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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-18T16:08:01","documenter_version":"1.8.0"}}
{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-18T19:48:22","documenter_version":"1.8.0"}}
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result = solve_greedy_rule(branching_region, graph, vs)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">OptimalBranchingResult{BitBasis.LongLongUInt{1}, Float64}:
optimal_rule: DNF{BitBasis.LongLongUInt{1}}: (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ #5 ∧ #7 ∧ #9 ∧ ¬#11 ∧ ¬#12 ∧ ¬#15 ∧ ¬#16 ∧ ¬#19 ∧ ¬#20) ∨ (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ ¬#5 ∧ #6 ∧ #7 ∧ #9 ∧ #11 ∧ #12 ∧ ¬#13 ∧ ¬#14 ∧ ¬#15 ∧ ¬#16 ∧ ¬#19 ∧ ¬#20) ∨ (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ #5 ∧ ¬#7 ∧ #8 ∧ #9 ∧ ¬#11 ∧ ¬#12 ∧ #15 ∧ #16 ∧ ¬#17 ∧ ¬#18 ∧ ¬#19 ∧ ¬#20) ∨ (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ ¬#5 ∧ #6 ∧ ¬#7 ∧ #8 ∧ #9 ∧ #11 ∧ #12 ∧ ¬#13 ∧ ¬#14 ∧ #15 ∧ #16 ∧ ¬#17 ∧ ¬#18 ∧ ¬#19 ∧ ¬#20) ∨ (¬#1 ∧ #2 ∧ #3 ∧ ¬#4 ∧ ¬#5 ∧ ¬#6 ∧ ¬#7 ∧ ¬#8 ∧ #9 ∧ ¬#19 ∧ ¬#20) ∨ (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ #5 ∧ #7 ∧ ¬#9 ∧ #10 ∧ ¬#11 ∧ ¬#12 ∧ ¬#15 ∧ ¬#16 ∧ #19 ∧ #20 ∧ ¬#21 ∧ ¬#22) ∨ (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ ¬#5 ∧ #6 ∧ #7 ∧ ¬#9 ∧ #10 ∧ #11 ∧ #12 ∧ ¬#13 ∧ ¬#14 ∧ ¬#15 ∧ ¬#16 ∧ #19 ∧ #20 ∧ ¬#21 ∧ ¬#22) ∨ (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ #5 ∧ ¬#7 ∧ #8 ∧ ¬#9 ∧ #10 ∧ ¬#11 ∧ ¬#12 ∧ #15 ∧ #16 ∧ ¬#17 ∧ ¬#18 ∧ #19 ∧ #20 ∧ ¬#21 ∧ ¬#22) ∨ (#1 ∧ ¬#2 ∧ ¬#3 ∧ ¬#4 ∧ ¬#5 ∧ #6 ∧ ¬#7 ∧ #8 ∧ ¬#9 ∧ #10 ∧ #11 ∧ #12 ∧ ¬#13 ∧ ¬#14 ∧ #15 ∧ #16 ∧ ¬#17 ∧ ¬#18 ∧ #19 ∧ #20 ∧ ¬#21 ∧ ¬#22) ∨ (¬#1 ∧ #3 ∧ #4 ∧ ¬#7 ∧ ¬#8 ∧ ¬#9 ∧ ¬#10) ∨ (¬#1 ∧ #2 ∧ ¬#3 ∧ #4 ∧ ¬#5 ∧ ¬#6 ∧ #7 ∧ ¬#9 ∧ ¬#10 ∧ ¬#15 ∧ ¬#16)
branching_vector: [28.0, 34.0, 34.0, 40.0, 24.0, 34.0, 40.0, 40.0, 46.0, 16.0, 24.0]
γ: 1.0842073740067577</code></pre><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="../../quick-start/">« Quick Start</a><a class="docs-footer-nextpage" href="../../benchmarks/">Benchmarks »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 16:08">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
γ: 1.0842073740067577</code></pre><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="../../quick-start/">« Quick Start</a><a class="docs-footer-nextpage" href="../../benchmarks/">Benchmarks »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 19:48">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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archivePrefix={arXiv},
primaryClass={math.OC},
url={https://arxiv.org/abs/2412.07685},
}</code></pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="quick-start/">Quick Start »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 16:08">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
}</code></pre></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="quick-start/">Quick Start »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 19:48">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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Closest candidates are:
mis_size(::Graphs.AbstractGraph; branching_strategy, reducer)<span class="sgr91"> got unsupported keyword argument &quot;bs&quot;</span>
