Cactus Stack Approach with Dijkstra’s Algorithm

Cactus Stack Approach with Dijkstra’s Algorithm Advance Dijkstra’s Algorithm with Cactus Stack Implementation Logic Idea Proposed for the Cactus Stack Approach with Dijkstra’s Algorithm Palak Kalani Nayyar Khan Abstract— This paper illustrates a possible approach to reduce the complexity and calculation burden that is normally encountered in the Shortest Path Problems. We intend to give a new concept based on the look ahead values of the input nodes given in the shortest path problem as proposed by the famous Djktras Algorithm. A new data structure called as Cactus Stack could be used for the same and we could try to minimize and the loop back issues and traversals in a given graph by looking at the adjacency matrix as well as the creation of a cactus stack 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 algorithm however by our concept we are trying to reduce the complexity of calculation to a larger extent. Index Terms—Component, formatting, style, styling, insert. (key words) I. Introduction With the advancement in technology, there is increase in demand for development of industries to fulfill the requirements of the people. But in industries there are 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 fire. However, fire extinguishers and other preventive measures are also available at the security, but they are not proven executive and we have 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 original Dijkstra algorithm. This algorithm gives us optimum solution in less time and also reduces the calculation.[1] II. Dijkstra Algorithm Dijkstra was one of the most forceful promoter of programming as a scientific discipline. He has made contribution to the areas of operating systems, programming languages, including deadlock avoidance, contain the notion of structured programming, and algorithms. We will now consider the general problem of finding the length of a shortest path between a and z in an undirected connected simple weighted graph. Dijkstra’s 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 second vertex, and so on, until the length of a shortest path from a to z is found. As aside benefit, this algorithm is easily 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 distinguished set of vertices is constructed by adding one vertex at each iteration. A labeling procedure is carried out for iteration. In this labeling procedure, a vertex w is labeled with the length of a shortest path from a tow that contains only 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 Dijkstra’s 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 before any iterations have taken place (the subscript 0 stands for the â€Å"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 path Between a and this vertex.)Dijkstra’s algorithm proceeds by forming a distinguished set of vertices. Let S k denote this set after k iterations of the labeling procedure. We begin with S0 = ∅. The set Skis formed from Sk−1 by adding a vertex u not in S k−1 with the smallest label. Lk(a, v) = min{Lk−1(a, v),Lk−1(a, u) + w(u, v)}, ALGORITHM: Procedure Dijkstra(G: weighted connected simple graph, with all 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 G} fori := 1 to n L(vi ) :=∞ L(a) := 0 S :=∅ {the labels are now initialized so that the label of a is 0 and all other labels are∞, and S is the empty set} whilez ∈S u:= a vertex not in S with L(u) minimal S :=S ∠ª {u} forall vertices v not in S ifL(u) + w(u, v) then L(v) := L(u) + w(u, v) {this adds a vertex to S with minimal label and updates the labels of vertices not in S} returnL(z) {L(z) = length of a shortest path from a to z}[2] IV. Limitations of Dijkstra’s Algorithm Although Dijkstra’s 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 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 last element other than destination and last element is connected with only one element then we are not able to reach destination It distracts when both next nodes are same then which node we are going to choose for operation. We have to check 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 more 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 limitations First we use look ahead dijkstra : A. Precode Wnext = min [Wvu ,Wvw] Look ahead [Wnext ,Wua , Wsub] { Wfinal = min[Wnextà ¯Ã†â€™Ã‚  Wua, Wnextà ¯Ã†â€™Ã‚  Wub] Return [Wfinal;:a?b] } Min[∑_(i=1)^2à £Ã¢â€š ¬-(Ti)+Li-1à £Ã¢â€š ¬-] Problem