This work proposes two new Resource Block (RB) allocation algorithms for the LTE uplink. They take into account the RB adjacency constraint and update the allocation metric. Two different heuristics are proposed: an Opportunistic and Efficient RB allocation Algorithm (OEA) and a Quality of Service based Opportunistic and Efficient RB allocation Algorithm (QoS based OEA). Both algorithms seek to maximize the aggregate throughput and avoid RB wastage unlike other algorithms in the literature. The complexity of the proposed algorithms are also computed analytically and compared to other well known heuristics.