Cactus Stack Approach with Dijkstra’s Algorithm

Cactus hoi polloi Approach with Dijkstras AlgorithmAdvance Dijkstras Algorithm with Cactus Stack Implementation LogicIdea Proposed for the Cactus Stack Approach with Dijkstras AlgorithmPalak KalaniNayyar caravan innAbstract This paper illustrates a possible approach to reduce the complexity and advisement burden that is ordinarily encountered in the Shortest racecourse Problems. We intend to bring in a new concept based on the see ahead values of the input lymph glands checkn in the shortest path problem as proposed by the known Djktras Algorithm. A new data structure called as Cactus Stack could be utilize for the same and we could establish to moimize and the loop back issues and traversals in a given graph by looking at the adjacency intercellular substance as well as the creation of a cactus destiny which is linked in a listed manner. The calculation of the node values and the total value shall be the same as proposed by the ancient algorithmic rule however by our concept we be trying to reduce the complexity of calculation to a larger extent.Index TermsComp wiznt, formatting, style, styling, insert. (key words)I. IntroductionWith the advancement in technology, there is increase in demand for development of industries to fulfill the requirements of the people. But in industries there atomic number 18 a lot of chemicals and lubricants used for equipment some of these chemicals and lubricants are volatile in nature and may cause accidents such as draw out. However, fire extinguishers and other preventive measures are also available at the security, but they are not turn up executive and we make up to flee the area as soon as possible.This research paper proposes a new algorithm which calculates the shortest path forget away of such problems. The proposed algorithm is based on the master copy Dijkstra algorithm. This algorithm gives us optimum solution in less clipping and also reduces the calculation.1II. Dijkstra AlgorithmDijkstra was o ne of the most forceful promoter of programming as a scientific discipline. He has made persona to the areas of operating systems, programming languages, including deadlock avoidance, contain the notion of structured programming, and algorithms. We depart now consider the frequent problem of finding the length of a shortest path between a and z in an planless attached simple weighted graph. Dijkstras algorithm proceeds by finding the length of a shortest path from a to a first vertex, the length of a shortest path from a to a atomic number 42 vertex, and so on, until the length of a shortest path from a to z is found. As aside benefit, this algorithm is slow extended to find the length of the shortest path from a to all other vertices of the graph, and not just to z.The algorithm relies on a series of iterations. A high-minded clan of vertices is constructed by adding one vertex at each iteration. A labeling procedure is carried out for iteration. In this labeling procedu re, a vertex w is labeled with the length of a shortest path from a tow that contains completely vertices already in the distinguished set. The vertex added to the distinguished set is one with a minimal label among those vertices not already in the set.We now give the details of Dijkstras algorithm. It begins by labeling a with 0 and the other vertices with . We use the notation L0(a) = 0 and L0(v)=for these labels in front every iterations confound taken place (the subscript 0 stands for the 0th iteration). These labels are the lengths of shortest paths from a to the vertices, where the paths contain only the vertex a.(Because no path from a to a vertex different from a exists, is the length of a shortest pathBetween a and this vertex.)Dijkstras algorithm proceeds by forming a distinguished set of vertices. allow S k denote this set after k iterations of the labeling procedure. We begin with S0 = . The set Skis form from Sk1 by adding a vertex u not in S k1 with the smallest label.Lk(a, v) = minLk1(a, v),Lk1(a, u) + w(u, v),ALGORITHMProcedure Dijkstra(G weighted connected simple graph, withall weights positive)G has vertices a = v0, v1, . . . ,vn= z and lengths w(vi , vj )where w(vi , vj )=if vi , vj is not an edge in Gfori = 1 to nL(vi ) =L(a) = 0S =the labels are now initialized so that the label of a is 0 and allother labels are, and S is the exonerate setwhilez Su= a vertex not in S with L(u) minimalS =S uforall vertices v not in SifL(u) + w(u, v) then L(v) = L(u) + w(u, v)this adds a vertex to S with minimal label and updates thelabels of vertices not in SreturnL(z) L(z) = length of a shortest path from a to z2IV. Limitations of Dijkstras AlgorithmAlthough Dijkstras algorithm is an effective algorithm but still there are a lot of circumspections. Some of these are discussed below.Presence of calculations bounteously.Solutions pleaded by this algorithm are not equitable.The reasons for ever-changing paths and beading elements are not favoured.It is not explicit when the problem is not closed loop or cyclic i.e. we are having a finis element other than destination and last element is connected with only one element then we are not able to reach destinationIt distracts when both next nodes are same then which node we are going to choose for operation.We have to assay distance or path after one step which is not favourable. For example, if we want to go neemuch from indore and distance of Ujjain from indore is much than distance of devas from indore then according to dijkstra we should go to devas and check distance of desvas between neemuch and if we find more