solution Vi=Vj: Min(P1[∑_(i=1)^2wi], P2[∑_(j=1)^2wj]) =next node . B. Proposed Method Cs1 pop(a) { Cs2(b) { Weight (a,b); } Cs2(c) { Weigth(a,c); } Return[min( Cs2(b),Cs2(c)) } (V+Cs)+ look ahead C. Dijkstra with VFS traversal and cactus stack VFS(vertical first search) In the vfs we search in vertical order of cactus stack f(a,b)≈ f(n,m) n=a f(a,’m’) m=b,c,d,e†¦Ã¢â‚¬ ¦.. struct node { int*prev; int*next; int data; } D. Complexity Comparison In dijkstra’s complexity is more whereas in proposed method i.e. shortest path with cactus stack is less. In dijkstra’s 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 Matrix In mathematics and computer science, an adjacency matrix is a means of representing which vertices (or nodes) of graph are adjacent to which other vertices.[3][4] Adjacency matrix of above graph is F. Weighted Adjacency Matrix The matrix which represents graph with respect to its weight. Now we have to convert matrix into another matrix by using the following program. Adjacency Matrix is CODE : #include #include #define INF 9999 int main( ) { intarr[4][4] ; int cost[4][4] = { 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 ( cost[i][j] == 0 ) arr[i][j] = INF ; else arr[i][j] = cost[i][j] ; } } printf ( Adjacency matrix of cost of edges:n ) ; for ( i = 0 ; i { for ( j = 0; j printf ( %dt, arr[i][j] ) ; printf ( n ) ; } for ( k = 0 ; k { for ( i = 0 ; i { for ( j = 0 ; j { if ( arr[i][j] >arr[i][k] + arr[k][j] ) arr[i][j] = arr[i][k] + arr[k][j]; } } } Now we take an above example and use this steps to convert into another adjacency matrix: . G. Traversal of Adjacency Matrix For solving adjacency matrix, we take the 1st 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 infinity 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 user’s last node is not the last node of matrix then we simply traverse the matrix till the node entered by user then we will back traverse rest of node that is we will start traversing last node. VI. Cactus Stack A 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 parent 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 parallel data structures to exist with the same root. A. Creation of Cactus Stack Let us understand this matrix with the help of an example showed above. Series of steps should be as following: First, We should know the starting and ending point. Let us assume 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 Stack After plotting the vertices in cactus stacks. If there is connection between element of cs1, cs2 then we have to join them. Similarly we will join elements of each stack to its consecutive stack. VII. Conclusion With the help of Cactus Stack and Linked List for the shortest path the time complexity is reduced theoretically than the theory proposed by Dijkshtra’s Shortest path algorithm. Thus we conclude that time complexity is reduced. References List and number all bibliographical references 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 â€Å"[3]†Ã¢â‚¬â€do not use â€Å"Ref. [3]† or â€Å"reference [3]†. Do not use reference citations as nouns of a sentence (e.g., not: â€Å"as the writer explains in [1]†). Unless there are six authors or more give all authors’ names and do not use â€Å"et al.†. Papers that have not been published, even if they have been submitted for publication, should be cited as â€Å"unpublished† [4]. Papers that have been accepted for publication should be cited as â€Å"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]. Wang Tian-yu, The Application of the Shortest Path Algorithm in the Evacuation System, 2011 International Conference of Information Technology, Computer Engineering and Management Sciences (references) Kenneth H. Rosen, Discrete_Mathematics_and_Its_Applications_7th_Edition_Rosen, page-710-713 Fuhao Zhang, Improve On Dijkshtra’s Shortest Path Algorithm for Huge Data R. Nicole, â€Å"Title of paper with only first word capitalized,† J. Name Stand. Abbrev., in press. Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, â€Å"Electron spectroscopy studies on magneto-optical media and plastic substrate interface,† IEEE Transl. J. Magn. Japan, vol. 2, pp. 740–741, August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982]. IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 8, AUGUST 2006 1803 †Phase Noise and Jitter in CMOS Ring Oscillators†, Asad A. Abidi. pp1803-1816. M. Young, The Technical Writers Handbook. Mill Valley, CA: University Science, 1989.

