Many Polytopes Meeting the Conjectured Hirsch Bound
نویسندگان
چکیده
منابع مشابه
More polytopes meeting the conjectured Hirsch bound
In 1957 W.M. Hirsch conjectured that every d-polytope with n facets has edge-diameter at most n ? d. Recently Holt and Klee constructed polytopes which meet this bound for a number of (d; n) pairs with d 13 and for all pairs (14; n). These constructions involve a judicious use of truncation, wedging, and blending on polytopes which already meet the Hirsch bound. In this paper we extend these te...
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In 1957, Hirsch conjectured that every d−polytopes with n facets has edge-diameter at most n − d. Recently Holt and Klee constructed polytopes which meet this bound for a number of (d, n) pairs with d ≤ 13 and for all pairs (14, n). The main purpose of this paper is to present linear Hirsch bound ⌊ 2 ⌋+ d− 2 for all pairs (d, n) and to review mathematical ideas behind simplex methods, investiga...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1998
ISSN: 0179-5376
DOI: 10.1007/pl00009372