Add to ORKGWe show that the decision problem of determining whether a given (abstract simplicial) k-complex has a geometric embedding in Rd is complete for the Existential Theory of the Reals for all d≥3 and k∈{d−1,d}. This implies that the problem is polynomial time equivalent to determining whether a polynomial equation system has a real solution. Moreover, this implies NP-hardness and constitutes the first hardness results for the algorithmic problem of geometric embedding (abstract simplicial) complexes
In the study of geometric problems, the complexity class ∃ R plays a crucial role since it exhibits ...
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whe...
In this article we give an explicit algorithm which will determine, in a discrete and computable way...
We show that the decision problem of determining whether a given (abstract simplicial) k-complex has...
We show that the decision problem of determining whether a given (abstract simplicial) k-complex has...
We show that the decision problem of determining whether a given (abstract simplicial) k-complex has...
We consider the following decision problem EMBEDk→d in computational topology (where k ≤ d are fixed...
It is proved that the decision problem about existence of an embedding of face-width 3 of a given gr...
International audienceWe consider the problem of deciding whether an input graph G admits a topologi...
International audienceWe consider the embeddability problem of a graph G into a two-dimensional simp...
We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is...
AbstractThere exist very efficient algorithms to decide whether a graph is planar. How difficult can...
n this article we give an explicit algorithm which will determine, in a discrete and computable way,...
We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial comple...
AbstractWe show that the problem of recognising a partitionable simplicial complex is a member of th...
In the study of geometric problems, the complexity class ∃ R plays a crucial role since it exhibits ...
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whe...
In this article we give an explicit algorithm which will determine, in a discrete and computable way...
We show that the decision problem of determining whether a given (abstract simplicial) k-complex has...
We show that the decision problem of determining whether a given (abstract simplicial) k-complex has...
We show that the decision problem of determining whether a given (abstract simplicial) k-complex has...
We consider the following decision problem EMBEDk→d in computational topology (where k ≤ d are fixed...
It is proved that the decision problem about existence of an embedding of face-width 3 of a given gr...
International audienceWe consider the problem of deciding whether an input graph G admits a topologi...
International audienceWe consider the embeddability problem of a graph G into a two-dimensional simp...
We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is...
AbstractThere exist very efficient algorithms to decide whether a graph is planar. How difficult can...
n this article we give an explicit algorithm which will determine, in a discrete and computable way,...
We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial comple...
AbstractWe show that the problem of recognising a partitionable simplicial complex is a member of th...
In the study of geometric problems, the complexity class ∃ R plays a crucial role since it exhibits ...
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whe...
In this article we give an explicit algorithm which will determine, in a discrete and computable way...