The Traveling Salesman Problem Computer Science Essay

The Traveling Salesman Problem Computer Science Essay Travelling sales man problem is one of the challenging problems in the real life and also most well studied combinatorial optimization problem. Many Researches from different fields like operational research, algorithms design and including artificial intelligence attract by it. This problem has been studied by different researches and come up with different solutions and this problem has been solved by using different algorithms like Blind search, Branch and Bound Search , Heuristic algorithm and Genetic algorithms etc. the problem was formulated as a mathematical problem in 1930 and later it is used as bench mark for many optimal solution. 1.1 TRAVELING SALESMAN PROBLEM: A Travelling salesman has a task of visiting N number of cities. He will start from a home location and want to visit each city just once and return back to the original location from where he starts. Travelling salesman route will be plan in such a way that in a given N number of cities cost of travelling from one city to any other city what is the minimum round trip route that visit each city once and then return to the starting place. The goal is to find the shortest tour that visit each city in a given cities exactly ones and then return to the starting city. The only solution to the travelling salesman problem is to calculate and compare the length of all possible ordered combinations. 1.2 History of travelling salesman problem: The travelling salesman problem was treated by a Irish mathematician sir William Rowan Hamilton and British mathematician Thomas Penyngton kirkman in the early 1800s. Hamilton and kirkman work on game called Hamilton Icosian game that requires player to complete tours through 20 points using only the specified connections. The general form of the travelling salesman problem studied by mathematician Karl menger during 1930s. He defines the problem using brute force algorithms and observed nearest neighbour heuristic non optimality. Soon after the name travelling salesman problem introduced by hassler Whitney at princeton university. In the 1940s the Travelling salesman problem was studied by statisticians Mahalanobiss, Jessen, Gosh, Marks. Among them P.C .Mahalanobiss took a sample survey of acreage under jute in Bengal discussed aspects of travelling salesman solutions through randomly chosen locations in the Euclidean plane. And this work is deal with survey of form lands one of the major cost to carrying out the survey was the transport ion of men equipment from one survey point to next. During the period between 1950s and 1960 the problem becomes more popular in scientific group in Europe and USA. a number of solutions designed by George B.Dantzing, Fulkerson and Johnson(1954) . in 1954 Heller publi shed an 88 report which contains many basic solutions on the travelling salesman polytype. In 1957 L.L.Barachet published graphic solution of travelling salesman problem which describes an enumeration scheme for computing near optimal tours. In 1964 R.L Karg and G.L. Thompson were applied heuristic algorithm for a 57 city problem. During the period R.M Karp and M.Held published an article about the travelling salesman and minimum spanning tree which introduced one tree relaxation of the travelling salesman problem and using node weights to improve the bound given by optimal tree. In 1990s Bixby and Cook developed the programme for travelling salesman problem which are using recently. 2.0 GRAPH: 2.1 Travelling salesman problem modelled as graph: Travelling salesman problem can be modelled as Graph where as the cities are the graph vertices, path is graph edges and path distance is edge distance. Our goal is to find the shortest tour that visits each city in a given graph exactly ones and then return to the starting city. 3.0 Search Algorithms: To solve travelling salesman problem we can use different types of algorithms like blind search, heuristic algorithms, uniform cost search etc 3.1 Blind search: Blind search algorithms are such algorithms which does not contain domain knowledge of the problem and it search blindly, hence it is called blind search algorithm. The only thing a blind search can do is it describes a non goal state from goal state. Assume that you are at city A and you want to reach at city D, if we draw a search tree level 1: city E, city B, city C. a blind search will have no idea which node should explore first, hence it explore