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2. Karmarkar–Karp bin packing algorithms - Wikipedia

   en.wikipedia.org/wiki/Karmarkar–Karp_bin...

   2-a. Let be an instance constructed from by grouping items and rounding the size of items in each group to the highest item in the group. 3-a. Construct the configuration linear program for , without the integrality constraints. 4. Compute a (fractional) solution x for the relaxed linear program. 3-b.

3. Fractional programming - Wikipedia

   en.wikipedia.org/wiki/Fractional_programming

   In mathematical optimization, fractional programming is a generalization of linear-fractional programming. The objective function in a fractional program is a ratio of two functions that are in general nonlinear.

4. Bin packing problem - Wikipedia

   en.wikipedia.org/wiki/Bin_packing_problem

   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.

5. Linear-fractional programming - Wikipedia

   en.wikipedia.org/wiki/Linear-fractional_programming

   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 ...

6. Python (programming language) - Wikipedia

   en.wikipedia.org/wiki/Python_(programming_language)

   Since 7 October 2024, Python 3.13 is the latest stable release, and it and, for few more months, 3.12 are the only releases with active support including for bug fixes (as opposed to just for security) and Python 3.9, [55] is the oldest supported version of Python (albeit in the 'security support' phase), due to Python 3.8 reaching end-of-life.

7. Partition problem - Wikipedia

   en.wikipedia.org/wiki/Partition_problem

   An instance of SubsetSum consists of a set S of positive integers and a target sum T; the goal is to decide if there is a subset of S with sum exactly T. Given such an instance, construct an instance of Partition in which the input set contains the original set plus two elements: z 1 and z 2, with z 1 = sum(S) and z 2 = 2T.

8. Best brokers for buying fractional shares in May 2024 - AOL

   www.aol.com/finance/best-brokers-fractional...

   Fractional purchases: Only Vanguard in mutual funds and ETFs. Fractional dividend reinvestment: Yes. Securities in the program: Stocks, ETFs and mutual funds. Tastytrade.

9. Fixed-point arithmetic - Wikipedia

   en.wikipedia.org/wiki/Fixed-point_arithmetic

   A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...