Increasing Time Efficiency of Insertion Sort

Increasing Time Efficiency of Insertion Sort Increasing Time Efficiency of Insertion Sort for the Worst Case Scenario Surabhi Patel, Moirangthem Dennis Singh Abstract. Insertion sort gives us a time complexity of O(n) for the best case. In the worst case where the input is in the descending order fashion, the time complexity is O(n2). In the case of arrays, shifting is taking O(n2) while in the case of linked lists, comparison is coming to O(n2). Here a new way of sorting for the worst case problem is proposed. We will use arrays as data structures and take more space. We will take 2n spaces where n is the number of elements and start the insertion from (n-1)th location of the array. In this proposed technique the time complexity is O(nlogn) as compared to O(n2) in the worst case. Keywords. Insertion Sort, Time Complexity, Space Complexity Introduction Insertion sort is a simple sorting algorithm[1], a comparison sort in which the sorted array (or list) is built one entry at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. Every repetition of insertion sort removes an element from the input data, inserting it into the correct position in the already-sorted list, until no input elements remain. The best case input is an array that is already sorted. In this case insertion sort has a linear running time which is O(n). During each iteration, the first remaining element of the input is only compared with the right-most element of the sorted subsection of the array. The worst case input is an array sorted in reverse order. In this case, every iteration of the inner loop will scan and shift the entire sorted subsection of the array before inserting the next element. For this case insertion sort has a quadratic running time which is O(n2). The average case also has a quadratic running time of O(n2). Literature Survey In an insertion sort algorithm, there are always two constraints in time complexity. One is shifting the elements and the other one is comparison of the elements. The time complexity is also dependent on the data structure which is used while sorting. If we use array as data structure then shifting takes O(n2) in the worst case. While using link list data structure, searching takes more time, viz. O(n2). We will take the following examples: Sort 50, 40, 30, 20, 10 using arrays. Shifting = 0, Comparison = 0 Shifting = 1, Comparison = log1 Shifting = 2, Comparison = log2 Shifting = 3, Comparison = log3 Shifting = 4, Comparison = log4 Time Complexity in Shifting: O(n2) Time Complexity in Comparison: O(nlogn) Total time complexity: O(n2) Here as the array is sorted, we can use binary search for comparison which will lead to a time complexity of O(nlogn) but Shifting takes O(n2). Therefore the total time complexity becomes O(n2) To solve this problem, link list can be used as illustrated in the following example. Sort 50, 40, 30, 20, 10 using link list. In a link list shifting takes O(1) as new elements can be inserted at their right positions without shifting. Comparison = 0 Comparison = 1 Comparison = 2 Comparison = 3 Comparison = 4 Time Complexity in Shifting: O(1) Time Complexity in Comparison: O(n2) Total time Complexity: O(n2) Here as we cannot use binary search for comparison which will lead to a time complexity O(n2) even though shifting takes a constant amount of time. As we have observed in the examples illustrated above, in both the cases the Time complexity is not getting reduced. Hence we are proposing an improvised insertion sort taking additional space to sort the elements. As space complexity is less important than time complexity[2][3], we have concentrated more over the time taken instead of space. Proposed Work In the insertion sort technique proposed here, we will take 2n spaces in an array data structure, where n is the total number of elements. The insertion of elements will start from n-1th position of the array. The same procedure of a standard insertion sort is followed in this technique. Finding the suitable positions of the elements to be inserted will be done using binary search. In the following cases we will discuss the details of our work. Case 1 For the best case scenario in a standard Insertion Sort is the input elements in ascending order using proposed technique. e.g. 10, 20, 30, 40, 50 Shifting =0 , Comparison = 0 Shifting =0 , Comparison = 1 Shifting =0 , Comparison = 1 Shifting =0 , Comparison = 1 Shifting =0 , Comparison = 1 Total Shifting =0, Total Comparison = n-1 Therefore time complexity is O(1)+O(n) = O(n) Case 2: For the worst case scenario in a standard Insertion Sort is the input elements in descending order using proposed technique. e.g. 50, 40, 30, 20, 10 Shifting =0 , Comparison = 0 Shifting =1 , Comparison = log1 Shifting =1 , Comparison = log2 Shifting =1 , Comparison = log3 Shifting =1 , Comparison = log4 Total Shifting =n-1, Total Comparison =log( 1*2*3*4) =log((n-1)!) =log((n-1) (n-1)) =(n-1)log(n-1) =nlog(n-1) log(n-1) Therefore time complexity is O(n)+O(nlogn) = O(nlogn) Case 3: For the average case scenario in a standard Insertion Sort, the input elements are in random order. We are following the same procedure but comparison is done via binary search algorithm. Hence it takes O(nlogn) for comparison. For shifting the elements, the time taken tends to O(n2) but is not equal to O(n2). As we have more spaces, there are possibilities that the shifting of some elements may be reduced because elements may be inserted both at the end as well as in the beginning. Results Now we compare the time complexities of proposed sorting technique and the standard Insertion sort. Conclusion We are decreasing the time complexity of worst case scenario in Insertion sort algorithm by increasing the space complexity. Our future scope of work includes decreasing time complexity of the average case which is O(n2) currently. There are promising results shown in the average case scenario where the time complexity may be reduce from O(n2), if the probability of the input elements is a combination of increasing and decreasing order. Acknowledgement We would like to thank Prof Anirban Roy, Department of Basic Sciences Christ University Faculty of Engineering for helpful discussions and support. REFERENCES Insertion Sort,http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Insertion_sort.html Michael A. Bender, â€Å"Insertion Sort is O(nlogn),† Third International Conference on Fun With Algorithms(FUN), Pages 16-23, 2004 H. W. Thimbleby, â€Å"Using Sentinels in Insert Sort,† Software Practice and Experience, Volume 19(3), Pages 303–307, 1989.

