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Consider a graph G=(V,E) of order n. In the minimum graph-coloring problem we try to color V with as few colors as possible so that no two adjacent vertices receive the same color. This problem is among the first ones proved to be intractable, and hence, it is very unlikely that an optimal polynomial-time algorithm could ever be devised for it. In this paper, we survey the main polynomial time approximation...
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the diffusion is large enough, then there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the boundary-value problem under consideration. Furthermore,...
This paper considers the inverse 1-center location problem with edge length augmentation on a tree network T with n + 1 vertices. The goal is to increase the edge lengths at minimum total cost subject to given modification bounds such that a predetermined vertex s becomes an absolute 1-center under the new edge lengths. Using a set of suitably extended AVL-search trees we develop a combinatorial algorithm...
It was previously shown that the problem of verifying whether a finite concurrent system is linearizable can be done with an $$\mathsf{EXPSPACE}$$ EXPSPACE complexity. However, the best known lower bound is $$\mathsf{PSPACE}$$ PSPACE -hardness, and can be obtained using a reduction from control-state reachability to linearizability. In this paper, we close the complexity gap between the...
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