Henry Clay :: essays research papers

Clay was born on April 12, 1777, in Hanover County, Virginia. He was born to John Clay, a minister. His mother Elizabeth Hudson was After studying for the bar with the eminent George Wythe, Clay, at the age of 20, moved to Lexington, Kentucky, where he developed a thriving practice. He was blessed with a quick mind, a flair for oratory, and an ability to charm both sexes with his easy, attractive manner. That he loved to drink and gamble was no drawback in an age that admired both vices. Clay, ambitious for worldly success, married into a wealthy and socially prominent family and soon gained entry into Kentucky's most influential circles. While still in his 20s, he was elected to the state legislature, in which he served for six years, until 1809. Clay established his great reputation in the United States House of Representatives, where he served intermittently from 1811 to 1825. In his first term, he became one of the leading "War Hawks"—the young men whose clamor for hostilities with England helped bring about the War of 1812. Clay was selected as one of the commissioners who in 1814 negotiated the Treaty of Ghent, ending that war. In 1820-21 it was Clay above all who engineered the Missouri Compromise, quieting the harsh controversy that had erupted by maintaining an equal balance between free and slave states. Although he himself was a slave owner, Clay's views on slavery—as on most other issues—were moderate. He was thus able to command the support of men fearful of extremism.In the presidential election of 1824, after his own candidacy had failed, Clay threw his support to John Quincy Adams, whom the House early in 1825 elected as the sixth president. When Adams named Clay secretary of state, his Jacksonian opponents charged "corrupt bargain!" The charge was unfair, but Clay was haunted by it throughout his subsequent career. Although Clay was a practical politician of flexible rather than rigid beliefs, he did emerge as the great champion of the "American System." He called for a protective tariff in support of home manufactures, internal improvements (federal aid to local road and canal projects), a strong national bank, and distribution of the proceeds of federal land sales to the states.Elected to the U.S. Senate in 1831, Clay served in that body until 1842 and again from 1849 until his death. In 1833 he devised a compromise tariff that resolved the crisis brought on by South Carolina's attempt to "nullify" the prevailing tariff set by Congress.

Hospitals are Driving toward a Leaner Organization Essay

To obtain sustainable organizational efficiency and service quality, many hospitals have adopted an Open Systems Perspective by using â€Å"lean management† procedures borrowed from leading car manufacturers, in an effort to â€Å"reduce and remove waste from work processes†. These processes improved organizational efficiency reduced costs and provided better patient care. i What ‘seems’ to be the Problem: Secondary Symptoms Full waiting rooms, long wait times, inefficient use of supplies and budgets, needless stress and high mortality rate is feedback from the external environment that the hospitals are not meeting the needs of their stakeholders, or fitting in with their environment. Before adapting lean management processes, hospital staff and patients alike shared the burden of what appeared to be the inevitable consequences of health care delivery and a closed systems perspective.ii These problems are manifestations of organizational deficiencies which negatively affect the quality of patient care, the distribution of hospital resources and employee morale. The Real Reasons Hospitals are Facing Difficulties: Primary Problems The secondary symptoms are indicative of underlying issues, highlighting their poor organizational-environmental fitiii and the ineffectiveness of communication between Internal Subsystems.iv To a large extent hospitals have not adapted to their external environment nor have hospitals managed it effectively.v Hospital management, for example, has not adequately promoted the appropriate use of hospitals as opposed to family physicians. The departmentalization of hospitals has unintentionally caused a disconnection between internal subsystems. The lack of coordination between hospital management, physicians, hospital staff and patients prevents the flow and use of information within the organization. The ultimate result is that resources (staff, equipment, financial resources) are not allocated to their optimal use causing superfluous procedures and purchases.vi Solutions, Recommendations and Implementation Plan: Open Systems Perspective and Lean Management strategies will promote organizational efficiency and resolve the underlying problems. Steven L.  McShane explains that collaborative efforts between internal subsystems have proven to reduce the time, efforts and costs contributing to the primary problems. vii Hospitals can use information technology and incentives to staff to share information about where efficiencies can be realized. For example, those responsible for hospital purchases will be greatly assisted by pertinent information from those using the equipment and supplies. The strategy will be financial costly in the short to medium term as the costs associated with implementing such a system will not be compensated for until efficiencies realized over the long run exceed its cost. Furthermore, cost and effort may be required to change the organizational and departmental cultures within hospitals to foster the collaboration necessary for the exchange of information. Including hospital staff in decision making of management may also increase job satisfaction and morale. Efficiencies discovered through information sharing will take stress of budgets and savings may be allocated to areas in need of more resources. A second organizational fit strategy is to transfer resources from underutilized areas to areas in need of greater health care services. Hospitals have likely not allocated their resources to respond demographic changes. Transferring health care resources will almost certainly result in public discontent in areas from which some health care resources are removed. There is also a financial cost and time associated with transferring resources from one geographic area to another more needy one, such as construction costs. In the medium to long term, however, moving resources from areas where they are not needed to an underserviced environment increases efficiency which addresses long wait times, lower quality of care and higher mortality. A further strategy from the Open Systems perspective is to manage the environment by engaging and educating the public about how to more efficiently access health care services. Hospital management will be required, in pursuing this strategy, to spend resources on promotion and education which may exacerbate wait times and the other secondary problems discussed earlier. In the medium to long term, the more efficient use of hospital resources on those that truly require them and diverting other potential hospital users to the appropriate health care provider, such as a family physician, will necessarily alleviate wait times, increase quality of care and improve hospital budgets. Finally, from the internal sub-systems  perspective, through expending resources on gathering empirical data concerning the relationship between resources and health care outcomes, as well as developing and employing greater diagnostic testing, physical resources and time can be managed more efficiently. Hospital management must implement a system and allocate resources to data gathering and analysis. Physicians must participate in providing data and expertise. Through continuous improvement the benefits of not expending hospital resources superfluously may be realized in the medium to long term. These solutions will positively impact full waiting rooms, long wait times, inefficient use of supplies and budgets, needless stress and potentially contribute to a decrease in the mortality rate. This allows hospitals to better fit and manage their environment.

