Tropical algebra solves complex problems with only sum and min/max operations replacing expensive multiplication and addition in linear algebra. Due to the low computing cost, tropical algebra has recently gained significant attention in a broad range of areas such as combinatorial optimization, scheduling, machine learning, etc. In this paper, we propose a generic hardware accelerator architecture for tropical algebra supporting a wide range of applications. Novel time-domain (TD) computing accelerators with special mapping, precision expansion and, unrolling techniques are proposed to further improve hardware efficiency. Test results on various tropical calculations including linear regression, dynamic programming, and neural network are shown to demonstrate an energy saving from 1.5X to 2.1X, latency saving from 2.6X to 5.2X, or an overall energy-delay-product (EDP) improvement from 3.9X-10.5X compared with conventional digital implementation manifesting the promise of the algebraic solution on low power edge devices.