 
Summary: Approximation Schemes for Degreerestricted
MST and RedBlue Separation Problem
Sanjeev Arora # Kevin L. Chang +
Abstract
We develop a quasipolynomial time approximation scheme for
the Euclidean version of the Degreerestricted MST problem by adapt
ing techniques used previously by Arora for approximating TSP.
Given n points in the plane, d = 3 or 4, and # > 0, the scheme finds
an approximation with cost within 1+# of the lowest cost spanning
tree with the property that all nodes have degree at most d.
We also develop a polynomial time approximation scheme for
the Euclidean version of the RedBlue Separation Problem, again
extending Arora's techniques. Given # > 0, the scheme finds an
approximation with cost within 1 + # of the cost of the optimum
separating polygon of the input nodes, in nearly linear time.
# arora@cs.princeton.edu. Princeton University, Princeton, NJ. Supported by
David and Lucille Packard Fellowship, and NSF Grants CCR0098180 and CCR009818.
Work done partially while visiting the CS Dept at UC Berkeley.
+ kevinc@cs.yale.edu. Yale University, New Haven, CT.
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