Communication locality plays a key role in the performance of collective operations on large HPC systems, especially on oversubscribed networks where groups of nodes are fully connected internally but sparsely linked through global connections. We present Bine (binomial negabinary) trees, a family of collective algorithms that improve communication locality. Bine trees maintain the generality of binomial trees and butterflies while cutting global-link traffic by up to 33%. We implement eight Bine-based collectives and evaluate them on four large-scale supercomputers with Dragonfly, Dragonfly+, oversubscribed fat-tree, and torus topologies, achieving up to 5x speedups and consistent reductions in global-link traffic across different vector sizes and node counts.