Synopsis
Excerpt from An Algorithm for the Traveling Salesman Problem
Held and Karpta] have solved problems up to 13 cities by dynamic programming using an ibm 7090. A 13 city problem required 17 seconds. But such is the power of an exponential that, if their computation grows at the same rate as that of Gonzalez, a 20 city problem would require about 10 hours. Storage requirements, however, may become prohibitive before then. For larger problems than 13 cities, Held and Karp develop an approximation method which seems to work well but does not guarantee an optimal tour. Our concern here will be with methods that must eventually yield an optimal tour.
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An Algorithm for the Traveling Salesman Problem (Classic Reprint)
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Paperback. Condition: New. Print on Demand. In the realm of mathematical optimization, this book presents a ground-breaking algorithm for solving the renowned traveling salesman problem. The author ingeniously devised a method that breaks complex problems into smaller, more manageable subsets, leveraging an approach that has since become known as "branch and bound." This technique has expanded the scale of problems that can be efficiently solved, enabling significant advancements in the field. At its core, the book explores the intricate balance between computational efficiency and the quest for optimal solutions. It elucidates how the algorithm operates, from its initial branching to its meticulous lower bound calculations, providing a comprehensive understanding of its workings. Through illuminating examples and detailed analysis, the book equips readers to grasp the mathematical underpinnings and practical applications of this powerful optimization technique. Its insights have had a far-reaching impact, solidifying the "branch and bound" approach as a cornerstone in the field of mathematical optimization and paving the way for further breakthroughs in solving complex real-world problems. 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. Seller Inventory # 9781334214998_0
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