{"product_id":"9789814704892","title":"Advances In Combinatorial Optimization: Linear Programming Formulations Of The Traveling Salesman And Other Hard Combinatorial Optimization Problems: Linear Programming Formulations of the Traveling Salesman and Other Hard Combinatorial Optimization Probl","description":"\u003cp\u003eCombinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research\/management science, artificial intelligence, machine learning, and software engineering.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eAdvances in Combinatorial Optimization\u003c\/i\u003e presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes \"P\" (polynomial time) and \"NP\" (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).\u003c\/p\u003e\u003cp\u003eOn a whole, \u003ci\u003eAdvances in Combinatorial Optimization\u003c\/i\u003e offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.\u003c\/p\u003e\u003cp\u003eCombinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research\/management science, artificial intelligence, machine learning, and software engineering.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eAdvances in Combinatorial Optimization\u003c\/i\u003e presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes \"P\" (polynomial time) and \"NP\" (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).\u003c\/p\u003e\u003cp\u003eOn a whole, \u003ci\u003eAdvances in Combinatorial Optimization\u003c\/i\u003e offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.\u003c\/p\u003e\u003cb\u003eReadership:\u003c\/b\u003e Professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.\u003cbr\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThe book offers a new proof of the equality of the complexity classes \"P\" and \"NP\"\u003c\/li\u003e\n\u003cli\u003eAlthough our approach is developed using the framework of the TSP, it has natural analogs for the other problems in the NP-Complete class thus providing a unified framework for modeling many combinatorial optimization problems (COPs)\u003c\/li\u003e\n\u003cli\u003eThe book makes a contribution to the theory and application of Extended Formulations (EFs) refining the notion of EFs by separating the case in which that notion is degenerate from the case in which the notion of EF is well defined\/meaningful. It separates the case in which the addition of redundant constraints and variables (for the purpose of establishing EF relations) matters from the case in which the addition of redundant constraints and variables does not matter\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47120833085680,"sku":"9789814704892","price":51.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814704892_p0.jpg?v=1763691411","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814704892","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}