alan turing Essay -- essays research papers

Alan Turning   Ã‚  Ã‚  Ã‚  Ã‚  Alan Turning is known to be a pioneer of many facets of the computer age. The digital computer, artificial intelligence, memory subroutines, the Turning Machine, the Turing Test, and the application of algorithms to computers are all ideas somehow related to this man. Alan Mathison Turing was born in Paddington, London, on June 23, 1912. He was a precocious child and began his interests in science and mathematics at a young age, but was never concerned about other right-brain classes such as English. This continued until an important friend of his passed away and set Turing on a path to achieve what his friend could no longer accomplish. When his friend Christopher Morcom died, Turing was launched into thoughts in physics about the physical mind being embodied in matter and whether quantum-mechanical theory affects the traditional problem of mind and matter. Many say today that this was the beginnings of Turing’s Turning Machine and the test still used today for artificial intelligence, the Turing Test. Soon after his public schooling Turing began working on his undergraduate at King’s College. Here he became interested in the readings of Von Neumann’s quests into the logical foundations of quantum mechanics. Through these readings Turing was believed to structure his thinking from the emotional states that he had been suffering from to a more valid form of thought. Turing earned a fellowship at King’s college and the following year the Smith’s Prize for his work in probability theory. Afterward, he chose a path away from pure math into mathematical logic and began to work on solving the Entscheidungsproblem, a problem in decidability. This was an attempt to prove that there was a method by which any given mathematical assertion was provable. As he began to dive in to this he worked on first defining what a method was. In doing so he began what today is called the Turing Machine. The Turing Machine is a three-fold inspiration composed of logical instructions, the action of the mind, and a machine which can in principle be embodied in a practical physical form. It is the application of an algorithm embodied in a finite state machine. The Turing Machine is a simple kind of computer. It is limited to reading and writing symbols on a tape and moving the tape along to the left or right. The tape is marke... ...at today is known as the Turing Test. This was a test where a person would ask questions from both a human and a machine without knowing which was which. If after a reasonable amount of time the difference between the two was not obvious, then the machine was thought to be somewhat intelligent. A version of this test is still used today by the Boston Museum of Computers to host a contest of the best artificial machines for the Loebner Prize. Turing continued working on the digital computer and ideas in artificial intelligence until he died on June 7, 1954. He was found with a half-eaten apple loaded with cyanide, the half-eaten apple a familiar symbol of innocence. Some say he had committed suicide over an embarrassing incident with a 19-year old student , while his mother says he was just performing another experiment with household chemicals and became careless. Whichever it may be, Alan Turing passed away and left the world with many raw ideas to work out. In my opinion, the biggest contribution that he left with us was his idea of a single machine running off a finite number of algorithms to perform multiple tasks. This being the vision of the computers we all use today.

