Mobile communication systems are continuously evolving to provide higher data rates and to pave the way for ubiquitous, high speed broadband wireless coverage. LTE is a complex system where a large number of control mechanisms are executed at different nodes in the architecture to perform resource allocation tasks at different levels of granularity (in terms of the time-scale they operate). The success of LTE heterogeneous networks (Het-Nets) with macro cells and pico cells critically depends on efficient spectrum sharing between high-power macros and low-power picos. Our algorithm has provable guarantee, and furthermore, it accounts for network topology, traffic load, and macro-pico interference map. Our solution is standard compliant and can be implemented using the notion of Almost Blank Subframes (ABS) and Cell Selection Bias (CSB) proposed by LTE standards. We also show extensive evaluations using RF plan from a real network and discuss self-optimized networking (SON)-based enhanced inter-cell interference coordination (eICIC) implementation.