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Probabilistic Analysis of the 1-Tree Relaxation for the Euclidean Traveling Salesman Problem (Classic Reprint) - Brossura
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Excerpt from Probabilistic Analysis of the 1-Tree Relaxation for the Euclidean Traveling Salesman Problem
Christofides [3] and Johnson the relative gap is often less or much less than l%. On a theoretical ground, a result due to Wolsey [21] states that the Held Karp lower bound is never less than of the length of the optimal tour when the triangle inequality is satisfied. However, this worst - case analysis does not capture the efficiency of the bound in practice. The probabilistic analysis developed in this paper is aimed at shedding new light on the behavior of the held-karp lower bound.
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Probabilistic Analysis of the 1Tree Relaxation for the Euclidean Traveling Salesman Problem Classic Reprint
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9781332986781
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Probabilistic Analysis of the 1Tree Relaxation for the Euclidean Traveling Salesman Problem Classic Reprint
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9781332986781
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Probabilistic Analysis of the 1-Tree Relaxation for the Euclidean Traveling
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Paperback. Condizione: New. Print on Demand. This book delves into the probabilistic analysis of the Held-Karp lower bound, a key concept for solving the Euclidean Traveling Salesman Problem (ETSP). The ETSP is a classic combinatorial optimization problem that finds applications in various fields, such as logistics and circuit board designing. The Held-Karp lower bound provides a crucial estimate for the length of the optimal tour in the ETSP. The author takes a novel approach by combining the combinatorial interpretation of the lower bound with the theory of subadditive Euclidean functionals. This enables a probabilistic analysis of the bound, leading to new insights into its behavior. The book establishes that the Held-Karp lower bound is asymptotically close to a constant times the optimal tour length when the number of points in the ETSP tends to infinity. This result provides a theoretical explanation for the practical observation that the lower bound often closely approximates the optimal solution. The analysis also establishes the complete convergence of the Held-Karp lower bound, a significant theoretical result that further strengthens the understanding of its behavior. Overall, this book offers a rigorous and innovative examination of the Held-Karp lower bound, contributing to the understanding of both the ETSP and probabilistic analysis in combinatorial optimization. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781332986781_0
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