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Questions tagged [simplex]

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4 votes
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Higher dimensional automata?

An NFA is just the data of a labelled, directed multigraph with a accepting predicate over the vertices. Simplicial sets generalize directed multigraphs by allowing the existence of higher dimensional ...
Steven Schaefer's user avatar
4 votes
0 answers
193 views

LP-type vs. Approximation

I'm interested in an computational geometry problem that's sensibly expressed as an infinite dimensional 0-1 integer program. I'm not worried about finding an actual minimum for the objective ...
Jeff Burdges's user avatar
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3 votes
0 answers
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Using Baire Category to analyze the efficiency of the Simplex Method

I read from the wiki page of the Simplex Algorithm that we can "use Baire category theory from general topology, and to show that (topologically) "most" matrices can be solved by the ...
Ruiyuan Huang's user avatar
3 votes
1 answer
267 views

Generating points uniformly distributed over the SURFACE of a standard simplex

I would like to generate points that are uniformly distributed over the SURFACE of a standard $k$-simplex ($k$ dimensions, $k+1$ vertices). One way to efficiently generate points that are uniformly ...
okj's user avatar
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1 vote
0 answers
116 views

Is this proof of $LP$ being in $coNP$ correct?

I am referring to the natural decision version of the Linear Programming problem: given $A \in \mathbb{Q}^{m \times n}, \ b \in \mathbb{Q}^m, \ c \in \mathbb{Q}^n, \ \alpha \in \mathbb{Q}$, does there ...
reservoir's user avatar
1 vote
0 answers
359 views

Does simplex algorithm run in polynomial on Bipartite Perfect matching polytope?

It is well known that simplex algorithm runs in exponential time in worst case. However are there situations (necessary and sufficient conditions) where simplex algorithm runs in polynomial time? In ...
Turbo's user avatar
  • 13k
1 vote
0 answers
241 views

Optimizing along a cube $s=\{0,1\}^n$

I am doing an optimization on a n-dimensional cube. That means that every solution is a set of $0$ and $1$, hence $s=\{0,1\}^n$. Most optimization algorithms though need a differential to work. E.g. ...
tarrasch's user avatar
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0 votes
0 answers
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Using Simplex for Difference Logic

I'm interested in what happens when using the Simplex algorithm on Difference logic, inspired by problem 5.4 in Kroening and Strichman's Decision Procedures. Clearly, in this case, all constraints of ...
Jova's user avatar
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