The station change. Many solution routes, the experimental results are reported in section 4 and information from this computation can be able to conclusion in section 5. This is a graph search algorithm that solves the single- 2. Background Theory source shortest path problem for a graph with nonnegative edge path costs, producing a shortest 2. One of the main reasons for the the source city to destination city. Shortest path popularity of Dijkstra's Algorithm is that it is one problem is the finding a path between two vertices of the most important and useful algorithms or nodes such that the sum of the weights of its available for optimal solutions to a large class of constituent edges is minimized.
An example is shortest path problem. Therefore, physical distance finding the quickest way to get from one location to of two points is not enough to describe the path.
The interconnected algorithm is the most commonly used to solve the objects are represented by mathematical a called single source shortest path problem today. For a vertices, and the links that connect some pairs of graph G V,E , where V is the set of vertices and E vertices are called edges.
A graph may be is the set of edges, the running time and finding a constructed by choosing the vertices to be the path between two vertices varies. GIS , telecommunication networks and, The graph instatements in important role as the Reconfigurable Hardware, Public Transport maps are used as graphs. This graph consisting of vertices that represent cargoes which emerged globally has caused range of setback such as traffic congestion and fuel telephone line, network line, road map, where each expensive.
For that reason, people are encouraged edge connect two distinct vertices and no two edges connect same pairs of vertices. This system is able to suggest unfamiliar public users to choose a route based on their weights assigned to their edges.
As use the algorithm implies new bound on both the all-pairs preferences. The system uses a shortest path route and single-source shortest path problems. Therefore, undirected graph is the destination city.
There are many systems to extract data from database. In some of them, many forms 3. It is the set of begin lines has the shortest coverall distance. Any shortest path algorithm must Choose a vertex w in V-S such that D[w] is a examine each in the graph at least once, since any minimum; of the edges could be a shortest path. An edge v0 to v that lies wholly within S except for v weight is also referred to an edge length.
Calculation of the table is explained by mathematically. Assign to every node a distance value. Set it to zero for our initial node and to infinity for all other nodes. Mark all nodes as unvisited.
Set initial node, Kyaikhto v18 , as current. For current node, consider all its unvisited neighbors and calculate their distance. In loop 1 of above table Wall v17 is marked and which distance becomes 22miles. If this distance is less than the previously recorded distance, overwrite the distance.
Each edge is associated with a weight, representing the physical distance or the transmission delay of the transmission line. The target of shortest path algorithms is to find a route between any pair of vertices along the edges, so the sum of weights of edges is minimum.
If the edges are of equal weights, the shortest path algorithm aims to find a route having minimum number of hops. Calculate the shortest distances iteratively. An array, Q , containing all nodes in the graph. One is per- forming computation on expanding to next level, checking for duplicate and neighboring checking between DS A[m] and B[q]. This part is like FFSP1, the difference is that each DS here grows following a geometric progression with common quotient 2 and initial term 1 as shown in corollary 3.
The other part is performing computation on finding dominant elements. However, message overhead is very high in FB. There are two cases of message overhead when an informed node A wants to inform node X. Case 1, node X has been informed already. Thus, X must have lower or equal level to A. Case 2, uninformed node X can be informed by nodes B,C,D, which have the same level as A, at the same time.
For case 1, we need to compare the shortest-path length between X and A to originator. For case 2, we have to define some conditions, based on these conditions only A or B or C or The following theorems are proposed for calculating path length. Theorem 3: given p is shortest-path length between node a and b, the min- imum length of matched strings between a and b is k-p dBG d,k.
Proof: as shown in fig. The minimum matched string[5] can be obtained in type R,L among them. And length for this minimum matched string is k-p. These cases are the general cases for 3 types presented in fig. To solve the above two cases of message overhead, a Boolean valued function SPL is proposed. Step 1,2,3 solve message overhead of case 1.
Step 1 is a result of theorem 3. Step 4,5,6 solve case 2 message overhead. In case 2, we have several shortest paths from S to X. Then, shortest path which begin with shifting right is chosen. These strings are 11, , , 01, , , , , Step 2: path lengths for strings in step 1 are 12, 10, 8, 14, 12, 10, 8, 13, Step 3: shortest path length is 8.
Step 4: matched string, which make shortest path length 8, are , If we apply SPL for all 2d neighbors of one node, then it cost 0 2d for running our algorithm. The following theorems reduce from 0 2d to 0 1. Following are some notations used, where T is the previous shifting string. Proof: given a node a0 a By proving similarly for case LRL, theorem 5 is proved.
Proof: assume the beginning node is a0 a Shift string Ru LR makes duplicate as shown in theorem 3. As a result, broadcasting algorithm is proposed as shown in fig. Theorem 7: in the worst case, time complexity for our broadcasting algo- rithm is 0 1.
So, theorem 7 is proved. Our routing algorithms can provide shortest path in the case of failure existence. In broadcasting, our algorithm requires maximum k steps to finish broadcasting process in dBG d,k. And there is no message overhead during broadcasting. Time complexity at each node is 0 23 d. Therefore, the algorithms can be considered feasible for routing and broadcasting in real interconnection networks. References 1. Yang, Z. Esfahanian and S.
C , Alfred V. Aho, Margaret J. Esfahanian, G. Ganesan, D. Ohring, D.
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