each and every node blindly. In blind search we may not get information we can use. We just be looking for an answer and we wonà ¢Ã¢â€š ¬Ã¢â€ž ¢t no until we found it. The blind search is also called as un informed search. Blind search is divided into two searches Algorithm they are 1) Breadth first search and 2) Depth first search 3.2 Breadth first search: Breadth first search is a search which starts at one node and it expands the all the neighbour node then after completing those nodes, it expands remaining nodes unexpanded it process is continues up to reaching a goal. The technique followed by breadth first search is FIFO first in first out) queue, the difference between breadth first and depth first search is, the depth first uses stack i.e. LIFO (last in first out). In this logic the items which are added is equal to the item which are deleted. This process continues up to reach a goal. 3.3 Depth first search: Depth first search is a general technique for traversing a graph. The technique which organise the to Do list was stack that is last in first out (LIFO). Depth first search start at one node and it explore as far as possible along each branch until a required goal node is found. Then it takes backtracking and return to the next node which it hasnà ¢Ã¢â€š ¬Ã¢â€ž ¢t finished exploring and it keep on repeat the same procedure until it reaches to its goal. If Depth first search goes down a infinite branch and if it does not find a goal state or if it does not find the solution may be a better solution at a higher level in tree. Therefore depth first search is neither complete nor optimal. ALGORITHM: INPUT : A connected graph G ,a starting vertex 1 OUTPUT: An ordered spannig tree T of graph G with root vertex 1 Initialize tree as vertex 1 Initialize S as the set of proper edges incident on vertex 1 While s not equal to null Let e = dfs next edge(G,S). Let w be the non tree end point of edge e. Add edge e and vertex w to tree T. Update Frontier(G,S). Return Tree T. 4.0 DEPTH FIRST SEARCH APPLY TO GRAPH STARTING AT NODE 1: For the above tree diagram we are using Depth first search, from the graph the sales man starts at node a and visits each node and return to original node Step1: from node 1 there is a three ways to travel i.e. node 2, node3 and node5 in level 2 Step2: by following depth first search condition LIFO it expands node 2 until the goal reach So for node 2 there is a two ways to travel i.e. node5 and node4 there is only one way for sales man to reach node 3 so this is not minimal path to travel. After expanding first branch sales man reaches node 3 from node 3 sales man reaches node4 With path length of 8 and from node 4 he reaches node2 with path length of 5 and from node 2 sales man reaches node5 with path length of 6 then length of whole sub tree is 27. After expanding of second branch sales man expands node 5, from node 5 sales man travels node 2 with path length of 6 then from node2 sales man reaches node 4 with path length of 5 From node 4 sales man reaches node 3 path length of 8.then length of whole sub tree is 26 Here we follow the condition that sales man will not visit those not which have already visited. the left vertices in the graph are chosen before right, from above to roots the minimum spanning tree path is 1-5-2-4-3 =26.this is the best minimum root for sales man to visit each city started at city1. 4.1 DEPTH FIRST SEARCH APPLYING TO THE GRAPH STARTING AT NODE 2: For the above tree diagram we are applying depth first search on which sales man starting at node 2. From starting city we have three ways to travel i.e. node 1, node4 and node5. From node 1 sales man has again to two ways to travel i.e. node3 and node5.from node 3 it reaches node 4. but here if we want to visit node5 we have to backtrack again it will not satisfy the condition visiting a city once so we didnà ¢Ã¢â€š ¬Ã¢â€ž ¢t reach goal here sales man expands neighbour node 4, from node 4 sales man reaches node 3 with path length of 8, then sales man processed to node 1with path length of 8, then sales man visits node 5 from node 1 with path length of 7. The length of whole sub tree is 2-4-3-1-5=28. After expanding node4 travel sales man moves to node 5, from node 5 he reaches node1 path length of 7,from node 1 sales man reaches node 3 the path length of 8 and he proceeds to node 4 from node 3 with path length of 8,then whole length of sub tree is 2-5-1-3-4=29. Here sales man follow the condition that visiting each city, then the the best minimum cost route starting at node 2 is 2-4-3-1-5=28. 