Virgin and Child with Saint Anne

The Virgin and Child with Saint Anne Rebecca Townsend Hum2235 Dr. Hoover Edison College Fall 2012 Townsend 1 The painting of The Virgin and Child with Saint Anne took more than a decade to complete. It was created in the 16th century, in Florence Italy. A young master artist declined the original commission for The Virgin and Child with Saint Anne and suggested Leonardo da Vinci. The monks who commissioned the painting, an artifact of Christ’s family tree, gave Leonardo a workroom.The figures in the picture are of Saint Anne representing the grandmother, the Virgin as mother (Mary/Madonna), the Child as Christ, and the lamb as the future sacrifice of Jesus. They are closely intertwined in the painting showing their tight bond in Christian History. Da Vinci could not separate Christianity from his work. Leonardo in his painting as well as in his life seemed to cultivate a sense of mystery (Capra XIX). The monks of the Florentine Santissima Annunziata commissioned Leonardo to pa int The Virgin and Child with St. Anne as an altarpiece for their high altar. In his typical fashion, Leonardo did not complete the work on time.The monks, eager for their altarpiece had to commission another artist to complete the work. The monks approached Filippo Lippi to complete the work Leonardo had started. Filippo Lippi was the artist that painted Madonna and Child with Two Angels in 1465. Lippi was the artist who had initially rejected the commission suggesting the monks give the project to Leonardo. Lippi considered Leonardo to be a superior artist. Lippi agreed to finish the project but died before its completion. After Lippi died, the monks had a young Florence artist named Perugino finally complete the piece.At last, the monks of the Santissima Annuziata in Florence had their painting for their high altar. Some consider the painting to be a treasure of esoteric and occult wonders. Some are fascinated by the sight of St. Anne supporting her heavy daughter on her knee, wi th no visible means of support (Budny36). Townsend 2 It’s hard to find any evidence of Leonardo’s beliefs in his paintings, since there are no written records that have survived if they ever existed. Leonardo believed that a good artist must also be a good scientist in order to best understand and describe nature.The humanistic, naturalistic, and scientific aspects of Leonardo’s life and work are not always clear because he was an original Renaissance man [Leonardo’s art, scientific investigations, technological inventiveness, and humanistic philosophy were all bound] together. During the 16th century he made numerous drawings and sketches with different themes that eventually lead to this famous artifact The Virgin and Child with Saint Anne. Various designs still exist of the version painted in 1510. Leonardo could not fuse the two qualities he desired: an abstract formula and the immediacy of life.The final painting now hangs in the Louvre in Paris. The painting is a complex and masterful synthesis of his previous variations (Capra 105). In some research it is stated that this artifact is unfinished, even though he had worked on this painting possibly for eight or nine years (Bramly 321). Leonardo had a habit of never finishing his work. Leonardo had drawn many different cartoons painting and sketches leading up to the final painting of The Virgin and Child with Saint Anne. One of his cartoon sketches had St. John the Baptist kneeling next to Christ (Capra 105). Leonardo switched St.John to a lamb in the final painting. The lamb (sacrificial animal) represents passion suffering in Christ’s destiny. It is not known why Leonardo replaced St. John, who was Christ’s cousin, with a lamb. He painted the Christ child as being about a year old. It looks as if he is slipping out of his mother’s hands and trying to grab hold of his destiny, the lamb. The lamb, being embraced by Christ has his head bent, while its tail a nd hind legs are clearly indicated to be in a comfortable place (Johannes 86). Townsend 3 Leonardo put his thoughts to paper and painted through, light, shadow, and geometry, using three dimensions.Da Vinci declared, â€Å"There are three kinds of perspective. † The first is concerned with the reason for the diminution of things as they form from the eye. Second contains the way in which colors vary as they form the eye. The third and last declaration of how objects should appear less distinct the more distant they are. Examples, perspective of disappearance (Capra 219). Perspective in painting was his destiny. From the pyramidal construction to the fact that only three feet belonging to the figures are visible, everything in the picture seems to