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Questions tagged [optimization]

general questions about selecting a best element from some set of available alternatives.

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computing the minimal NFA for a DFA

Many years ago I heard that computing the minimal NFA (nondeterministic finite automaton) from a DFA (deterministic) was an open question, as opposed to the vice versa direction which has been known ...
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What classes of mathematical programs can be solved exactly or approximately, in polynomial time?

I am rather confused by the continuous optimization literature and TCS literature about which types of (continuous) mathematical programs (MPs) can be solved efficiently, and which cannot. The ...
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Approximation algorithms for min vector subset-sum over GF(2)

In this question vzn asked about the following problem, which I'll call Vector-Subset-Sum. Given a set of vectors $v_i$ over GF(2) and a target vector $y$, is there a subset of the $v_i$ summing to ...
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Iteratively minimizing the function

Consider the problem $$\min_{x\in X, y \in Y} f(x,y)$$ Can I solve the problem by iteratively solving the following two sub problems? x_{k+1} = \arg\...
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minimal finite automata given in-words and out-words

this seems an interesting FSM optimization problem; have not seen it studied, wondering if it has been and/ or looking for other insight. given: two finite sets of words $S_{in}$ and $S_{out}$. ...
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Optimization problems with minimax characterization, but no polynomial-time algorithm

Consider optimization problems of the following form. Let $f(x)$ be a polynomial-time computable function that maps a string $x$ into a rational number. The optimization problem is this: what is the ...
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Solving semidefinite programs in polynomial time

We know that linear programs (LP) can be solved exactly in polynomial time using the ellipsoid method or an interior point method like Karmarkar's algorithm. Some LPs with super-polynomial (...
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Second Smallest $s$-$t$-Cut in a Network

Is anything known about the second smallest $s$-$t$-cut in a flow network? Or, more general, about this problem: Input: A network $N$ and a number $k$, all in binary. Output: A $k$th smallest $s$-...
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1 vote
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Is the matching polytope integral?

In this document https://courses.engr.illinois.edu/cs598csc/sp2010/Lectures/Lecture9.pdf they prove the integrality of the matching polytope using the integrality of the perfect matching polytope. The ...
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