5.0 INFORMED SEARCH: Informed search is an estimate availability of the distance (cost) from each node(city) to the goal. This estimation will help you to head into the correct direction. The outline of inform search are heuristic search, best first search, greedy search and A* search 5.1 Heuristic search: Heuristic uses domain specific knowledge to estimate the quality or potential of partial solution .A heuristic search that find a good solution in less time comparing to blind search but not always find best solution. This search is very much useful for solving big problem which may may not solved by using other search and this search generate a possible solution which can be either route from the initial location or goal in the problem. For travelling salesman problem the nearest neighbour heuristic work well, but some time due to the arrangement of cites it will not find the shortest route. 5.2 Best first search: Best first search is a general approach of the tree search algorithm. In which it expand a nodes which is based upon a evaluation function. The estimation of cost is constructed as evaluation function then the node with minimum evaluation is expanded first. A best search is a combination of both breadth first search and depth search, a breath first is good because it will not go deeper and the depth first search is best because it can be found without searching all the nodes, hence the best first search allows us to gain benefit both the approaches 5.3 Greedy search: Greedy search select the path that has lowest heuristic value or estimated distance to the goal. Greedy search is a example of best first strategy, and it some cases like depth breast search I may never find the solution and greedy search is not optimal solution take into costly paths . This can be happen in the last step or in the first step. 5.4 A* search: The most widely known form of best first search is called a* search or best first search is simplified as A*search. The evaluation of nodes is carried in A* search was combination of g(n) the cost reached and h(n) the cost get from the node to the goal f(n)=g(n)+h(n) Here f(n) estimate cost of cheapest solution through node n, A* search is both complete and optimal which is identical to uniform cost search. From the above equation: g(n) is the total length between starting place to current location. h(n) is estimated length from current location to goal. A heuristic function which estimate how much distance it takes to reach goal. f(n) is the sum of g(n) and h(n) .then this will be a current estimated shortest path which founds until a A* algorithm is completed. A* Algorithm: A* Algorithm starts with initial nodes then it will take the best node on open such that f(n)=g(n)+h(n) is minimum. If Best is a goal node quit then return to the path from the intial to best or remove the best from open and all among best node naming each node with its path from initial node. 6.0 A* Algorithm applying for given graph: from the above graph , it shows that the node 1 is the initial node where salesman starts and reaches the node 3 which is the current location . then sum of the distance between initial to current location is consider as g (n) ie 1-5-2-4-3= 26.then the estimated length from current location to the goal is consider as h(n) ie 8 and then total minimal distance of path is A*=1-5-2-4-3-1=34 Then this is the minimal path in which salesman can travel starting at node 1. 7.0 Comparison table for depth first search and A* algorithm Algorithm Domain knowledge Memory space Minimum route Time complexity efficient Depth first search It doesnà ¢Ã¢â€š ¬Ã¢â€ž ¢t contain domain knowledge more It find after complete search It takes more time less A* search It contain domain knowledge less It has information about it It takes less time more 8.0 CONCLUSION: The Idea of Travel sales man problem has much application in different fields .To Find best routes of travelling salesman we are used two algorithms they are Depth First search and A* Algorithm. Hence we conclude that A* algorithm is more efficient then depth first search algorithm, the time complexity of depth first is more comparing to A* search and it takes less memory space comparing to depth first search. Depth first search algorithm is more suitable finding minimum tour for limited number of cities, because if we take 50 to 100 cites depth first search expands each node of a tree to reach to the goal which is time consuming and memory waste.

