diff --git a/Project.toml b/Project.toml
index b81edb6..acfe5d7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -14,8 +14,9 @@ julia = "1"
 
 [extras]
 GenericTensorNetworks = "3521c873-ad32-4bb4-b63d-f4f178f42b49"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "Random", "GenericTensorNetworks"]
+test = ["Test", "Random", "GenericTensorNetworks", "LinearAlgebra"]
diff --git a/notebooks/tutorial.jl b/notebooks/tutorial.jl
index cdb9d73..f54ed28 100644
--- a/notebooks/tutorial.jl
+++ b/notebooks/tutorial.jl
@@ -70,10 +70,10 @@ LuxorGraphPlot.show_graph(graph)
 md"We can use the `map_graph` function to map the unweighted MIS problem on the Petersen graph to one on a defected King's graph."
 
 # ╔═╡ c7315578-8bb0-40a0-a2a3-685a80674c9c
-unweighted_res = map_graph(graph; vertex_order=Branching());
+unweighted_res = map_graph(graph; vertex_order=MinhThiTrick());
 
 # ╔═╡ 3f605eac-f587-40b2-8fac-8223777d3fad
-md"Here, the keyword argument `vertex_order` can be a vector of vertices in a specified order, or the method to compute the path decomposition that generates an order. The `Branching()` method is an exact path decomposition solver, which is suited for small graphs (where number of vertices <= 50). The `Greedy()` method finds the vertex order much faster and works in all cases, but may not be optimal.
+md"Here, the keyword argument `vertex_order` can be a vector of vertices in a specified order, or the method to compute the path decomposition that generates an order. The `MinhThiTrick()` method is an exact path decomposition solver, which is suited for small graphs (where number of vertices <= 50). The `Greedy()` method finds the vertex order much faster and works in all cases, but may not be optimal.
 A good vertex order can reduce the depth of the mapped graph."
 
 # ╔═╡ e5382b61-6387-49b5-bae8-0389fbc92153
@@ -150,7 +150,7 @@ md"## Generic Weighted Mapping"
 md"A Maximum Weight Independent Set (MWIS) problem on a general graph can be mapped to one on the defected King's graph. The first step is to do the same mapping as above but adding a new positional argument `Weighted()` as the first argument of `map_graph`. Let us still use the Petersen graph as an example."
 
 # ╔═╡ 2fa704ee-d5c1-4205-9a6a-34ba0195fecf
-weighted_res = map_graph(Weighted(), graph; vertex_order=Branching());
+weighted_res = map_graph(Weighted(), graph; vertex_order=MinhThiTrick());
 
 # ╔═╡ 27acc8be-2db8-4322-85b4-230fdddac043
 md"The return value is similar to that for the unweighted mapping generated above, except each node in the mapped graph can have a weight 1, 2 or 3. Note here, we haven't added the weights in the original graph."
diff --git a/notebooks/unweighted.jl b/notebooks/unweighted.jl
index f117753..6fc1613 100644
--- a/notebooks/unweighted.jl
+++ b/notebooks/unweighted.jl
@@ -82,11 +82,11 @@ show_graph(g5)
 # ╔═╡ 625bdcf4-e37e-4bb8-bd1a-907cdcc5fe24
 md"""
 #### Step 2: Map the source graph to an unweighted King's subgraph (KSG)
-The vertex order is optimized with the Branching path decomposition algorithm
+The vertex order is optimized with the Branching path decomposition algorithm (MinhThi's Trick)
 """
 
 # ╔═╡ f9e57a6b-1186-407e-a8b1-cb8f31a17bd2
-g5res = UnitDiskMapping.map_graph(g5; vertex_order=Branching())
+g5res = UnitDiskMapping.map_graph(g5; vertex_order=MinhThiTrick())
 
 # ╔═╡ e64e7ca4-b297-4c74-8699-bec4b4fbb843
 md"Visualize the mapped KSG graph in terminal"
diff --git a/src/UnitDiskMapping.jl b/src/UnitDiskMapping.jl
index 247bdbd..628f921 100644
--- a/src/UnitDiskMapping.jl
+++ b/src/UnitDiskMapping.jl
@@ -37,7 +37,9 @@ export @gg
 export is_independent_set, unitdisk_graph
 
 # path decomposition
-export pathwidth, PathDecompositionMethod, Branching, Greedy
+export pathwidth, PathDecompositionMethod, MinhThiTrick, Greedy
+
+@deprecate Branching MinhThiTrick
 
 include("utils.jl")
 include("Core.jl")
diff --git a/src/mapping.jl b/src/mapping.jl
index 4a1c4e1..1297393 100644
--- a/src/mapping.jl
+++ b/src/mapping.jl
@@ -318,16 +318,16 @@ function crossat(ug::MappingGrid, v, w)
 end
 
 """
-    embed_graph([mode,] g::SimpleGraph; vertex_order=Branching())
+    embed_graph([mode,] g::SimpleGraph; vertex_order=MinhThiTrick())
 
 Embed graph `g` into a unit disk grid, where the optional argument `mode` can be `Weighted()` or `UnWeighted`.
 The `vertex_order` can be a vector or one of the following inputs
 