be threefold.In fact in this painting, Leonardo was pursuing a theological meditation on the destiny of Christ, which had begun in his early painting Virgin of the Rocks (Bramly 320). Most research indicates the rocks, mountain strea ms, and escarpments of his childhood made up his private landscape in his paintings (Bramly 86). Leonardo depicts the women as sister like in age even though they are indeed mother and daughter. Saint Anne, the mother of Virgin and Child, sits with her daughter on her lap. The Virgin is half rising from her sitting position and she appears to want to restrain her daughter from separating the Child and lamb (Kemp 273).It is unusual for Mary to be portrayed in her mother’s lap. The painting may have more meaning to it than the Passion of Christ. Saint Anne perhaps represents the Church in this painting. Art critics have admired the unity of the three figures, the freedom of movement, the sweet and melting quality of the faces, and the mountains in the background. The family figures almost blend into each other in their rhythmic balance, with Leonardo’s dreamy mountains, foreshadowing the landscape of the Madonna, in the background (Capra 105). What better way to describe the bond of maternal love uniting three generations?Leonardo had written in a short note in one of his journals, The Virgin and Child Townsend 4 with Saint Anne means â€Å"the glorification of motherhood†. The Virgin and Saint Anne in this masterpiece seem to be about the same age in the painting, with their two bodies merging almost into one. Leonardo gave the child two mothers both graced with the blessed smile of happiness. To the viewer’s eye, the painting may imply to evoke his thoughts on his childhood which the painter wanted our thought as childhood had been divided between his real mother and his stepmother.He may have united them in his mind as he did in his painting, a picture that no one could have painted except of Leonardo De Vinci (Bramly 318). Both women, Saint Anne and the Virgin, have dedicated their lives to God, which had touch Da Vinci. One research source stated that in the painting Virgin and Child with Saint Anne, the Virgin is designed first, as she is in so many of his drawing, and the landscape seems to flow from her. The Painting is designed by Da Vinci in a diagonal, where we formerly saw a pronounced swing down from top right at the crown of the tree, through St .Anne’s left arm and elbow, through the successive arm/knee/arm/knee configuration of the Virgin, down to the placement of St. Anne’s feet on the then more brightly â€Å"spotlighted† left section of the rocky foreground. Against that progression, we saw in the earlier state how Leonardo had orchestrated a countervailing upper left to the bottom right sweep through the principal heads and the arms of the Virgin and the Child, down to the rump and tail of the lamb. This movement was decisively echoed and enforced by the parallel diagonals of the Virgin’s right leg and St.Anne’s left leg (Johannes 3). It is stated that Saint Anne’s left arm was painted the same way in another Leonardo da Vinci painting. Townsend 5 Leo nardo’s composition of the Virgin and Child with Saint Anne is perhaps the one which, of all his designs, he contemplated the longest and in great depth. Perhaps, he felt attracted by the particular formal and iconographical problems presented by the subject. When we were asked to select an artifact to research and write about, the painting of the Virgin and Child with Saint Anne caught my eye.The love and compassion in the women’s eyes and their expressions towards the innocent child reminds me of the love I have for my own children. Although much research has been done to discover why Leonardo painted the picture the way he did, it is still unclear. It is unclear why the women appear to be the same age and why he substituted St. John with the lamb for the final painting. Research is still being done on his journals and notes. Leonardo, who was left handed, wrote all his notes in mirror writing, from right to left (Capra, 27).Perhaps further analysis of his notes and sketches will reveal more insight into the painting of the Virgin and Child with Saint Anne. [pic] Work Citied Bramly Serge. Leonardo the Artist and the Man. Penguin Group. Great Britain. 1994. Print. Budny Virginia. The Art Buletin. Vol. 65, No. 1 (Mar. , 1983), pp. 34-50. Print. Capra Fritjof. The Science of Leonardo. New York. Anchor. December 2008. Print Johannas Nathan. Miteilungen. 36. Bd. H. ? (1992), pp. 85-102. Article. Kemp Martin. Leonardo on Painting. Yale Nota Bene. Yale University. 2001. Print. Marani Pietro C. Leonardo Da Vinci. Abrams Harry N. New York: 2000. Print.