reasonable doubt :: essays research papers

  Ã‚  Ã‚  Ã‚  Ã‚  A Burden Worth Having I don’t quite remember what I was doing in Baltimore. Suddenly, through a chain of random events, I ended up in jail for grand larceny. Although I was confident of my innocence, even my best friends testified against me. I found no hope in our judicial system. Fortunately, I could escape that situation. My alarm rang, and I woke up. Others, however, don’t have that option. Such is the story of Kirk Bloodsworth. In 1985, he was sent to death row accused of killing and raping a 9-year-old girl from Maryland. In 1992, when DNA testing was in its infancy, Bloodsworth pushed for a DNA test to prove he was not the killer. It was not a match. The state of Maryland set him free and paid him $300,000 for wrongful imprisonment. The government’s burden to prove â€Å"beyond a reasonable doubt† the culpability of a suspect is ideal because it represents the recognition, on the part of the government, that our judicial system is not infallible, as Mr. Bloodsworth’s case points out. When instituted in the late 18th century, the burden of proof was a response to arbitrary arrests for political or economic interests. The government’s decision to enact the burden of proof symbolizes the popular resentment of these violations of liberty. Hence, the principle of â€Å"it is better for 10 guilty men to go free than for one innocent man to go to prison.† The United States has historically promoted the rights of man and liberty. The sentencing of an innocent person not only displays the inefficiency of a government’s judicial system to uphold these values, but also the irreversible damage done to the individual. The pressure that law enforcement officials face from the public to find closure to cases highlight one reason why the burden of proof is essential in the judicial system. When a police department cannot find suspects to charge for a crime, it is then seen as a failure on its part. In October, a rally was organized against the death penalty in Houston, Texas. Amnesty International revealed 180 boxes containing unexamined files with vital information about cases involving prisoners on death row. Potential evidence that could lead to the exoneration from death row of these individuals was not taken into consideration during their trials. This revelation demonstrates how law enforcement officials and the judicial system can carelessly make mistakes and why the burden of proof is necessary.

