The search space can be reduced by the use of an efficient heuristic function. Without heuristic or when the heuristic function equals to zero, A* becomes Dijkstra‟s **path** finding algorithm. In addition, if it is extremely high, A* turns into BFS. Therefore, the heuristic function plays a vital role in controlling the behavior of A*. If the heuristic function gives a very little value, then A* will become slow to find the **shortest** **path**. If heuristic evaluation is very high value, then A* will become very fast. It shows that the tradeoff between speed and accuracy of the algorithm is dependent on heuristics. Therefore, a heuristic should be chosen very cautiously, keeping in mind this tradeoff. A heuristic that is specific to the problem should be used in algorithms.The time complication of A* depends on the heuristic.

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The **shortest** **path** problem was one of the first network problem studied in terms of graph theory. A directed acyclic network is a network consists of a finite set of nodes and a set of directed acyclic arcs. Consider the edge weight of the network as uncertain: which means that is either imprecise or unknown.

Figure 3 shows interface of the system. In this interface, user determines the starting point of location’s delivery item, and then there are 5 choices of location of customers need to be specified. This is compulsory input into system. The next step is the system gives results from calculation, as shown in figure 4.0 This interface, list of sequence of location was stated, the guideline of reading the result also shown in left side of the interface. Figure 5.0 shows detail, roads that give the **shortest** **path** to each destination. In this interface, the road should be used for that route, also indicated.

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Abstract— Online **Shortest** **path** computation using live traffic index in road networks aims at computing the **shortest** **path** from source to destination using Live traffic index.In this paper,index transmission model along with Live traffic index technique is used.In this technique,first the traffic provider collects the traffic data and transmits to the traffic server broadcaster.The traffic server broadcaster indexes and optimizes the traffic data and broadcasts to the navigation client.Graph partitioning and stochastic process are the new techniques used to optimize the index.The fast query response time and short tune in cost at client side ,small broadcast size and maintainence time at server side are the extra features achieved in the system.

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The fuzzy **shortest** **path** problem is an extension of fuzzy numbers and it has many real life applications in the field of communication, robotics, scheduling and transportation. Dubois [4] introduced the fuzzy **shortest** **path** problem for the first time. Klein [6] introduced a new model to solve the fuzzy **shortest** **path** problem for sub-modular functions. Lin and Chern [8] introduced a new design to find the fuzzy **shortest** **path** problem on single most vital arc length in a network by using dynamics programming approach. Li et.al. [9] solved the fuzzy **shortest** **path** problems by using neural network approach. Chuang et al. [3] used two steps to find the **shortest** **path** from origin to destination.

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The computation cost to compute the **path** using an approach, such as the algorithm proposed by Fujita et al. [2] or other similar approaches [3–6] such as Dual Dijkstra’s Search (DDS) were unlike randomized algorithms, it searches over the entire configu- ration space to simultaneously generate the global optimal **path**, in addition to several distinct local minima. The procedural part of this approach is to run the Dijkstra’s search twice so that it produces a list of ranked paths that span the entire graph in order of opti- mality. There have been numerous ways that helps to calculate the **shortest** **path** by using several techniques as the one proposed in [2] and they work perfectly but they have a high cost of computation specially when the number of nodes increases. The computa- tion of typical algorithms for K-best paths [7, 8] is linear in the number of paths (K), that may be enormous if the paths are to span throw the entire graph. In contrast, the Dual Dijkstra’s Search computes paths that span the entire graph at a computational cost that is independent of the number of paths generated. The DDS requires two Dijkstra’s searches, similar to K = 2 [2].

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The basic idea of Dijkstra algorithm is: it is assumed that G= (V, E) is a weighted directed graph. The vertex set v in the graph is divided into two groups. The first group is vertex set S with the **shortest** **path** calculated and the second group is vertex set U with the **shortest** **path** undetermined. Add the vertex of the second group into S successively according to the increasing order of the **shortest** **path** length. During addition, always keep the length of the **shortest** **path** from the source point v to each vertex in S at not more than that from the source point v to each vertex in U. Besides, each vertex corresponds to a distance. The distance of the vertex in S is the length of the **shortest** **path** from v to this vertex and that of the vertex in U is the length of current **shortest** **path** from v to this vertex which regards the vertex in S as the middle vertex.

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In this paper we studied online **shortest** **path** computa-tion; the **shortest** **path** result is computed/updated based on the live traffic circumstances. We carefully analyze the existing work and discuss their inapplicability to the problem (due to their prohibitive maintenance time and large transmission overhead). To address the problem, we suggest a promising architecture that broadcasts the index on the air. We first identify an important feature of the hierarchical index structure which enables us to compute **shortest** **path** on a small portion of index. This important feature is thoroughly used in our solution, LTI. Our ex-periments confirm that LTI is a Pareto optimal solution in terms of four performance factors for online **shortest** **path** computation. In the future, we will extend our solution on time dependent networks.

