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Lecture Notes in Computer Science
We consider the problem of designing a near-optimal linear decision tree to classify two given point sets B and W in n . A linear decision tree de nes a polyhedral subdivision of space; it is a classi er if no leaf region contains points from both sets. We show hardness results for computing such a classi er with approximately optimal depth or size in polynomial-time. In particular, we show that unless NP=ZPP, the depth of a classi er cannot be approximated within any constant factor, and thatdoi:10.1007/3-540-61332-3_161 fatcat:ycr7nx2wkjextmoyw3uj36z2tq