Family Stress and Their Relation to Academic Performance

Chapter I The Problem and Its Background Introduction The term stress had none of its contemporary connotations before the 1920s. It is a form of the Middle English destresse, derived via Old French from the Latin stringere, â€Å"to draw tight. † It had long been in use in physics to refer to the internal distribution of a force exerted on a material body, resulting in strain. In the 1920s and 1930s, the term was occasionally being used in biological and psychological circles to refer to a mental strain, unwelcome happening, or, more medically, a harmful environmental agent that could cause illness.Stress plays a role in the body, behavior and feelings of people. Stress comes in many forms. Things like our environment, physiological well being, thoughts and social stresses and stress inside our homes can have an effect on learning Stress, particularly family related stress can have an impact on a student’s academic performance. College students have many obstacles to o vercome in order to achieve their finest academic performance. Different stressors such as time management, financial problems, sleep deprivation; social activities can all pose their own threat to a student’s academic performance.The way that academic performance is measured is through the ordinal scale of general weighted average (GWA). A student’s GWA determines many things such as class rank. Much research has been done looking at the correlation of many stress factors that college students’ experience and the effects of stress on their GWA. There are many factors that can cause stress and influence a student’s academic performance and therefore affect his or her overall GWA.A college student may find him or herself in a juggling act, trying to support a family, taking care of job responsibilities, and at the same time trying to make the most of the college career. All of these factors can affect the grades of students, which ultimately affect the res t of their lives. Conceptual Framework Stress is a large part of everyday life. Most stress occurs at busiest moment like at home. It’s one of the most common places for stress to build. Nevertheless stress is unavoidable.According to Marilyn Wedge, a family therapist, stressful situations at home like a parent losing a job, an illness, marital discord, or even conflicts about day-to-day issues may be troubling to a child without the parents even being aware of it. And often children go about trying to solve the family problem in the only way they know which may the cause of stress and, subconsciously or not, the children tend to bring the family problem outside home making the situation worst. These changes can cause health problems if experienced to frequently. If a child is stress the body responds negatively to it.The body often becomes worn down making it more susceptible to becoming sick. Depending on how serious the stress, can determine the severity of its impact. The brain, nerves, and central nervous system interpret stress. There are several side effects that occur from stress. Insomnia is another factor that stress may bring on. This occurs when a child is disrupted with thoughts and questions that drive them crazy and cause an inability to sleep. Chronic pain, headaches and backaches can be stress induced when under pressure. The muscles in these areas become tense under stress.Heart problems are the most common side effect. The pain felt in the chest is tension caused by an oxygen shortage to the heart. Heart attacks occur due to high blood pressure and can be fatal. Some behaviors that child takes part in to reduce or cope with stress may also bring on heart problems. Stress can also hurt emotionally as with depression. Research paradigm is shown on Figure 1. This included the input, the process, and the output. The input contains the profile of the 2nd year Accountancy students of De La Salle Araneta University, the family stress they en counter, and their academic performance.In the process, questionnaires were distributed and observations were conducted to gather relevant information from the respondents. It also included the analy -sis and evaluation of the gathered data and information from the respondents. The output consists of the findings about the effect of family stress to academic performance of the respondents. Figure 1: The schematic paradigm used in the study. Statement of the Problem The purpose of the study was to identify the effects of family stress to the second year accountancy students of De La Salle Araneta University regards to their academic performance.Specifically, the study aims to answer the following questions: a. How may the profile of the second year accountancy students of De La Salle Araneta University be described in terms of gender? b. What are the family experiences/stress and the academic performance base on GWA of the respondents? c. Is there a significant difference between mal e and female students in handling family stress? d. Is there any relationship between family stress and the academic performance of the respondents? HypothesisFamily-related stress has no significant effect on the academic performance of second year Accountancy students at De La Salle Araneta University. Scope and Delimitation This research is delimited only to preparation and evaluation of stress level aimed at correlating the family related stress and academic performance of students through their GWA. The students were asked to complete a survey, including the perceived stress scale. Along with this test the students were asked to complete a demographic data sheet that asked questions such as age and gender, and also their classes and grades the prior semester.The respondents are thirty college Accountancy sophomore students of De La Salle Araneta University (which includes 8 boys and 22 girls) during the 1st semester of academic year 2012-2013. The respondents are chosen randoml y from a block section of Accountancy. Significance of the Study The researchers intend to show the impact of family related stress in the academic performance of second year Accountancy students of De La Salle Araneta University through their General Weighted Average (GWA).Moreover this study, address itself to: the students that they may understand the impact of family related stress in their academic performance and eventually help themselves , to the professors that they may observe the behavior of students and help them through guidance and referral to the University Guidance Office for help, to families, specially the parents and the guardians that they may help their family member cope with stress from its roots (family related stress) and bring out their optimum academic performance, and to interested people in the academe and community that they may gain insights on this research to help people around them understand the possible impact of family-related stress to the acade mic performance of a student, and to other interested individuals that they may find knowledge on this research. Definition of Terms To further understand this research, below are terms used in the research.GWA (General Weighted Average). It is a term that refers to the average of grades in all subjects taken, whether passed or failed. It is the result of combining the performance rating based on the screening criteria or subject. It serves as the indicator of a student's academic performance in a given semester or school year. Stress. It is a term that defined as an organism's total response to environmental demands or pressures. When stress was first studied in the 1950s, the term was used to denote both the causes and the experienced effects of these pressures. More recently, however, the word stressor has been used for the stimulus that provokes a stress response.

Personal Characteristics of Nick Thomas, Charles Henry, and Chairman Lup In Wisdom Sits in Places

