For addressing real root isolation problem of transcendental function polynomials， an interval isolation algorithm for exponential function polynomials named exRoot was proposed. In the algorithm， the real root isolation problem of non-polynomial real functions was transformed into sign determination problem of polynomial， then was solved. Firstly， the Taylor substitution method was used to construct the polynomial nested interval of the objective function. Then， the problem of finding the root of the exponential function was transformed into the problem of determining the positivity and negativity of the polynomial in the intervals. Finally， a comprehensive algorithm was given and applied to determine the reachability of rational eigenvalue linear system tentatively. The proposed algorithm was implemented in Maple efficiently and easily with readable output results. Different from HSOLVER and numerical calculation method fsolve， exRoot avoids discussing the existence of roots directly， and theoretically has termination and completeness. It can reach any precision and can avoid the systematic error brought by numerical solution when being applied into the optimization problem.

RP2P algorithm combines arbitrary neighbor selection, typically used only in unstructured P2P networks, with a Distributed Hash Table (DHT) ring. It is the first of its kind to resolve requests in d hops with a chosen probability of 1－c. However, the capacities of the hosts participating in the network, such as bandwidth, memory, CPU, are very different, which will affect the efficiency of the whole system. On the other hand, the shock caused by some of the nodes in the network frequent joining in/departing from the system is also one of the factors affecting the performance. This paper analyzed the capacities of the nodes and proposed an efficient RP2P network based on hierarchical dividing. It improves the efficiency of the system, and solves the problem of system shocks.