Corporate Entrepreneurship Essays

Corporate Entrepreneurship Essays Corporate Entrepreneurship Essay Corporate Entrepreneurship Essay Corporate entrepreneurship is also commonly known as corporate venturing or  Intrapreneurship. It is coined by legendary management thinker and management guru   Peter. F. Drucker. It is the act of initiating new ventures or creating value with an already established  organization  or social entity. It is basically a process of creating new business within established firms to improve organizational profitability and enhance a firm’s competitive position or the strategic renewal of existing business. â€Å" Innovation â€Å"is at the very core of corporate entrepreneurship.So corporate entrepreneurship is done to enhance an organization`s competitive edge through innovative ideas which creates a unique place for itself in the industry or creates a new industry by itself. It can also be called a process by which organizations try to change its existing image. Corporate entrepreneurship activities can be internal or external. Internal activities are the process or acti vities which are developed within a organization. These type of activities are done in order to test a market, technology, production methods or effectiveness of employees. These activities may cover at various levels of the firm.Internal entrepreneurship can be applied on the following stages like: administrative, opportunistic, imitative, technical or organizational. External entrepreneurship is the process of combining resources which are located at different areas in the environment by individual entrepreneurs with his own unique resources to create a new combination of resources, which is independent of all others. External activities are in the form of mergers, joint ventures, corporate venture, venture nurturing, venture spin-off and others. Corporate entrepreneurship can be applies to any business size at any point of a organization`s life cycle.Today there is a growing desire by business houses to apply corporate entrepreneurship in order to enhance the innovative abilities of their employees and to increase corporate success by creating of new corporate ventures. However, the creation of corporate activity is difficult since it involves radically changing internal organisational behaviour patterns. Both entrepreneurship and corporate entrepreneurship are a viable means of creating business growth and stimulating the economy. Large companies implementing  entrepreneurial   culture can receive many benefits to help them tap into innovation and be competitive in this global market.If the company is encouraged to take risks, the employees are allowed to be creative and innovative, it becomes easier to generate new products for the market. It becomes clear from the findings and research that there is a strong link between large organizations using corporate entrepreneurship and their growth and increased profitability because it encourages a culture that promotes pro-activeness. Another plus point of  corporate entrepreneurship  is that it brings knowledge as everyone in the organization works towards the same goal.This creates valuable knowledge and understanding between all members. Thus the organization develops a continuous knowledge base of information that results in increased and better informed innovative behavior in decision making and risk taking. Some examples of corporate entrepreneurs are: Philips Philips faced a situation where it`s standard set of distribution , promotion and sales policies apllied uniformly to all product lines was ineffective in coping with the large volume chains that dominated the retail.Philips reorganized the structure of its consumer electronics marketing division based on an analysis of changes in its product line and a growing concentration in its distribution channels. To cope with these problems, Philips abolished its uniform structure and organized the marketing department into three groups: an advanced-system, group for technologically sophisticated, high-margin products such as c ompact disk players; a mainstay group for high-volume mature products and in mass merchandizing group for older, declining products (such as portable cassette players).Meanwhile, increasing concentration in the distribution channels and a growing need for distinct marketing approaches for different products became manifest throughout Europe. The new model for the marketing organization developed by the British subsidiary was clearly appropriate for other subsidiaries. Despite initial resistance, the innovation was soon transferred to most other international organizations. Proctor and Gamble For  Proctor and Gamble, the innovation meant something new. When applied to a product, â€Å"new† meant different things.One of the best examples of product innovation was the way in which Proctor amp; Gamble developed a global liquid detergent. Despite the success or liquid laundry detergents in the United States, all attempts to create a heavy-duty liquid detergent category in Europe had failed due to different washing practices and the superior performance of European powder detergents. which contained enzymes, bleach, and phosphates at levels not permitted in the United States. But Pamp;G’s European scientists were convinced that the liquid detergent’s performance could be enhanced to match local powdery.After several years of work, they developed a bleach substitute as well as a  means to give enzymes stability in liquid form. Meanwhile, researchers in the United States were working on a new liquid better able to deal with the high clay soil content in dirty clothes in the United States. Each product incorporated the best developments created in response to European, US, and Japanese market needs. Relatively speaking, however, a product already introduced in one market may be an innovation elsewhere because it is new and different for the targeted market. .

