二维有限能量约束下最优导航问题的理论分析
黎勇;钭斐玲;樊瑛;狄增如
【期刊名称】《物理学报》 【年(卷),期】2012(061)022
【摘要】最近，Li等研究了在Kleinberg导航模型中引入总能量／l=cⅣ约束后的最优导航问题，其中4为网络中所有长程连边的长度之和，C为正常数，Ⅳ为网络节点总数．他们通过在1维和2维导航模型中的模拟结果推测，在有限能量约束下Kleinberg导航模型中按照幂律方式添加长程连边的最优幂指数应该是α=d＋1，其中d为导航模型的维数．本文在平均场理论下，建立了2维有限能量约束下的导航过程的动态微分方程，通过对该方程进行数学分析以及数值求解，从理论上证明了当网络规模足够大且总能量相对较小时，2维有限能量约束下的最优导航幂指数确实为α=3，这一结果证实了Li等之前的推测．%Recently, a certain total energy constraint A = cN was introduced into the Kleinberg's navigation model, where A is the total length of the long-range connections, c is a positive constant and N is the network size. The simulation results obtained in the one and two-dimensional cases indicate that with total cost restricted the optimal power-law exponent for adding extra long-range links between any two nodes seems to be α = d+ 1, where d is the dimension of the underlying lattice. Based on the mean field theory, the navigation process on the two-dimensional energy constrained navigation model is described by dynamical equations in this paper. Based on our theoretical analysis and
二维有限能量约束下最优导航问题的理论分析
