{"product_id":"colourful-linear-programming-feasibility-problem-von-guohong-rong","title":"Colourful Linear Programming Feasibility Problem","description":"\u003cp\u003eThis problem was presented by  Barany and Onn in 1997 and it is still not known if a polynomial-time algorithm  for the problem exists. The monochrome version of this problem, expressing p  as a convex combination of points in a set S, is a traditional linear programming  feasibility problem. The colourful Caratheodory Theorem, due to Barany in  1982, provides a sufficient condition for the existence of a colourful set of points  containing p in its convex hull. Barany's result was generalized by Holmsen  et al. in 2008 and by Arocha et al. in 2009 before being recently further  generalized by Meunier and Deza. We study algorithms for colourful linear  programming under the conditions of Barany and their generalizations. In  particular, we implement the Meunier-Deza algorithm and enhance previously  used random case generators. Computational benchmarking and a performance  analysis including a comparison between the two algorithms of Barany and Onn  and the one of Meunier and Deza, and random picking are presented.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783659286773\"\u003e\u003ch3\u003eAlgorithms\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783659286773","offer_id":39486436868189,"sku":"9783659286773","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/fd9b978a-c1ba-48b4-9a6b-1bc1d0f7533d.jpg?v=1773382317","url":"https:\/\/shop.autorenwelt.de\/en\/products\/colourful-linear-programming-feasibility-problem-von-guohong-rong","provider":"Autorenwelt Shop","version":"1.0","type":"link"}