Due to high system capacity requirement, 3GPP Long Term Evolution (LTE) is likely to adopt frequency reuse factor 1 at the cost of suffering severe inter-cell interference (ICI). One of combating ICI strategies is network cooperation of resource allocation (RA). For LTE uplink RA, requiring all the subcarriers to be allocated adjacently complicates the RA problem greatly. This paper investigates the joint multi-cell RA problem for LTE uplink. We model the uplink RA and ICI mitigation problem using pure binary-integer programming (BIP), with integrative consideration of all users' channel state information (CSI). The advantage of the pure BIP model is that it can be solved by branch-and-bound search (BBS) algorithm or other BIP solving algorithms, rather than resorting to exhaustive search. The system-level simulation results show that it yields 14.83% and 22.13% gains over single-cell optimal RA in average spectrum efficiency and 5th percentile of user throughput, respectively.