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Although the SPDCM problem is NP-hard, we will show that, by transforming the original graph to an auxiliary graph, the **Shortest** **Path** under the Nodal Deterministic Correlated Model (SPNDCM) problem is solvable in polynomial time. For any node a, there are generally two cases of nodal correlation, namely (1) links in the form of (a, b) and (a, c), and (2) links in the form of (a, b) and (b, c) are correlated. When (a, b) and (a, c) are correlated, a simple **path** cannot traverse both of them, since looping is not allowed. In this sense, any simple **path** only traverses at most one of them, which means that the links’ correlation will not affect the cost calculation of any simple **path**. There- fore, we only need to consider the case when (a, b) and (b, c) are correlated. We first define that if (a, b) and (b, c) are correlated, then a and b are called correlated nodes, which is represented by C n , else they are uncorrelated nodes, which is denoted by U n .

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In this paper we have developed an algorithm for finding complement **shortest** **path** and **shortest** **path** length using possibility measure with complement type-2 fuzzy number. The order of getting the degree of possibility for possible paths for the given edge weights in a network is getting reversed while we use the complement of the edge weights in a same network. We conclude that the complement **shortest** **path** is not at all a **shortest** **path** for the given edge weight but it is the **shortest** **path** for complement of given type-2 fuzzy number.

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The approach works and certainly is useful for any agencies and personnel who deal with stress or non-stress operations like building emergency rescue and missions, evacuations and training purposes. Implementation of Dijkstra’s algorithm in 3D network makes the **shortest** **path** analysis for multi-levels buildings can be more accurate and efficient for navigation or simulation in a building.

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predicate-argument structures that share a common argument, then the **shortest** **path** will pass through this argument. This is the case with the **shortest** **path** between ’stations’ and ’workers’ in Figure 1, pass- ing through ’protesters’, which is an argument com- mon to both predicates ’holding’ and ’seized’. In Table 1 we show the paths corresponding to the four relation instances encoded in the ACE corpus for the two sentences from Figure 1. All these paths sup- port the L OCATED relationship. For the first **path**, it is reasonable to infer that if a P ERSON entity (e.g.

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The **Shortest** **Path** (SP) problem has accustomed abundant absorption in the literature. Many applications such as communication, robotics, scheduling, transportation and routing, in which, **Shortest** **Path** (SP) is applied importantly. While considering a network, the arc length may represent time or cost. Therefore, in real life applications, it can be advised to be a fuzzy set. Fuzzy set theory, proposed by Zadeh [19], is frequently used to accord with uncertainties in a problem.

The problem of searching the **shortest** **path** is very common and is widely studied on graph theory and optimization areas. To achieve the best **path**, there are many algorithms which are more or less effective; depending on the particular case. **Shortest**-**Path** Problems play an important role in routing messages efficiently in networks. Each method has got independent merit of its own address, different types of **path** searching in different situations. These algorithms of **path** searching are not always based on precise data. So to deal with uncertainty fuzzy logic will be the appropriate tool. This is used to simultaneously associate more costs to those arcs, but this new feature increments computational efforts.

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The **shortest** **path** problem concentrates on finding the **path** with minimum distance to find the **shortest** **path** from source node to destination node is a fundamental matter in graph theory. A directed acyclic network is a network that consists of a finite set of nodes and a set of direct acyclic arcs.

We consider a connected acyclic network having a source vertex u and and a sink vertex z . Each edge i − j of the network represents the cost (or distance) parameter between vertices i and j . We consider these parameters to determine the **shortest** **path** in a network. The edges of our network are associated with a pair of ordered inducing variable and TrIFN, 〈u h , φ h 〉. The significance of such a pair in the context of the connected network is as follows:

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Computing the **shortest** **path** is important task in the spatial databases. The **path** computed using the pre-stored data is not accurate. Hence, there is necessity for the live traffic data. There are several online service traffic providers like Navteq[1],Tom tom[2],Google maps[3].But these traffic providers does not provide data continuously due to high costs. Client-server architecture is previously used for the **shortest** **path** retrievals where the client sends the request and server responds to it. This architecture scales poorly if there are more than two clients. According to telecommunication expert[4],In 2015 the capacity provided by the cellular networks should increase 100 times than in 2011.The communication costs spent on retrieving the **shortest** route is high Malviya et al[5] used the client server architecture for **shortest** routes. In this

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It is an algorithm that is used to find the **shortest** **path** or minimum cost and is represented in the graph. In this algorithm first, start at the ending vertex by making it with a distance of 0. It is 0 units from the end. It is called the current vertex. All of the vertices are connected to the current vertex with an edge and calculate their distance. Note each distance with their corresponding distance. If it is less than the previous distance visits the vertex and note the new one. Continue these processes until the **shortest** **path** is found.

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The standard AODV [6], [9] protocol always selects the **shortest** **path** between source and destination, the **shortest** **path** is the easiest broken due to the limited wireless transmission range between neighboring nodes or the intermediate nodes located at the end of the transmission range. Routes failure is caused by the break of the most fragile **path**[7]. to address this problem, the most effective method is to find most stable **path** as possible. To reduce the effect of mobility, we propose AMAODV protocol that is based on the AODV protocol for MANETs. AMAODV is reactive routing protocol; no permanent routes are stored in nodes. The paths, in this protocol, are chosen based on the distance, relative velocity, queue length and hop count. This allows selecting stable routes and so, reducing control message overhead.

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