Geometric Separator Theorems & Applications
نویسندگان
چکیده
| We nd a large number of \geometric separator theorems" such as: I: Given N disjoint iso-oriented squares in the plane, there exists a rectangle with 2N=3 squares inside, 2N=3 squares outside, and (4 + o(1)) p N partly in & out. II: There exists a rectangle that is crossed by the minimal spanning tree of N sites in the plane at (4 3 1=4 + o(1)) p N points, having 2N=3 sites inside and outside. These theorems yield a large number of applications, such as subexpo-nential algorithms for traveling salesman tour and rec-tilinear Steiner minimal tree in R d , new point location algorithms, and new upper and lower bound proofs for \planar separator theorems."
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