Arorawhich had prohibitive running time, yet within a year, Arora refined the ideas into a linear time algorithm. Such algorithms are also worthwhile in some applications where the running times and cost can be justified e.g....
The first approximation algorithm combines exhaustive search for sub-optimal representatives for the clusters with dynamic programming for estimating the obtained variants and it is PTAS when k=O(logn). The second one is based on the Arora (1998)’s PTAS in the case of classical Euclidean TSP ...