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Set-Union Knapsack Problem: SUKP is defined by Kellerer et al [ 2 ] (on page 423) as follows: Given a set of n {\displaystyle n} items N = { 1 , … , n } {\displaystyle N=\{1,\ldots ,n\}} and a set of m {\displaystyle m} so-called elements P = { 1 , … , m } {\displaystyle P=\{1,\ldots ,m\}} , each item j {\displaystyle j} corresponds to a ...
The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of n {\displaystyle n} items numbered from 1 up to n {\displaystyle n} , each with a weight w i {\displaystyle w_{i}} and a value v i {\displaystyle v_{i}} , along with a maximum weight capacity ...
Viewing a decision problem as a formal language in some fixed encoding, the set NPC of all NP-complete problems is not closed under: union; intersection; concatenation; Kleene star [example needed] It is not known whether NPC is closed under complementation, since NPC=co-NPC if and only if NP=co-NP, and since NP=co-NP is an open question. [16]
Set covering is equivalent to the hitting set problem. That is seen by observing that an instance of set covering can be viewed as an arbitrary bipartite graph , with the universe represented by vertices on the left, the sets represented by vertices on the right, and edges representing the membership of elements to sets.
The bin packing problem can also be seen as a special case of the cutting stock problem. When the number of bins is restricted to 1 and each item is characterized by both a volume and a value, the problem of maximizing the value of items that can fit in the bin is known as the knapsack problem.
Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given:
One man who filled up his 2022 Jeep Wagoneer Jan. 19 at the Circle K told WOIO he didn't notice any problems until the following day. When he went to start his vehicle, "it just started sputtering.
A knapsack auction is an auction in which several identical items are sold, and there are several bidders with different valuations interested in different amounts of items. The goal is to choose a subset of the bidders with a total demand, at most, the number of items and, subject to that, a maximum total value.