{"product_id":"9789811999512","title":"Pedigree Polytopes: New Insights on Computational Complexity of Combinatorial Optimisation Problems","description":"\u003ch1\u003ePedigree Polytopes: New Insights on Computational Complexity of Combinatorial Optimisation Problems\u003c\/h1\u003e \u003ch2\u003eArthanari, Tirukkattuppalli Subramanyam\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book defines and studies a combinatorial object called the pedigree and develops the theory for optimising a linear function over the convex hull of pedigrees (the Pedigree polytope). A strongly polynomial algorithm implementing the framework given in the book for checking membership in the pedigree polytope is a major contribution.\u003c\/p\u003e\u003cp\u003eThis book challenges the popularly held belief in computer science that a problem included in the \u003ci\u003eNP-complete\u003c\/i\u003e class may not have a polynomial algorithm to solve. By showing \u003ci\u003eSTSP\u003c\/i\u003e has a polynomial algorithm, this book settles the \u003ci\u003eP\u003c\/i\u003e vs \u003ci\u003eNP\u003c\/i\u003e question.\u003c\/p\u003e\u003cp\u003eThis book has illustrative examples, figures, and easily accessible proofs for showing this unexpected result. This book introduces novel constructions and ideas previously not used in the literature. Another interesting feature of this book is it uses basic max-flow and linear multicommodity flow algorithms and concepts in theseproofs establishing efficient membership checking for the pedigree polytope. Chapters 3-7 can be adopted to give a course on \u003ci\u003eEfficient Combinatorial Optimization\u003c\/i\u003e. This book is the culmination of the author's research that started in 1982 through a presentation on a new formulation of STSP at the XIth International Symposium on Mathematical Programming at Bonn.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2023-03-28\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811999512\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-19-9952-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 221\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":44809997451404,"sku":"9789811999512","price":161.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811999512.jpg?v=1772945733","url":"https:\/\/lateknightbooks.com\/products\/9789811999512","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}