Near-optimal Linear Decision Trees for k-SUM and Related Problems
Skip to main content
Open Access Publications from the University of California

UC San Diego

UC San Diego Previously Published Works bannerUC San Diego

Near-optimal Linear Decision Trees for k-SUM and Related Problems

  • Author(s): Kane, Daniel M
  • Lovett, Shachar
  • Moran, Shay
  • et al.

Published Web Location

We construct near-optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant k , we construct linear decision trees that solve the k -SUM problem on n elements using O ( n log 2 n ) linear queries. Moreover, the queries we use are comparison queries, which compare the sums of two k -subsets; when viewed as linear queries, comparison queries are 2 k -sparse and have only { −1,0,1} coefficients. We give similar constructions for sorting sumsets A+B and for solving the SUBSET-SUM problem, both with optimal number of queries, up to poly-logarithmic terms. Our constructions are based on the notion of “inference dimension,” recently introduced by the authors in the context of active classification with comparison queries. This can be viewed as another contribution to the fruitful link between machine learning and discrete geometry, which goes back to the discovery of the VC dimension.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View