{"product_id":"an-algorithmic-theory-of-numbers-graphs-and-convexity-paperback-softback-9780898712032","title":"An Algorithmic Theory of Numbers, Graphs and Convexity (Paperback \/ softback) 9780898712032","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAn Algorithmic Theory of Numbers, Graphs and Convexity\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eStudies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eLászló Lovász (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780898712032\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 28 February 1987\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e96 pages\u003cbr\u003e25.9 x 18.1 x 0.5 cm, 0.202 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eA study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume especially useful.  Two algorithms are studied in detail: the ellipsoid method and the simultaneous diophantine approximation method. Although both were developed to study, on a theoretical level, the feasibility of computing some specialized problems in polynomial time, they appear to have practical applications. The book first describes use of the simultaneous diophantine method to develop sophisticated rounding procedures. Then a model is described to compute upper and lower bounds on various measures of convex bodies. Use of the two algorithms is brought together by the author in a study of polyhedra with rational vertices. The book closes with some applications of the results to combinatorial optimization.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHow to Round Numbers\u003cbr\u003e Preliminaries: On Algorithms Involving Numbers\u003cbr\u003e Diophantine Approximation, Problems\u003cbr\u003e Lattices, Bases, and the Reduction Problem\u003cbr\u003e Diophantine Approximation and Rounding\u003cbr\u003e What is a Real Number How to Round a Convex Body\u003cbr\u003e Preliminaries: Inputting a Set\u003cbr\u003e Algorithmic Problems on Convex Sets\u003cbr\u003e The Ellipsoid Method\u003cbr\u003e Rational Polyhedra\u003cbr\u003e Some Other Algorithmic Problems on Convex Sets\u003cbr\u003e Integer Programming in Fixed Dimension\u003cbr\u003e Some Applications in Combinatorics\u003cbr\u003e Cuts and Joins\u003cbr\u003e Chromatic Number, Cliques and Perfect Graphs\u003cbr\u003e Minimizing a Submodular Function.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52410745749784,"sku":"9780898712032","price":36.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780898712032i.jpg?v=1784251355","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/an-algorithmic-theory-of-numbers-graphs-and-convexity-paperback-softback-9780898712032","provider":"Freshly Printed Books","version":"1.0","type":"link"}