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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Knapsack problem with value range constraint
The traditional knapsack problem is that: given a sequence of $i$ items with positive weights $w_1,w_2,...,w_i$, positive values $v_1,v_2,...,v_i$, and a bag with capacity $B$, we want to insert items …
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Is this variant of knapsack problem strongly NP-hard?
Suppose we have a sequence of containers each of which contains multiple items. Each item $I_i$ is associated with an nonnegative weight $w_i$, a nonnegative value $v_i$, and $I_i(C)$ denotes the ID o …
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Knapsack problem with capacity constraint
The traditional knapsack problem is that: given a sequence of $i$ items with positive weights $w_1,w_2,...,w_i$, positive values $v_1,v_2,...,v_i$, and a bag with capacity $B$, we want to insert items …