Why it matters

MIS solves scheduling, packing. Understanding shapes NP-hard problems.

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The architecture

MIS(G) = MaxClique(G-complement).

Branch-and-bound with pruning.

Bipartite: polynomial via matching.

MIS approachesMIS problemno adjacent in setReduce= max clique in complementSpecial classesbipartite polynomialBy König's theorem, MIS = V - max matching on bipartite graphs
MIS.
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How it works end to end

Branch on vertex: include or exclude.

Include: remove neighbors.

Prune with upper bounds.

Bipartite: König's theorem.