Understanding Huntingtons Disease Essay - 1032 Words

Understanding Huntingtons Disease Diagnosis of Huntingtons Disease Today, a blood test is available to diagnose a person displaying suspected Huntingtons symptoms. The test analyzes DNA in the blood sample and counts the number of times the genetic code for the mutated Huntingtons gene is repeated. Individuals with Huntingtons Disease usually have 40 or more such repeats; those without it, 28 or fewer. If the number of repeats falls somewhere in between then more extensive neurological and diagnostic testing are called for. Tests of the patients hearing, eye movements, strength, feeling, reflexes, balance, movement and mental condition will follow. The patient may also be asked about any recent intellectual or emotional†¦show more content†¦Most often, symptoms begin between the ages of 35 and 50, although onset may occur at any time from childhood to old age. Research continues to progress rapidly, but up to this point no cure has been found. Huntingtons disease is inherited in an autosomal dominant fashion. The child of an affected parent has a 50% chance of inheriting the disease. The discovery of the HD gene in 1993 has made it possible to test at-risk individuals for Huntingtons disease before symptoms occur. Clinical Features The clinical features of Huntingtons disease can be thought of as a triad of emotional, cognitive and motor disturbances. Symptoms include chorea (dance-like involuntary movements), clumsiness, slurred speech, depression, irritability, and apathy. Cognitive losses may include attention, intellectual speed, and short-term memory. Huntingtons disease affects people in different ways. One member of a family may have more trouble with clumsiness while another may have emotional outbursts. Moreover, symptoms of Huntingtons disease in the same individual change over time. Neuropathology Huntingtons disease is characterized by atrophy of the caudate nucleus and putamen. There are two populations of GABAergic striatal efferent neurons that are involved and this is evident based on their projection targets and neuropeptide content. In the very early stages of the disease there is a major loss ofShow MoreRelatedEssay on Understanding Huntingtons Disease2054 Words   |  9 PagesUnderstanding Huntingtons Disease Huntingtons disease is an inherited neurodegenerative disorder. It is passed on to children from one or both parents (though two parents with Huntingtons is extraordinarily rare) in an autosomal dominant manner. This is different from autosomal recessive disorder, which requires two altered genes (one from each parent) to inherit the disorder. 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