Free Essays on Winston Church Hill

meant. He was in trouble a lot at school. His greatest pleasure was reading. He liked to read poetry. He hated Math and Latin, but loved History, Poetry and butterflies. At the age of 12, he was transferred from St. James School to Brighton Harrow. He was treated poorly by the older boys because he wasn’t afraid to speak his mind and stand up for himself. He was a kid that always dreamed of being a soldier. He loved looking at armor. At age 15, he passed his military exam and went to Sandhurst. He graduated with honors at age 18 and became an officer in the Calvary. His father died after the new year. In 1895, he became a war correspondent during the Cuban Rebellion. In 1896, he was sent to India. While there, he realized how much stuff he didn’t learn in school. He started studying and reading to get knowledge. In 1889, they went to war with the Boars, and Winston and sixty British Soldiers were imprisoned. They wanted to escape. Winston climbed the bathroom wall, snuck aboard a train, and returned to England. About a month later, he ran for office. He was elected into Parliament. In 1901, at the House of Commons, he made his first parliamentary speech. Seven years later, in 1908, he married Clementine Hosier. A couple of months later, he got kicked out of office. In 1911, he was elected first Lord of Ad miralty, during World War I. When one of his strategies failed, he was a... Free Essays on Winston Church Hill Free Essays on Winston Church Hill Title: The Story of Winston Churchill Author: Alida Sims Malkus This story tells of Winston Churchill’s life from birth until he was knighted by Queen Elizabeth, II. Winston Churchill was born November 30, 1874. He went to St. James School near Ascot when he was 7 years old. At school he lived in a dorm. Winston had one brother named Jack. His mother and father were always gone for great periods of time. He always had a hard time in Latin. He could remember it, but he didn’t understand what the words meant. He was in trouble a lot at school. His greatest pleasure was reading. He liked to read poetry. He hated Math and Latin, but loved History, Poetry and butterflies. At the age of 12, he was transferred from St. James School to Brighton Harrow. He was treated poorly by the older boys because he wasn’t afraid to speak his mind and stand up for himself. He was a kid that always dreamed of being a soldier. He loved looking at armor. At age 15, he passed his military exam and went to Sandhurst. He graduated with honors at age 18 and became an officer in the Calvary. His father died after the new year. In 1895, he became a war correspondent during the Cuban Rebellion. In 1896, he was sent to India. While there, he realized how much stuff he didn’t learn in school. He started studying and reading to get knowledge. In 1889, they went to war with the Boars, and Winston and sixty British Soldiers were imprisoned. They wanted to escape. Winston climbed the bathroom wall, snuck aboard a train, and returned to England. About a month later, he ran for office. He was elected into Parliament. In 1901, at the House of Commons, he made his first parliamentary speech. Seven years later, in 1908, he married Clementine Hosier. A couple of months later, he got kicked out of office. In 1911, he was elected first Lord of Ad miralty, during World War I. When one of his strategies failed, he was a...

Program Evaluation Plan Assignment Example | Topics and Well Written Essays - 500 words

Program Evaluation Plan - Assignment Example The two slide presentation workshops will concentrate on the effectiveness and informative value of the visual aids used by the supervisors. From the workshops, it is expected that the supervisors will increase the quality of their oral presentation skills by 30th April, 2015. The supervisors will also get three sessions of one-on-one coaching on how to give employees positive and negative feedback on their work performance. Later, the supervisors will also get a tutorial on how to provide accurate, complete, useful written performance feedback that is in compliance with company’s policy and state law. The company will provide the required venue, table, and chairs. The ABC Company HR communication specialist will conduct all sessions. From the coaching sessions and the tutorial, it is expected that the supervisors will have increased the quality of their ability to provide performance feedback to employees by April 30, 2015. Progress on the indicators will be measured by the number of sessions delivered, the number of sessions each supervisor attended, the level of participation of each supervisor, length of sessions and the adherence to workshop delivery plan by the official in charge (Fink, 2015). Program process will be evaluated by examining whether the program was implemented with fidelity and adapted to the target population. It is expected that an acceptable degree of program fidelity will be maintained, and the program will be reviewed for appropriateness. Program outcomes will be evaluated by examining program’s influence on the supervisors’ communication skills. Monthly communication skills assessments will be updated every month by the Communication Specialist. The attendance and participation rates will also be recorded and an implementation record developed by the Communication Specialist upon conclusion of every session. Surveys will be

A jornal opinion article Essay Example | Topics and Well Written Essays - 750 words

A jornal opinion article - Essay Example The country’s exports also fell, considerably, due to slow-down of economies in countries like China and Euro zone nations. According to the article, the corporate decision makers are delaying their investment plans, as they have their own apprehensions on Federal Budget Policies and forthcoming US elections. These factors, among others are reasons for delaying the investment decisions by those responsible for corporate spending. As they are delaying the implementation of big projects, partly due to slow demand, world-wide, the big businesses are looking forward to government action on issues involving ‘tax cuts’ and ‘fiscal deficit’. During the meeting with President Obama, top executives of leading companies, including Apple and JP Morgan Chase agreed to work together for betterment of investment climate in the country. As the article date is 19 Nov 2012, it informs the readers that the spending by major corporate businesses was excellent during the whole year, except the recent months when it slowed down considerably. This was supported by the figures quoted in the article, which showed that S&P’s listed 500 stock index companies spent around $ 580 billion on the purchase of plant and equipment for business expansion. However, the reversal in the capital expenditure plans, during the third quarter of 2012 was a sign of worry for the future, although the current scenario presented in the article was not that gloomy. The slow down was due to lower fuel prices, higher job opportunities and better housing market. The article has held the global slowdown responsible for the reversal of investment plans in third quarter of 2012. Giving an example of reducing demand of coal and other minerals in China, the article informs that the result of this has been reduced orders for earth moving and other heavy equipment for American giant ‘Caterpillar Inc.’. Other areas of concern provided by