论文标题
拥塞网络中加权直径和半径的量子复杂性
Quantum Complexity of Weighted Diameter and Radius in CONGEST Networks
论文作者
论文摘要
本文研究了计算量子通讯模型中图的加权直径和半径的圆形复杂性。我们提出了一种$（1+o（1））$的量子算法 - 与圆形复杂性$ \ widetilde o \ left（\ min \ left \ left \ {n^{9/10} d^{3/10}，n \ right \} \ right \ right）$，其中$ d $ DICETE近似于In.这表明了量子通信比经典通信的优势，因为计算$（3/2- \ varepsilon）$ - 在经典的Encest网络中的直径和半径的近似需要$ \ \ \ \widetildeΩ（n）$ rounds，即使$ d $ command $ d $ constand [abboud，Censor-Hillel，Censor-Hillel，khoury，disce '16]。我们还证明了$（3/2- \ varepsilon）$的$ \widetildeΩ（n^{2/3}）$的下限 - 即使$ d =θ（\ log n）$，近似于量子colest网络中的加权直径/半径。因此，在量子拥堵网络中，由于Le Gall和Magniez的$ \ wideTilde o \左（\ sqrt {nd} \ right）$ - 圆形的algorithm for未加权的直径/adius/madius/madius/madius/godc'18 podc'18 podc'18 podc'18 pod'podc'18 podc'18 podc'18 podc'18 podc'18 pod'podc'18 podc'18
This paper studies the round complexity of computing the weighted diameter and radius of a graph in the quantum CONGEST model. We present a quantum algorithm that $(1+o(1))$-approximates the diameter and radius with round complexity $\widetilde O\left(\min\left\{n^{9/10}D^{3/10},n\right\}\right)$, where $D$ denotes the unweighted diameter. This exhibits the advantages of quantum communication over classical communication since computing a $(3/2-\varepsilon)$-approximation of the diameter and radius in a classical CONGEST network takes $\widetildeΩ(n)$ rounds, even if $D$ is constant [Abboud, Censor-Hillel, and Khoury, DISC '16]. We also prove a lower bound of $\widetildeΩ(n^{2/3})$ for $(3/2-\varepsilon)$-approximating the weighted diameter/radius in quantum CONGEST networks, even if $D=Θ(\log n)$. Thus, in quantum CONGEST networks, computing weighted diameter and weighted radius of graphs with small $D$ is strictly harder than unweighted ones due to Le Gall and Magniez's $\widetilde O\left(\sqrt{nD}\right)$-round algorithm for unweighted diameter/radius [PODC '18].
