update readme

CITATION.bib

@@ -0,0 +1,21 @@
+@article{liu2021tropical,
+  title={Tropical tensor network for ground states of spin glasses},
+  author={Liu, Jin-Guo and Wang, Lei and Zhang, Pan},
+  journal={Physical Review Letters},
+  volume={126},
+  number={9},
+  pages={090506},
+  year={2021},
+  publisher={APS}
+}
+
+@article{liu2023computing,
+  title={Computing solution space properties of combinatorial optimization problems via generic tensor networks},
+  author={Liu, Jin-Guo and Gao, Xun and Cain, Madelyn and Lukin, Mikhail D and Wang, Sheng-Tao},
+  journal={SIAM Journal on Scientific Computing},
+  volume={45},
+  number={3},
+  pages={A1239--A1270},
+  year={2023},
+  publisher={SIAM}
+}

README.md

@@ -3,29 +3,33 @@
 [![Build Status](https://github.com/TensorBFS/TropicalGEMM.jl/workflows/CI/badge.svg)](https://github.com/TensorBFS/TropicalGEMM.jl/actions)
 [![codecov](https://codecov.io/gh/TensorBFS/TropicalGEMM.jl/branch/master/graph/badge.svg?token=8F6PH5Q9PL)](https://codecov.io/gh/TensorBFS/TropicalGEMM.jl)
 
-The fastest tropical matrix multiplication in the world!
+The fastest Tropical matrix multiplication in the world! Supported matrix element types include
+* max-plus algebra: `Tropical{BlasType}`
+* min-plus algebra numbers: `TropicalMinPlus{BlasType}`
+* max-times algebra numbers: `TropicalMaxMul{BlasType}`
 
-## See the discussion here
-
-https://github.com/JuliaSIMD/LoopVectorization.jl/issues/201
+Please check [`TropicalNumbers.jl`](https://github.com/TensorBFS/TropicalNumbers.jl) for the definitions of these types. The `BlasType` is the storage type, which could be one of `Bool, Float16, Float32, Float64, Int16, Int32, Int64, Int8, UInt16, UInt32, UInt64, UInt8, SIMDTypes.Bit`.
 
 ## Get started
 
 Open a Julia REPL and type `]` to enter the `pkg>` mode, and then install related packages with
 ```julia
-pkg> add TropicalNumbers, Octavian, TropicalGEMM, BenchmarkTools
+pkg> add TropicalGEMM, BenchmarkTools, TropicalNumbers
 ```
-
-In a julia REPL, you can try a minimum working example
+Loading `TropicalGEMM` module into the workspace affects the `*` on Tropical matrices immediately. The following is a minimum working example
 ```julia
-julia> using TropicalNumbers, Octavian, TropicalGEMM, BenchmarkTools
+julia> using TropicalNumbers, BenchmarkTools
 
-julia> a = Tropical.(randn(1000, 1000))
+julia> a = Tropical.(randn(1000, 1000));
 
-julia> @benchmark Octavian.matmul_serial($a, $a)
-```
+julia> @btime $a * $a;
+  2.588 s (6 allocations: 7.66 MiB)
 
-**Warning:** using TropicalGEMM will overload the `mul!` function for Tropical numbers.
+julia> using TropicalGEMM
+
+julia> @btime $a * $a;
+  66.916 ms (2 allocations: 7.63 MiB)
+```
 
 ## Benchmarks
 
@@ -35,8 +39,7 @@ The benchmark and plotting scripts could be found in the benchmarks folder.
 ![Float64](benchmarks/benchmark-float64.png)
 ![Float32](benchmarks/benchmark-float32.png)
 
-
-## Warnings
-
-It is expected to have an ambiguity error when one uses both `TropicalGEMM` and `CUDA`.
-If you see these errors, please include `example/cudapatch.jl` in your project.
+## References
+1. This package originates from the following issue:
+https://github.com/JuliaSIMD/LoopVectorization.jl/issues/201
+2. For applications, please check the papers listed in the [CITATION.bib](/CITATION.bib).