The significance of place-names is compounded in the personal characteristics of Nick Thompson, Charles Henry, and Chairman Lup. Although their personal characteristics differ significantly in terms of attitudes and approach to reality, their behavioral orientation are relatively the same. The subscription to a single set of norms (the rules attached to the place-names) ensures a relatively predictable pattern of behavior from the three characters.Hence, one can assume that the behavioral orientation of the three characters stemmed not from their intrinsic characteristics but rather to their personal interpretations of ‘reality. Here, reality takes the form of adjunctive reference to the past, the legacy of place-names. There is a need, however, to look into the personal characteristics (behavioral) of the characters to provide credence to the above-mentioned proposition. Charles is a traditionalist, an individual who clings to the general beliefs and rules of ancient customs. His minimal exposure to the vagrancies of modern life did not affect his behavioral orientation towards customs and tradition. In fact, most of his actions indicate a persona that embraces the beauty and glorious existence of place-names.In page 10 of the book, Charles said to Mosley: What he’s doing isn’t right. It’s not good. He seems to be in a hurry. Why is he in a hurry? It’s disrespectful. Our ancestors made this name. They made it just as it is. They made it for a reason. They spoke it first, a long time ago! He’s repeating the speech of our ancestors. He doesn’t know that. Tell him he’s repeating the speech of our ancestors. Charles’ obsession with mental images and speeches of his ancestors created a personal impression of sturdiness in his character.He refuses to allow changes that will affect his beliefs on place-names. Nick Thompson behavioral orientation is similar to that of Charles Henry. An old man who delighted in telling humorous and often embarrassing stories, his expression is quite mischievous and intimidating. In the tribe though, he is known as the true â€Å"Slim Coyote. † Thompson’s character can be described in four words: serious, generous, intelligent, and outspoken. In anthropology, the character of Nick Thompson exemplifies the character of an ideal elder who teaches the younger generation the essence of existence.In page 43 of the book, he said, â€Å"Start with the names. I will teach you like before. Come back tomorrow morning†¦ White men need paper maps. We have maps on our minds. † Due reference again is made to the highly revered place-names. The Western Apache’s reverence to place-names are generally rooted from the historical value of the place-names themselves. This historical value is imbued in the personal beliefs of every Apache. It can be said that Nick Thompson, by virtue of his age, has strong personal attachment to this histori cal value.In fact, his understanding bear more influence to his behavioral orientation than his actual belief in the place-names themselves. His motto in life is: â€Å"Learn the names† (a deep understanding of the place-names). Chairman Lup’s character is generally similar to that of Thompson. His obsession with stories about place-names is the primary foundation of his behavioral orientation. For the most, an understanding of his character forces one to assume that he is a strict traditionalist. His personal belief about place-names is actually greater than Charles Henry and almost equal to that of Nick Thompson.

Sexuality essays

Sexuality essays 5. Sexuality in the Twentieth Century Humanity is a long drawn out historical process. Somebody once said only that which is without history can be defined. Sexuality is a substantial example of this. In his lecture, Professor Simon argued that sexuality in the twentieth century has been changeable. He draws many points about the variable of sexuality, and how it changes with through the years. The Professor also lectures about how generations mend, and explains how one generation can have great influence and impact on one another. Meaning that the beliefs of a prior generation can give way to expansion and growth of even more different ways of thinking. Complex and unchangeable sexuality draws from many different sources such as tradition, culture, and fantasy. One of the first points the Professor states is explaining how the body compares to sexuality. Simons states that there have been many changes in sexual behavior. He claims that the body is the constant. This is one thing that basically has remained the same over throughout history only with minor changes. Noting that the variable is the behavior of sexuality. Beliefs and attitudes have changed over the years, even more dramatically recently. Sexuality needs to be examined in how it fits in everyday life, and how it is shaped by everyday life. Different eras have proved to produce different beliefs on sexuality. The Professor tells of many examples in his lecture. Lets focus on the twentieth century. Simons states that a study was conducted in the twenties that proved that premariadal sex had almost doubled from the years before. He then went into the explaining that this was due to society and the industrial boom that was going on at this time. This in his opinion started to show a change in attitude of a nation. People started to become more open of who they were and their sexuality. Then he went to the 1950s and talks ab ...