     * `Greedy()` fast but non-optimal.
-    * `Branching()` slow but optimal.
+    * `MinhThiTrick()` slow but optimal.
 """
-embed_graph(g::SimpleGraph; vertex_order=Branching()) = embed_graph(UnWeighted(), g; vertex_order)
-function embed_graph(mode, g::SimpleGraph; vertex_order=Branching())
+embed_graph(g::SimpleGraph; vertex_order=MinhThiTrick()) = embed_graph(UnWeighted(), g; vertex_order)
+function embed_graph(mode, g::SimpleGraph; vertex_order=MinhThiTrick())
     if vertex_order isa AbstractVector
         L = PathDecomposition.Layout(g, collect(vertex_order[end:-1:1]))
     else
@@ -368,7 +368,7 @@ struct MappingResult{NT}
 end
 
 """
-    map_graph([mode=UnWeighted(),] g::SimpleGraph; vertex_order=Branching(), ruleset=[...])
+    map_graph([mode=UnWeighted(),] g::SimpleGraph; vertex_order=MinhThiTrick(), ruleset=[...])
 
 Map a graph to a unit disk grid graph that being "equivalent" to the original graph, and return a `MappingResult` instance.
 Here "equivalent" means a maximum independent set in the grid graph can be mapped back to
@@ -385,13 +385,13 @@ Keyword Arguments
 Different vertex orders have different path width, i.e. different depth of mapped grid graph.
 It can be a vector or one of the following inputs
     * `Greedy()` fast but not optimal.
-    * `Branching()` slow but optimal.
+    * `MinhThiTrick()` slow but optimal.
 * `ruleset` specifies and extra set of optimization patterns (not the crossing patterns).
 """
-function map_graph(g::SimpleGraph; vertex_order=Branching(), ruleset=default_simplifier_ruleset(UnWeighted()))
+function map_graph(g::SimpleGraph; vertex_order=MinhThiTrick(), ruleset=default_simplifier_ruleset(UnWeighted()))
     map_graph(UnWeighted(), g; ruleset=ruleset, vertex_order=vertex_order)
 end
-function map_graph(mode, g::SimpleGraph; vertex_order=Branching(), ruleset=default_simplifier_ruleset(mode))
+function map_graph(mode, g::SimpleGraph; vertex_order=MinhThiTrick(), ruleset=default_simplifier_ruleset(mode))
     ug = embed_graph(mode, g; vertex_order=vertex_order)
     mis_overhead0 = mis_overhead_copylines(ug)
     ug, tape = apply_crossing_gadgets!(mode, ug)
diff --git a/src/pathdecomposition/pathdecomposition.jl b/src/pathdecomposition/pathdecomposition.jl
index 8960d09..cc93781 100644
--- a/src/pathdecomposition/pathdecomposition.jl
+++ b/src/pathdecomposition/pathdecomposition.jl
@@ -1,7 +1,7 @@
 module PathDecomposition
 using Graphs
 
-export pathwidth, PathDecompositionMethod, Branching, Greedy
+export pathwidth, PathDecompositionMethod, MinhThiTrick, Greedy
 
 struct Layout{T}
     vertices::Vector{T}
@@ -78,7 +78,22 @@ Graphs.vertices(layout::Layout) = layout.vertices
 ##### Interfaces #####
 abstract type PathDecompositionMethod end
 
-struct Branching <: PathDecompositionMethod end
+"""
+    MinhThiTrick <: PathDecompositionMethod
+
+A path decomposition method based on the Branching method.
+
+In memory of Minh-Thi Nguyen, one of the main developers of this method.
+She left us in a truck accident at her 24 years old.
+- https://www.cbsnews.com/boston/news/cyclist-killed-minh-thi-nguyen-cambridge-bike-safety/
+"""
+struct MinhThiTrick <: PathDecompositionMethod end
+
+"""
+    Greedy <: PathDecompositionMethod
+
+A path decomposition method based on the Greedy method.
+"""
 Base.@kwdef struct Greedy <: PathDecompositionMethod
     nrepeat::Int = 10
 end
@@ -90,9 +105,9 @@ Compute the optimal path decomposition of graph `g`, returns a `Layout` instance
 `method` can be
 
     * Greedy(; nrepeat=10)
-    * Branching
+    * MinhThiTrick
 """
-function pathwidth(g::AbstractGraph, ::Branching)
+function pathwidth(g::AbstractGraph, ::MinhThiTrick)
     return branch_and_bound(g)
 end
 
diff --git a/test/pathdecomposition/pathdecomposition.jl b/test/pathdecomposition/pathdecomposition.jl
index f710f51..2be885d 100644
--- a/test/pathdecomposition/pathdecomposition.jl
+++ b/test/pathdecomposition/pathdecomposition.jl
@@ -16,7 +16,7 @@ using Graphs
         @test sum(length, arem) == nv(g)
     end
     g = smallgraph(:tutte)
-    res = pathwidth(g, Branching())
+    res = pathwidth(g, MinhThiTrick())
     @test vsep(res) == 6
     g = smallgraph(:tutte)
     res = pathwidth(g, Greedy(nrepeat=50))