O'Rourke Chapter 7: Search & Intersection in PDF - Computer Science
O'Rourke Chapter 7: Search & Intersection in PDF - Computer Science
O'Rourke Chapter 7: Search & Intersection in PDF - Computer Science
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Extremal Polytope Queries<br />
Details<br />
source: O’Rourke<br />
Maximum Independent Set is NP-complete,<br />
but greedy heuristic performs well.<br />
Choose vertex of lowest degree, not<br />
adjacent to vertices already chosen.<br />
Algorithm 7.4: : INDEPENDENT SET<br />
Input: : graph G<br />
Output: : <strong>in</strong>dependent set I<br />
I 0<br />
Mark all nodes of G of degree >= 9<br />
while some nodes rema<strong>in</strong> unmarked<br />
do<br />
Choose an unmarked node v<br />
Mark v and all neighbors of v<br />
I I U {v}<br />
spurious<br />
edge<br />
Goal: tetrahedron<br />
triangulate<br />
polytope: lt use convex hll hull<br />
(d) octahedron<br />
(a) Icosahedron<br />
Schlegel<br />
diagram: 5<br />
triangles meet at<br />
each vertex.<br />
There exist at least n/2 vertices of degree<br />
at most 8 (derivation<br />
derivation).<br />
An <strong>in</strong>dependent set of a polytope graph of n vertices<br />
produced by INDEPENDENT SET has size at least n/18 (derivation).
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