Group Decision Making Essay Example | Topics and Well Written Essays - 1500 words

Group Decision Making - Essay Example There are studies which support the concept that groups influence work behavior. A group is composed of individuals working together towards common goals by interacting with one another and utilizing appropriate resources. They need a certain period of time for common interests to be discussed, explained and internalized so that stability and efficiency would ensue. From the cohesiveness that a group develops, certain level of performance is achieved. It is therefore the objective of this paper to proffer issues pertinent to group decision making by focusing on experiences with group decision making in a professional setting. One successful and one unsuccessful experience would be identified. Likewise, the reasons for the group’s good or poor performance, drawing from concepts in the course readings would be identified and discussed, accordingly. A group is composed of individuals working together towards common goals by interacting with one another and utilizing some resources. They need a certain period of time for common interests to be discussed, explained and internalized so that stability and efficiency would ensue. According to Martires & Fule (2000, 109), â€Å"many specific roles can be categorized according to the actual behaviors of the group members. Group-building roles lead the group toward positive member interaction and interpersonal behavior†. Different studies present varying models of a typical decision-making process depending on their perspectives. Some models follow eight steps, others five. For purposes of making intuitive choices, one structurally follows six steps in decision making. The six steps of this natural, intuitive decision-making process, according to Ethics Resource Center (2009) are: â€Å"Step 1: Define the problem; Step 2: Identify available alternative solutions to the problem; Step 3: Evaluate the identified alternatives; Step 4: Make the

Why is the British Government pursuing a policy of austerity while the Essay

Why is the British Government pursuing a policy of austerity while the economy is not growing - Essay Example The failure strategies and policies include the government opting to greatly cut down on the budgets of some of its departments to as low as thirty percent (Barrell and Liadze, 2009, p. 208). The Government had employed the austerity policies and hoped that it will greatly check on the budget deficit to minimum level of zero percent by the end of that financial year. This was also considered as a move by the government to boost its economic status and assist in paying off its public debt. Despite the above measures, the budget deficit of Britain has remained at an alarming rate and with the impact being felt most by the citizens following the increased recessions (Barrell and Liadze, 2009, p. 207) Pressure in now mounting on the government to come up with working solutions as well as cut down on the credit ratings. The austerity approach failed to meet its intended role of certifying things beyond reasonable doubt thus resulting to a huge setback in the economic development of Britai n. The Government of Britain is being accused of simply trying to experiment how efficient the austerity approach can be to its economy (Barrell, Holland, and Hurst, 2012, p. 933).This experiment has led the Britain citizens to live in depression for a long period of time.. From the look of things with regards to Britain economy, it is most likely that the austerity policies will not be easily implemented. Economists have come out strongly explaining that measures like cutting down on government expenditure may in the long run reduce the economic output largely, tax revenues to decrease, and spending on benefits to increase (Barrell and Liadze, 2009, p. 207). This however takes time and may end up resulting in an increase in the budget deficit. The government had intended to win back the favor of investors and businessmen by employing the austerity strategy. The effort to try and salvage the economic situation following the implementation of austerity policies has resulted to a big battle by the Bank of England to try slash investment spending (Delong and Summers, 2012, p. 78). This measure has however remained decimal and depressed. The government has also blamed the Eurozone for being its biggest business partners yet in has don e nothing to help it with the issue of recession. The government of Britain may try resolving this recession issue by loosening its fiscal policy (Delong and Summers, 2012, p. 78). Despite such positive advice, the government has remained adamant and has continued to propagate the pre-Keynesian economics. This approach has resulted in some positive changes in the country’s fiscal policy but most people have not yet felt the fruits of his efforts and opt for better contribution. Back in 2009, the government had forecasted that come 2013, the deficit would have gone down by 3.5 per cent of G.D.P. With time, the forecast has proven to have been too optimistic (Delong and Summers, 2012, p. 78). Despite the government coming up wit h measures to reduce economic budget deficit as well as government spending, it has not yet fully implemented these measures as it keeps on postponing them with the latest future date being put at them forward until 2016 to 2017 (Fatas, 2012, p. 78). The debt-to-G.D.P. ratio, which the government opted to go up by about seventy per cent, has surprisingly hit seventy-five per cent, and chances are that it will continue to increase up to eighty per cent in 2016. (Fatas, 2012, p. 78). The British government also blames the Eurozone crisis for the immense reduction of the amount of Britain exports goods. If the government realized that the external environment was unreliable it could have adapted to boosting the domestic market and solve