Computing Integral Points in Convex Semi-algebraic Sets
نویسندگان
چکیده
Let Y be a convex set in IR k deened by polynomial inequalities and equations of degree at most d 2 with integer coeecients of binary length l. We show that if Y \ ZZ k 6 = ;, then Y contains an integral point of binary length ld O(k 4). For xed k, our bound implies a polynomial-time algorithm for computing an integral point y 2 Y. In particular, we extend Lenstra's theorem on the polynomial-time solvability of linear integer programming in xed dimension to semideenite integer programming.
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