than Ujjain route then we again come back to indore.V. Solutions to mentioned limitationsFirst we use look ahead dijkstra A. PrecodeWnext = min Wvu ,WvwLook ahead Wnext ,Wua , WsubWfinal = minWnextWua, WnextWubReturn Wfinala?bMin_(i=1)2-(Ti)+Li-1-Problem solution Vi=VjMin(P1_(i=1)2wi, P2_(j=1)2wj) =next node.B. Proposed MethodCs1 pop(a)Cs2(b)Weight (a,b)Cs2(c)Weigth( a,c)Returnmin( Cs2(b),Cs2(c))(V+Cs)+ look aheadC. Dijkstra with VFS traversal and cactus loadVFS(vertical first search)In the vfs we search in vertical order of cactus stackf(a,b) f(n,m)n=af(a,m)m=b,c,d,e..struct nodeint*prevint*nextint dataD. Complexity ComparisonIn dijkstras complexity is more whereas in proposed method i.e. shortest path with cactus stack is less. In dijkstras we need to do calculation from each and every point but in proposed algorithm we need to do calculation from particular points which reduces calculations and complexities.E. Adjacency MatrixIn mathematics and estimator science, an adjacency hyaloplasm is a mode of representing which vertices (or nodes) of graph are adjacent to which other vertices.34Adjacency matrix of above graph isF. Weighted Adjacency MatrixThe matrix which represents graph with respect to its weight. Now we have to permute matrix into another matrix by using the following program.Adjacency Matrix is polity include include define IN F 9999int important( )intarr44 int cost44 = 7, 5, 0, 0,7, 0, 0, 2,0, 3, 0, 0,4, 0, 1, 0 int i, j, k, n = 4 for ( i = 0 i for ( j = 0 j if ( costij == 0 )arrij = INF elsearrij = costij printf ( Adjacency matrix of cost of edgesn ) for ( i = 0 i for ( j = 0 j printf ( %dt, arrij ) printf ( n ) for ( k = 0 k for ( i = 0 i for ( j = 0 j if ( arrij arrik + arrkj )arrij = arrik + arrkjNow we take an above example and use this steps to convert into another adjacency matrix.G. Traversal of Adjacency MatrixFor solving adjacency matrix, we take the beginning(a) node and observe the row of that node if there is weight on any vertex that means that vertex is connected to 1st node with respective weight.Similarly we check for all nodes and traverse the matrix.If any vertex have weight eternity that means that vertex is not directly connected to the main vertex whose row is being traverse. If vertex have weight zero that means there is no self loop present.If users last node is not the la st node of matrix then we simply traverse the matrix till the node entered by user then we volition back traverse rest of node that is we will start traversing last node.VI. Cactus StackA cactus stack is a set of stacks organized in a systematic format as a tree in which each path from the root to any leaf constitutes a stack.A Cactus Stack act both like a Tree and a Stack. Like a stack, items can only be added to or removed from only one end that is top of the cactus stack like a Tree, nodes in the Cactus Stack may have get up child relationships. Cactus Stacks are traversed from the child nodes to the parent nodes rather than vice-versa, as in a Binary Search Tree. One of the strongest benefits of a cactus stack is that it allows analog data structures to exist with the same root.A. Creation of Cactus StackLet us understand this matrix with the assist of an example showed above. Series of steps should be as followingFirst, We should know the starting and ending point. Let us a ssume that a is the starting point and f is the ending point. Then we put vertices of graph in cactus stack. Put a in cs1. Now a is connected to b and c. so b and c are put in cs2. b is connected to d and c is connected to e so we put d and e in cs3. Repeat same step till the last node is traversed. On traversing the adjacency matrix if two adjacent node has weight other than infinity and zero then we put that nodes in different cactus stacks.B. Linkage in Cactus StackAfter plotting the vertices in cactus stacks. If there is connection between element of cs1, cs2 then we have to kernel them. Similarly we will join elements of each stack to its consecutive stack.VII. ConclusionWith the help of Cactus Stack and Linked List for the shortest path the duration complexity is reduced theoretically than the theory proposed by Dijkshtras Shortest path algorithm. Thus we conclude that time complexity is reduced.ReferencesList and number all bibliographical credits in 9-point Times, single- spaced, at the end of your paper. When referenced in the text, enclose the citation number in square brackets, for example 1. Where appropriate, include the name(s) of editors of referenced books. The template will number citations consecutively within brackets 1. The sentence punctuation follows the bracket 2. Refer simply to the reference number, as in 3do not use Ref. 3 or reference 3. Do not use reference citations as nouns of a sentence (e.g., not as the writer explains in 1).Unless there are six authors or more give all authors names and do not use et al.. Papers that have not been published, even if they have been submitted for effect, should be cited as unpublished 4. Papers that have been accepted for publication should be cited as in press 5. Capitalize only the first word in a paper title, except for proper nouns and element symbols.For papers published in translation journals, please give the English citation first, followed by the original foreign-language citation 6.W ang Tian-yu, The Application of the Shortest Path Algorithm in the reasoning by elimination System, 2011 International Conference of Information Technology, Computer Engineering and Management Sciences (references)Kenneth H. 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