On the bounded integer programming

The best upper time bound for solving the bounded integer programming (BIP) up to now is poly(phi) ldr n^2n+o(n), where n and phi are the dimension and the input size of the problem respectively. In this paper, we show that BIP is solvable in deterministic time poly(phi) ldr n^n+o(n). Moreover we also show that under some reasonable assumptions, BIP is solvable in probabilistic time 2^O(n).