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Low-Dimensional Linear Programming with Violations
SIAM journal on computing (Print)
Two decades ago, Megiddo and Dyer showed that linear programming in 2 and 3 dimensions (and subsequently, any constant number of dimensions) can be solved in linear time. In this paper, we consider linear programming with at most violations: finding a point inside all but at most of Ò given halfspaces. We give a simple algorithm in 2-d that runs in Ç´´Ò · ¾ µÐÓ Òµ expected time; this is faster than earlier algorithms by Everett, Robert, and van Kreveld (1993) and Matoušek (1994) and is probablydoi:10.1137/s0097539703439404 fatcat:27xpybocjfgzvhaf3v72kbig7a