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Efficient solutions to general Bézout’s identity $a_1 b_1 + \dots + a_n b_n = 1$

Suppose I have integers $a_1, \dots, a_n$ which are coprime, meaning that $$a_1 b_1 + \dots + a_n b_n = 1$$ has a solution in integers $b_1, \dots, b_n$. I would like to get a bound saying ...
Kim's user avatar
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2 votes
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103 views

What does Lenstra's MILP do?

Honestly I do not understand why Lenstra's MILP is in $P$ if the number of integer dimensions is fixed. Here is what Lenstra says in 'http://people.csail.mit.edu/rrw/presentations/Lenstra81.pdf' in ...
Turbo's user avatar
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2 votes
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Reference request: Edmond's Algorithm for integer hull

I'm looking for a good reference for the algorithm (supposedly by Edmonds) to compute the integer hull of a polytope, not by cutting plane methods but by starting with a set of integer points and then ...
Richard's user avatar
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1 vote
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Complexity of Nested Linear Optimization

My question is motivated by the fact, that among other ways, it is possible to restrict a variable to two discrete values, e.g. the prototypical $0$ and $1$, via an optimization constraint: $$\max(\...
Manfred Weis's user avatar
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