Search results
Results from the WOW.Com Content Network
In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear ...
In the fractional set cover problem, it is allowed to select fractions of sets, rather than entire sets. A fractional set cover is an assignment of a fraction (a number in [0,1]) to each set in S {\displaystyle {\mathcal {S}}} , such that for each element x in the universe, the sum of fractions of sets that contain x is at least 1.
Instance variables are properties of that object. All instances of a class have their own copies of instance variables, even if the value is the same from one object to another. One class instance can change values of its instance variables without affecting all other instances. A class may have both instance variables and class variables.
In some languages, such as Python, Ruby or Smalltalk, a class is also an object; thus each class is an instance of a unique metaclass that is built into the language. [ 4 ] [ 35 ] [ 36 ] The Common Lisp Object System (CLOS) provides metaobject protocols (MOPs) to implement those classes and metaclasses.
A class variable is not an instance variable. It is a special type of class attribute (or class property, field, or data member). The same dichotomy between instance and class members applies to methods ("member functions") as well; a class may have both instance methods and class methods.
For the set cover problem, Lovász proved that the integrality gap for an instance with n elements is H n, the nth harmonic number. One can turn the linear programming relaxation for this problem into an approximate solution of the original unrelaxed set cover instance via the technique of randomized rounding. [2]
A variable or value of that type is usually represented as a fraction m/n where m and n are two integer numbers, either with a fixed or arbitrary precision.Depending on the language, the denominator n may be constrained to be non-zero, and the two numbers may be kept in reduced form (without any common divisors except 1).
The problem of fractional knapsack with penalties was introduced by Malaguti, Monaci, Paronuzzi and Pferschy. [44] They developed an FPTAS and a dynamic program for the problem, and they showed an extensive computational study comparing the performance of their models.