You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
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.
76
+
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.
77
77
A good vertex order can reduce the depth of the mapped graph."
md"The field `lines` is a vector of copy gadgets arranged in a `⊢` shape. These copy gadgets form a *crossing lattice*, in which two copy lines cross each other whenever their corresponding vertices in the source graph are connected by an edge.
94
96
```
@@ -121,7 +123,7 @@ unweighted_res.mis_overhead
121
123
md"We can solve the mapped graph with [`GenericTensorNetworks`](https://queracomputing.github.io/GenericTensorNetworks.jl/dev/)."
122
124
123
125
# ╔═╡ f084b98b-097d-4b33-a0d3-0d0a981f735e
124
-
res =solve(IndependentSet(SimpleGraph(unweighted_res.grid_graph)), SingleConfigMax())[]
126
+
res =solve(GenericTensorNetwork(IndependentSet(SimpleGraph(unweighted_res.grid_graph))), SingleConfigMax())[]
125
127
126
128
# ╔═╡ 86457b4e-b83e-4bf5-9d82-b5e14c055b4b
127
129
md"You might want to read [the documentation page of `GenericTensorNetworks`](https://queracomputing.github.io/GenericTensorNetworks.jl/dev/) for a detailed explanation on this function. Here, we just visually check the solution configuration."
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."
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."
@@ -180,7 +182,7 @@ md"Now that we have both the graph and the weights, let us solve the mapped prob
@@ -107,7 +107,7 @@ md"#### Step 3: Solve the MIS size of the mapped graph"
107
107
md"The independent set size can be obtained by solving the `SizeMax()` property using the [generic tensor network](https://github.com/QuEraComputing/GenericTensorNetworks.jl) method."
0 commit comments