Synopsis
This book offers a comprehensive exploration into the captivating world of network flows, a subfield of mathematical programming that intersects intricately with our daily lives through various physical networks like highways, electrical grids, and communication systems. The authors delve deep into the fundamental concepts, applications, and complexities of network optimization, presenting it not just as a subject of academic interest but as a vital tool with widespread applicability in operations research and applied mathematics. Throughout its chapters, this work discusses the basic properties of network flows, shortest path problems, maximum flow problems, minimum cost flow problems, and assignment problems. It highlights significant theoretical and algorithmic advances within these areas while focusing on the design of algorithms that are both provably good and practically efficient. The thematic depth is enriched by connecting historical methods such as price directive decomposition algorithms with cutting-edge techniques in optimization and computer science. By bridging ideas from optimization theory and computer science, this book illustrates how network optimization has been pivotal in inspiring foundational results across various domains of mathematics and technology. It serves not only as an advanced survey for specialists but also as an accessible introduction for non-specialists interested in the mathematical underpinnings that shape our understanding of networks. In essence, this book encapsulates the significance of network flows in optimizing the complex web of systems that underpin contemporary society. Its insights offer valuable perspectives for both practitioners looking to apply these concepts to real-world challenges and scholars seeking to further the frontiers of research in mathematical programming.
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