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Near-optimal linear decision trees for k-SUM and related problems
[article]
2017
arXiv
pre-print
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 ^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 2k-sparse and have only {-1,0,1} coefficients. We give similar constructions for
arXiv:1705.01720v1
fatcat:nut5sxgzybdkxpqakm2r7bg2ui