Sums of lexicographically ordered sets
Given a set \(A=\{a_ 1,..,a_ n\}\) of distinct positive integers where \(a_ i<a_{i+1}\), \(i=1,...,n-1\). The knapsack problem on A is the problem of determining for any integer b whether b can be expressed as a sum of distinct elements and, if so, of identifying such elements. The authors consider the problem of determining sets A which are knapsack- solvable in linear time (for any integer b) and where the largest element is as small as possible. This is done by studying the condition that the k-subsets (for fixed k) of A when lexicographically ordered have increasing sums, and by constructing such sets.
scientific article; zbMATH DE number 4145662