Probabilistic Analysis of the 1-Tree Relaxation for the Euclidean Traveling

Michel Xavier Goemans, Dimitris Bertsimas

ISBN 10: 1332986781 / ISBN 13: 9781332986781

Published by Forgotten Books, 2024

About this Item

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. Seller Inventory # 9781332986781_0

Bibliographic Details

Title: Probabilistic Analysis of the 1-Tree ...

Publisher: Forgotten Books

Publication Date: 2024

Binding: Paperback

Condition: New

Book Type: print-on-demand item

About this title

Synopsis:

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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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.