The Probabilistic Minimum Spanning Tree Problem (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
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Condition: New
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Print on Demand. This book explores the probabilistic minimum spanning tree problem (PMST), a probabilistic variation of the classic minimum spanning tree problem. Unlike its deterministic counterpart, the PMST considers situations where not all points are deterministically present, but instead have certain probabilities of presence. The author, a respected researcher in the field, delves into the complexity and combinatorial properties of the problem, proving that even a restricted version of the PMST with all weights equal is NP-complete, a surprising result given the simplicity of the MST problem. The book also examines the relationship between the PMST problem and the MST, network design, and re-optimization strategies, providing valuable insights into the problem's nature and potential applications. Through the author's rigorous analysis and clear explanations, this book offers a comprehensive understanding of the PMST problem, its complexities, and its implications in the broader field of 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 # 9781332276097_0
- Title
- The Probabilistic Minimum Spanning Tree Problem (Classic Reprint)
- Author
- Dimitris Bertsimas
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332276091
- ISBN 13
- 9781332276097
- Seller catalogs
- Calculus
In this paper we consider a natural probabilistic variation of this classical problem. In particular, we consider the case where not all the points are deterministically present, but are present with certain probability. Formally, given a weighted graph G (v, E) and a probability of presence p(s) for each subset S of V, we want to construct an a priori spanning tree of minimum expected length in the following sense: on any given instance of the problem delete the vertices and their adjacent edges among the set of absent vertices provided that the tree remains connected. The problem of finding an a priori spanning tree of minimum expected length is the probabilistic minimum spanning tree (pmst) problem. In order to clarify the definition of the pmst problem, consider the example in Figure 1. If the a priori tree is T and nodes are the only ones not present, the tree becomes ti. One can easily observe that if every node is present with probability p. 1 for all i E V then the problem reduces to the classical mst problem.
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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.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
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.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
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