Linear Decision Trees: Volume Estimates and Topological Bounds

Abstract. We describe two methods for estimating the size and depth of decision trees where a linear test is performed at each node. Both methods are applied to the question of deciding, by a linear decision tree, whether given n real numbers, some k of them are equal. We show that the minimum depth of a linear decision tree for this problem is (nlog(n/k)). The upper bound is easy; the lower bound can be established for k = O(n1/4) by a volume argument; for the whole range, however, our proof is more complicated and it involves the use of some topology as well as the theory of M

• Type: Conference
• Year: 1992
• Where: STOC
• Authors: Anders Björner, László Lovász, Andrew Chi-Chih Yao
• Keywords: Algorithms, Decision Tree, Linear Decision Tree, Linear Test, STOC 1992