<span class="sgr90"> @</span> <span class="sgr35">OptimalBranchingMIS</span> <span class="sgr90">~/work/OptimalBranching.jl/OptimalBranching.jl/lib/OptimalBranchingMIS/src/<span class="sgr4">interfaces.jl:14</span></span></code></pre><p>The default backend is also <code>HiGHS</code>. While the result is consistent, the rule searching is usually faster.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../benchmarks/">« Benchmarks</a><a class="docs-footer-nextpage" href="../man/core/">OptimalBranchingCore »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 16:08">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<span class="sgr90"> @</span> <span class="sgr35">OptimalBranchingMIS</span> <span class="sgr90">~/work/OptimalBranching.jl/OptimalBranching.jl/lib/OptimalBranchingMIS/src/<span class="sgr4">interfaces.jl:14</span></span></code></pre><p>The default backend is also <code>HiGHS</code>. While the result is consistent, the rule searching is usually faster.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../benchmarks/">« Benchmarks</a><a class="docs-footer-nextpage" href="../man/core/">OptimalBranchingCore »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 19:48">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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Clause{BitBasis.LongLongUInt{1}}: ¬#4</code></pre><p>For each candidate clause, we calculate the size reduction of the problem after applying the clause. Here, we use a simple measure: counting the number of variables eliminated by the clause.</p><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; Δρ = [length(literals(sc)) for sc in candidates]; println(Δρ)</code><code class="nohighlight hljs ansi" style="display:block;">[2, 5, 2, 1, 5, 4, 5, 5, 2, 2, 5, 1, 4, 1]</code></pre><p>Finally, we solve the set cover problem to find the optimal branching rule. The solver is set to be the <a href="../man/core/#OptimalBranchingCore.IPSolver"><code>IPSolver</code></a>. For more options, please refer to the <a href="../performance_tips/#Performance-Tips">Performance Tips</a> section.</p><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; res_ip = OptimalBranchingCore.minimize_γ(tbl, candidates, Δρ, IPSolver())</code><code class="nohighlight hljs ansi" style="display:block;">OptimalBranchingResult{BitBasis.LongLongUInt{1}, Int64}:
optimal_rule: DNF{BitBasis.LongLongUInt{1}}: (¬#1 ∧ ¬#3 ∧ #4 ∧ ¬#5) ∨ (¬#1 ∧ ¬#2 ∧ #3 ∧ ¬#4 ∧ #5) ∨ (#1 ∧ #2 ∧ #3 ∧ ¬#4 ∧ ¬#5)
branching_vector: [4, 5, 5]
γ: 1.2671683045421243</code></pre><p>The result is an instance of <a href="../man/core/#OptimalBranchingCore.OptimalBranchingResult"><code>OptimalBranchingResult</code></a>, which contains the selected clauses, the optimal branching rule, and the branching vector.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../generated/rule_discovery/">Automatic rule discovery »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 16:08">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
γ: 1.2671683045421243</code></pre><p>The result is an instance of <a href="../man/core/#OptimalBranchingCore.OptimalBranchingResult"><code>OptimalBranchingResult</code></a>, which contains the selected clauses, the optimal branching rule, and the branching vector.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../generated/rule_discovery/">Automatic rule discovery »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 18 January 2025 19:48">Saturday 18 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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