# Questions tagged [linear-programming]

Optimization with a linear objective function, subject to linear equality and linear inequality constraints.

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### Questions about Amdahl's law?

Doing exam papers now and I came across two questions which I cannot get my head around sadly. Both are regarding Amdahl's law and Parallel Computing but they seem rather simple and frustratingly ...
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### Choose N pairs of (job, time slot) with a constraint on the number of different jobs

I am making a solver to choose the best assignment to a set of people for an event, given their availability (chosen in a set $T$ of time slots), jobs preferences (among $J$ possible jobs) and some of ...
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### Comparing dual of a canonical primal program - Directly and by dual of the standard program

I have it as a homework question to compare dual programs in the following way: Take a canonical program and write its dual Take the same canonical program, write it as a standard program, take the ...
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### Efficient formulation for binary integer linear programming

Problem: There are two types of balls, big (B) and small (S), which need to packed into boxes. One box can contain either: nothing, or 1 S, or 1 B, or 2 S, or 2 B, or 1 B and 2 S We are given the ...
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### Find value of b

The following system of restrictions is given: $$y_1+ 2 y_2 \leq 4 \\ 2y_1+y_2 \leq 2 \\ y_1+b y_2 \leq 3 \\ y_1, y_2 \geq 0$$ For which values of b is there a degenarate basic feasible solution? ...
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### Does there exist a problem that is hard to do in parallel? [closed]

I am looking for a workload which is hard to paralellise/distribute between multiple machines. For example, integer factorization does not go 10 times faster if you have 10 machines to split the ...
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### Introduction to Linear Optimization: Driving the artificial variables out of the basis (case: no entries in the $j$-row are nonzero)

Reading the book Introduction to Linear Optimization by Bertsimas and Tsiklisis, I've come across the following subject: Driving the artificial variables out of the basis. The description is as ...
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### Why does absence of strongly polynomial time algorithm for LP imply restriction to rational instances?

From Bernhard Korte, Jens Vygen, Combinatorial Optimization, Instances of LINEAR PROGRAMMING are vectors and matrices. Since no strongly polynomial-time algorithm for LINEAR PROGRAMMING is known ...
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### Constrain traveling salesman: visit a given city within a given distance from start

I would like to add an additional constraint to the traveling salesman problem: that a given city is visited within a given distance (say 100) from start. Is there ...
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### Integrality gap and LP-rounding

I have a doubt about integrality gap. If I know that there is no integrality gap for a given problem, i.e.: $$\frac{\mathrm{OPT}(\mathrm{ILP})}{\mathrm{OPT}(\mathrm{LP})} = 1 \text{ (right?)},$$ ...
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### Determine aproximation factor in a greedy algorithm

Suppose we have n food dishes associated to a cost c, and we have i guests such that each one of them has a certain number of preferences. We want to choose a menu such that we minimize the cost and ...
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