Speedy Algorithm of Public Traffic Route Selection Based on Adaptive Backbone Network

The inquiry service of public traffic routes is the important part of urban information service, which core is the public traffic route selection algorithm. However the traditional public traffic route selection algorithms have high time complexities and cannot support the inquiry of multiple changes. In this article, we put forward the speedy algorithm of public traffic route selection based on adaptive backbone network. In this algorithm, if the public traffic routes which pass certain public traffic station exceed or equal a certain value, so the station is defined as the backbone station, and the backbone stations and the public routes which pass them compose backbones network. If changes are limited at the backbone stations, so we can realize multiple changes inquiry and reduce computation in 10% of traditional algorithms through changing the certain value to adjust the backbone network. 1. Introduction The inquiry service of public traffic routes is the important measure to convenient for people's daily life and enhance the operation efficiency of public traffic route network, and it is also the important composing of urban information service, which core is the public traffic route selection algorithm. At present, traditional public traffic route selection algorithms include Dijkstra algorithm, Floyd algorithm or their ameliorations


Introduction
The inquiry service of public traffic routes is the important measure to convenient for people's daily life and enhance the operation efficiency of public traffic route network, and it is also the important composing of urban information service, which core is the public traffic route selection algorithm. At present, traditional public traffic route selection algorithms include Dijkstra algorithm, Floyd algorithm or their ameliorations (Lu, 2001, p.68-70, Wang, 2007, p.63-67, Yue, 1999, p.209-212, Zhu, 2007, p.121-122 & Xu, 2005, which time complexities respectively are ( )  (Thomas, 2007, p.324-330), but when a large of public traffic stations exist, higher time complexity will induce that inquiry time far exceeds what inquirer hopes. At the same time, these two algorithms cannot support route inquiry of multiple changes and cannot realize the first aim of least change times (Yang, 2000, p.87-91 & Ma, 2004. Aiming at problems existing in traditional algorithms, in this article, we put forward the speedy algorithm of public traffic route selection based on adaptive backbone network. This algorithm induces computation quantity and expedites computation speed through the backbone network technique, and can support the route inquiry of multiple changes through the adaptability of backbone network.

Adaptive backbone network
Suppose that the public traffic stations are the crunodes in the public traffic network map and all public traffic routes between any two public traffic stations are the directional routes, so the public traffic network map can be noted as , where, V is the set of all public traffic stations, E is the set of all directional public traffic routes between any two public traffic stations, and L is the set of all public traffic routes.
Taking the public traffic route layout of the main city zone in Beijing, the main city zone in Beijing has 3957 public traffic stations ) and 520 public routes  ) and the next station of i v is j v , so the directional route ( ) j i, is one side in map G . Every public traffic route must pass some pubic traffic stations, and every public traffic station must at one public traffic route at least, and suppose that the set of all public traffic routes which pass station i v is ( ) , so the set of all stations which pass station i v on all the public traffic routes is Suppose that the station i v is the backbone station with n adaptive degree which fulfills ( ) n v L i ≥ ( N n ∈ ) and is noted as is the set of all backbone stations with n adaptive degree, n E is the set of all directional public traffic routes between any two backbone stations with n adaptive degree, n L is the set of public routes which pass the backbone station with n adaptive degree, and the sub-map of the public traffic network map which only includes all backbone stations with n adaptive degree is the backbone network with n adaptive degree, which is noted as To establish the backbone network with n adaptive degree should possess two conditions, one is which can cover most public traffic routes and the other is that the purpose station which is reachable on the public traffic route also can be reachable on the backbone network with huge probability. Suppose that the reachable probability η between any two stations on the backbone network is the square of the ratio between the sum of station which n L covers and the gross of public traffic stations, so Table 1 can be obtained through computation.
From Table 1 , i.e. the backbone stations which only occupy 8.47% of the gross of public traffic station cover 97.12% of public traffic routes, and the reachable probability between any two stations on the backbone network achieves 96.25%. Therefore, the reachability among most stations can be actualized through the backbone network and changes among backbone stations, and suppose that all changes can be actualized only at backbone stations in this article, thus it only needs to compute backbone stations not all public traffic stations, and when the gross of public traffic stations is large, this method can effectively reduce computation quantity and get approximate optimal solution. Suppose that the limitation of inquiry may induce the route obtained is not the optimal route, i.e. the approximate optimal solution, and considering the actual situations that the backbone stations are the zones that ten or tens of public traffic routes gather and the zones with dense human streams, so the route strange inquirer gets is convenient for memory and identification. If the station inquired cannot be reached through the backbone network, the backbone network needs to be extended. The so-called adaptive backbone network is to dynamically control the scale of backbone network according to actual needs of inquiry, which can not only ensure the solvability, but also achieve the speediness of solution.
The basic idea to establish adaptive backbone network algorithm is that the inquirer gives that start station start

Algorithm description
The basic idea of route selection algorithm based on the backbone network is that inquirer gives any start station start v and purpose station end v , firstly compute ( )  The steps of the algorithm are as follows: The inputs of the algorithm include the start station start v and the end station end v . The outputs of the algorithm include the sets of reachable routes.
Step 1: Suppose that cyclic variable , and if 520 ≠ i , so 1 + = i i and go to Step 1.
Step 2: , so record these reachable routes and exit.
Step 3: Suppose that cyclic variable Step 4: Suppose that cyclic variable Step 5: If , so record these reachable combined routes through one time change and exit.
Step 6: take i v and j v as the new start station and the new purpose station, recursively transfer the algorithms in Step 1 and Step 2, and if i v and j v can be reached directly, so start v and end v can be reached through two times changes, export route selection information and exit.
Step 7: take i v and j v as the new start station and the new purpose station, recursively transfer the algorithms in Step 3, Step 4, and Step 5, and if i v and j v can be reached directly, so start v and end v can be reached through three times changes, export route selection information and exit, recursively transfer until the feasible solution with least change times can be obtained.
The algorithm will get some feasible route combinations with "least change times", so we can evaluate these routes according to inquirer's actual needs and select one group or several groups of optimal route combinations which can fulfill inquirer's requirement.

Conclusion
In this article, we put forward the speedy algorithm of public traffic route selection based on adaptive backbone network. In this algorithm, if the public traffic routes which pass certain public traffic station exceed or equal a certain value, so the station is defined as the backbone station, and the backbone stations and the public routes which pass them compose the sub-map of public traffic network map, i.e. the backbones network. The algorithm supposes that change can only be actualized at the backbone station, and because backbone stations almost cover all pubic traffic routes, so most public traffic stations can be reached under that hypothesis. Because the quantity of backbone stations generally don't exceed 10% of the public traffic station gross, so the algorithm only needs to compute backbone stations not all public traffic stations when computing changes, and the computation quantity can be reduced fully comparing with traditional algorithms, and the speedy inquiry can be actualized. At the same time, the algorithm can actualize the inquiry with multiple changes through recursive computation, which can better fulfill inquirer's demand. Considering the solvability of the route inquiry among any public traffic stations, this article puts forward the method to dynamically control the scale of backbone network, i.e. adaptive backbone network, accordingly gives attention to the solvability and the speediness of the solution.
Symbol table. The set of all directional public traffic routes between any two backbone stations with n adaptive degree