Fast detection of heavy flows (e.g., heavy hitters and heavy changers) in massive network traffic is challenging due to the stringent requirements of fast packet processing and limited resource availability. Invertible sketches are summary data structures that can recover heavy flows with small memory footprints and bounded errors, yet existing invertible sketches incur high memory access overhead that leads to performance degradation. We present MV-Sketch, a fast and compact invertible sketch that supports heavy flow detection with small and static memory allocation. MV-Sketch tracks candidate heavy flows inside the sketch data structure via the idea of majority voting, such that it incurs small memory access overhead in both update and query operations, while achieving high detection accuracy. We present theoretical analysis on the memory usage, performance, and accuracy of MV-Sketch. Trace-driven evaluation shows that MV-Sketch achieves higher accuracy than existing invertible sketches, with up to 3.38x throughput gain. We also show how to boost the performance of MV-Sketch with SIMD instructions.