Simplex Methods Meeting the Conjectured Hirsch
نویسنده
چکیده
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, investigating the duality formation implying in them.
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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