A Subexponential Bound for Linear Programming

We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected minfO(d 22dn); e 2 pdln(n= p d)+O( p d+lnn)g time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise, the algorithm computes the lexicographically smallest nonnegative point satisfying n given linear inequalities in d variables. The expectation is over the internal randomizations Work by the rst author has been supported by a Humboldt Research Fellowship. Work by the second and third authors has been supported by the German-Israeli Foundation for Scienti c Research and Development (G.I.F.). Work by the second author has been supported by O ce of Naval Research Grant N00014-90-J-1284, by National Science Foundation Grants CCR-89-01484 and CCR-90-22103, and by grants from the U.S.-Israeli Binational Science Foundation, and the Fund for Basic Research administered by the Israeli Academy of Sciences. yA pre...

• Type: Conference
• Year: 1992
• Where: COMPGEOM
• Authors: Jirí Matousek, Micha Sharir, Emo Welzl
• Keywords: COMPGEOM 1992, Discrete Geometry, Science Foundation, Simple Randomized Algorithm, Smallest Nonnegative Point