3,577 research outputs found
Cop and robber game and hyperbolicity
In this note, we prove that all cop-win graphs G in the game in which the
robber and the cop move at different speeds s and s' with s'<s, are
\delta-hyperbolic with \delta=O(s^2). We also show that the dependency between
\delta and s is linear if s-s'=\Omega(s) and G obeys a slightly stronger
condition. This solves an open question from the paper (J. Chalopin et al., Cop
and robber games when the robber can hide and ride, SIAM J. Discr. Math. 25
(2011) 333-359). Since any \delta-hyperbolic graph is cop-win for s=2r and
s'=r+2\delta for any r>0, this establishes a new - game-theoretical -
characterization of Gromov hyperbolicity. We also show that for weakly modular
graphs the dependency between \delta and s is linear for any s'<s. Using these
results, we describe a simple constant-factor approximation of the
hyperbolicity \delta of a graph on n vertices in O(n^2) time when the graph is
given by its distance-matrix
Instruction Set Architectures for Quantum Processing Units
Progress in quantum computing hardware raises questions about how these
devices can be controlled, programmed, and integrated with existing
computational workflows. We briefly describe several prominent quantum
computational models, their associated quantum processing units (QPUs), and the
adoption of these devices as accelerators within high-performance computing
systems. Emphasizing the interface to the QPU, we analyze instruction set
architectures based on reduced and complex instruction sets, i.e., RISC and
CISC architectures. We clarify the role of conventional constraints on memory
addressing and instruction widths within the quantum computing context.
Finally, we examine existing quantum computing platforms, including the D-Wave
2000Q and IBM Quantum Experience, within the context of future ISA development
and HPC needs.Comment: To be published in the proceedings in the International Super
Computing Conference 2017 publicatio
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