build based on a571d02

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-25T19:14:44","documenter_version":"1.0.1"}}
+{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-25T20:20:03","documenter_version":"1.0.1"}}

dev/generated/Coloring/index.html

@@ -5,7 +5,7 @@
 
 locations = [[rot15(0.0, 2.0, i) for i=0:4]..., [rot15(0.0, 1.0, i) for i=0:4]...]
 
-show_graph(graph; locs=locations, format=:svg)</code></pre><img src="48da499f.svg" alt="Example block output"/><h2 id="Generic-tensor-network-representation"><a class="docs-heading-anchor" href="#Generic-tensor-network-representation">Generic tensor network representation</a><a id="Generic-tensor-network-representation-1"></a><a class="docs-heading-anchor-permalink" href="#Generic-tensor-network-representation" title="Permalink"></a></h2><p>We construct the tensor network for the 3-coloring problem as</p><pre><code class="language-julia hljs">problem = Coloring{3}(graph);</code></pre><h3 id="Theory-(can-skip)"><a class="docs-heading-anchor" href="#Theory-(can-skip)">Theory (can skip)</a><a id="Theory-(can-skip)-1"></a><a class="docs-heading-anchor-permalink" href="#Theory-(can-skip)" title="Permalink"></a></h3><p>Type <a href="../../ref/#GenericTensorNetworks.Coloring"><code>Coloring</code></a> can be used for constructing the tensor network with optimized contraction order for a coloring problem. Let us use 3-coloring problem defined on vertices as an example. For a vertex <span>$v$</span>, we define the degrees of freedom <span>$c_v\in\{1,2,3\}$</span> and a vertex tensor labelled by it as</p><p class="math-container">\[W(v) = \left(\begin{matrix}
+show_graph(graph; locs=locations, format=:svg)</code></pre><img src="562ae81f.svg" alt="Example block output"/><h2 id="Generic-tensor-network-representation"><a class="docs-heading-anchor" href="#Generic-tensor-network-representation">Generic tensor network representation</a><a id="Generic-tensor-network-representation-1"></a><a class="docs-heading-anchor-permalink" href="#Generic-tensor-network-representation" title="Permalink"></a></h2><p>We construct the tensor network for the 3-coloring problem as</p><pre><code class="language-julia hljs">problem = Coloring{3}(graph);</code></pre><h3 id="Theory-(can-skip)"><a class="docs-heading-anchor" href="#Theory-(can-skip)">Theory (can skip)</a><a id="Theory-(can-skip)-1"></a><a class="docs-heading-anchor-permalink" href="#Theory-(can-skip)" title="Permalink"></a></h3><p>Type <a href="../../ref/#GenericTensorNetworks.Coloring"><code>Coloring</code></a> can be used for constructing the tensor network with optimized contraction order for a coloring problem. Let us use 3-coloring problem defined on vertices as an example. For a vertex <span>$v$</span>, we define the degrees of freedom <span>$c_v\in\{1,2,3\}$</span> and a vertex tensor labelled by it as</p><p class="math-container">\[W(v) = \left(\begin{matrix}
     1\\
     1\\
     1
@@ -20,9 +20,9 @@
 vertex_color_map = Dict(0=&gt;&quot;red&quot;, 1=&gt;&quot;green&quot;, 2=&gt;&quot;blue&quot;)
 
 show_graph(graph; locs=locations, format=:svg, vertex_colors=[vertex_color_map[Int(c)]
-     for c in single_solution.c.data])</code></pre><img src="6948b7a5.svg" alt="Example block output"/><p>Let us try to solve the same issue on its line graph, a graph that generated by mapping an edge to a vertex and two edges sharing a common vertex will be connected.</p><pre><code class="language-julia hljs">linegraph = line_graph(graph)
+     for c in single_solution.c.data])</code></pre><img src="c2dd93f2.svg" alt="Example block output"/><p>Let us try to solve the same issue on its line graph, a graph that generated by mapping an edge to a vertex and two edges sharing a common vertex will be connected.</p><pre><code class="language-julia hljs">linegraph = line_graph(graph)
 
 show_graph(linegraph; locs=[0.5 .* (locations[e.src] .+ locations[e.dst])
-     for e in edges(graph)], format=:svg)</code></pre><img src="e6ffa2e3.svg" alt="Example block output"/><p>Let us construct the tensor network and see if there are solutions.</p><pre><code class="language-julia hljs">lineproblem = Coloring{3}(linegraph);
+     for e in edges(graph)], format=:svg)</code></pre><img src="beec6420.svg" alt="Example block output"/><p>Let us construct the tensor network and see if there are solutions.</p><pre><code class="language-julia hljs">lineproblem = Coloring{3}(linegraph);
 
-num_of_coloring = solve(lineproblem, CountingMax())[]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(28.0, 1800.0)ₜ</code></pre><p>You will see the maximum size 28 is smaller than the number of edges in the <code>linegraph</code>, meaning no solution for the 3-coloring on edges of a Petersen graph.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../PaintShop/">« Binary paint shop problem</a><a class="docs-footer-nextpage" href="../DominatingSet/">Dominating set problem »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.0.1 on <span class="colophon-date" title="Monday 25 September 2023 19:14">Monday 25 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+num_of_coloring = solve(lineproblem, CountingMax())[]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(28.0, 1800.0)ₜ</code></pre><p>You will see the maximum size 28 is smaller than the number of edges in the <code>linegraph</code>, meaning no solution for the 3-coloring on edges of a Petersen graph.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../PaintShop/">« Binary paint shop problem</a><a class="docs-footer-nextpage" href="../DominatingSet/">Dominating set problem »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.0.1 on <span class="colophon-date" title="Monday 25 September 2023 20:20">Monday 25 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>