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What (who) is caterer's problem - definition
SEQUENCE OF INTEGERS
Circle cutting problem; Lazy caterer sequence; Central polygonal numbers; Lazy Caterer's Sequence; A000124
.gif?width=200 "The maximum number of pieces from consecutive cuts are the numbers in the Lazy Caterer's Sequence.")
Knapsack problem
![multiple constrained problem]] could consider both the weight and volume of the boxes. <br />(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all except for the green box.)](https://commons.wikimedia.org/wiki/Special:FilePath/Knapsack.svg?width=200 "multiple constrained problem]] could consider both the weight and volume of the boxes. <br />(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all except for the green box.)")
PROBLEM IN COMBINATORIAL OPTIMIZATION
0/1 knapsack problem; 0-1 knapsack problem; Unbounded knapsack problem; Unbounded Knapsack Problem; Binary knapsack problem; Napsack problem; Backpack problem; 0-1 Knapsack problem; Integer knapsack problem; Knapsack Problem; Algorithms for solving knapsack problems; Methods for solving knapsack problems; Approximation algorithms for the knapsack problem; Bounded knapsack problem; Multiple knapsack problem; Rucksack problem; Computational complexity of the knapsack problem
The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
0/1 knapsack problem
PROBLEM IN COMBINATORIAL OPTIMIZATION
0/1 knapsack problem; 0-1 knapsack problem; Unbounded knapsack problem; Unbounded Knapsack Problem; Binary knapsack problem; Napsack problem; Backpack problem; 0-1 Knapsack problem; Integer knapsack problem; Knapsack Problem; Algorithms for solving knapsack problems; Methods for solving knapsack problems; Approximation algorithms for the knapsack problem; Bounded knapsack problem; Multiple knapsack problem; Rucksack problem; Computational complexity of the knapsack problem
<application> The knapsack problem restricted so that the
number of each item is zero or one.
(1995-03-13)
knapsack problem
PROBLEM IN COMBINATORIAL OPTIMIZATION
0/1 knapsack problem; 0-1 knapsack problem; Unbounded knapsack problem; Unbounded Knapsack Problem; Binary knapsack problem; Napsack problem; Backpack problem; 0-1 Knapsack problem; Integer knapsack problem; Knapsack Problem; Algorithms for solving knapsack problems; Methods for solving knapsack problems; Approximation algorithms for the knapsack problem; Bounded knapsack problem; Multiple knapsack problem; Rucksack problem; Computational complexity of the knapsack problem
<application, mathematics> Given a set of items, each with a
cost and a value, determine the number of each item to include
in a collection so that the total cost is less than some given
cost and the total value is as large as possible.
The 0/1 knapsack problem restricts the number of each items to
zero or one.
Such constraint satisfaction problems are often solved using
dynamic programming.
The general knapsack problem is NP-hard, and this has led to
attempts to use it as the basis for public-key encryption
systems. Several such attempts failed because the knapsack
problems they produced were in fact solvable by
polynomial-time algorithms.
[Are there any trusted knapsack-based public-key
cryptosystems? ].
(1995-04-10)
Wikipedia
Lazy caterer's sequence
The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point inside the circle, but up to seven if they do not. This problem can be formalized mathematically as one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, see arrangement of hyperplanes.
The analogue of this sequence in three dimensions is the cake numbers.
