...this paper we first see how NP problems can be categorized and look at some examples. We then analyze the subset sum problem and prove its NP completeness. We look at various algorithms used to solve the problem and the efficiency of each algorithm. Hence we prove that subset sum problem is NP complete. Keywords: NP complete, NP hard, complexity, subset sum, exponential I. Introduction In the study of computation complexity of problems, we find out the resources required during computation like time, memory and space required. We check if the problem can be solved in polynomial time by some algorithm. An algorithm is said to be solved in polynomial time if its worst case efficiency belongs to O (p (n)) where p (n) is the polynomial of the problems input size. Problems that can be solved in polynomial time are called tractable and those that cannot be solved in polynomial time are intractable. The formal definition of NP problem is as follows: A problem is said to be Non-deterministically Polynomial (NP) if we can find a nondeterministic Turing machine that can solve the problem in a polynomial number of nondeterministic moves. Equivalent definition of NP problem: A problem is said to be NP if 1. its solution comes from a finite set of possibilities, and 2. It takes polynomial time to verify the correctness of a possible solution. NP-complete problems NP-complete problems are a subset of class NP. An problem p is NP-complete, if 1. p ∈ NP (you can solve it in polynomial...
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...Algorithms Springer Berlin Heidelberg NewYork Barcelona Hong Kong London Milan Paris Singapore Tokyo To my parents Preface Although this may seem a paradox, all exact science is dominated by the idea of approximation. Bertrand Russell (1872–1970) Most natural optimization problems, including those arising in important application areas, are NP-hard. Therefore, under the widely believed conjecture that P = NP, their exact solution is prohibitively time consuming. Charting the landscape of approximability of these problems, via polynomial time algorithms, therefore becomes a compelling subject of scientific inquiry in computer science and mathematics. This book presents the theory of approximation algorithms as it stands today. It is reasonable to expect the picture to change with time. The book is divided into three parts. In Part I we cover a combinatorial algorithms for a number of important problems, using a wide variety of algorithm design techniques. The latter may give Part I a non-cohesive appearance. However, this is to be expected – nature is very rich, and we cannot expect a few tricks to help solve the diverse collection of NP-hard problems. Indeed, in this part, we have purposely refrained from tightly categorizing algorithmic techniques so as not to trivialize matters. Instead, we have attempted to capture, as accurately as possible, the individual character of each problem, and point out connections between problems and algorithms for solving them. In Part II, we...
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...Graphing Applications and the TSP Name: Institution: Graphing Applications and the TSP Question 1 A Hamiltonian cycle is a closed loop within a graph that visits all its vertices exactly once. An example of the Hamiltonian cycle is the Travelling salesman problem. The solution to the minimum length of a Hamiltonian cycle is an NP complete problem that cannot be computed in polynomial time. This means that the minimum possible path cannot be computed by a deterministic machine. When completing a Hamiltonian cycle, one has to make sure that there are only two edges getting in and out of a vertex. In addition one has to ensure that there are no sub-cycles in the cycle. In a Hamiltonian cycle with n vertices, the number of different cycles that can be completed is (n-1)! /2 in a complete undirected graph and (n-1)! In a complete directed graph (Narasimhan, 2009). Question 2 A Euler cycle is a path that passes through all the edges of a graph exactly once. It usually starts and ends at the same vertex. For one to construct a Euler cycle all the vertices in the graph must have an even degree. Therefore, one can conclude that any graph with all vertices of an even degree connected is a Euler cycle. Unlike the Hamiltonian cycle, the Euler cycle can be computed in polynomial time. The Euler cycle can be constructed using the Fleury’s or Hierholzer’s algorithm. Question 3 The minimum length of a Hamiltonian cycle is the shortest path that can...
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...the principal qualities, both positive and negative, of this abstract character? How does she interact with the humans who live among her? Why did Hémon choose to make her such a prominent element in the story? | 0 | 0 | 0 | | Critics of this novel accuse Hémon of have created not real people but mere stereotypes, lacking a depth of personality, only exemplifying an idealized vision of the Québec persona. Each of the main characters seems to exemplify the characteristics of a social role (husband, wife, etc.) rather than exist as a real person. Is this a valid critique of the novel? If so, why? If not, why not? | 0 | 0 | 0 | Maria Chapdelaine; Religion | Religion, specifically Roman Catholicism, plays an essential role in the lives of Hémon’s characters. The very first chapter opher choice of husband. In fact almost every element of life is tied to the Church. What is the role of religion in the lives of these ‘Canayans’? In what way(s) Hémon appear to be critical of this role? | 0 | 0 | 0 | Maria Chapdelaine: Love it or hate it! | In his introduction to this edition, Roch Carrier writes: That evening I learned that an intellectual Québecer is supposed to hate Maria Chapdelaine. You're supposed to hate it even if you haven't read it. Later he says: Maria Chapdelaine is a novel that will not end as long as there are French-Canadians. How do you interpret these comments? If you were a Québecer, would you 'love it' or 'hate it'? Please explain your choice...
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...1. Analyze what filters were in place to block effective communication between the hospital administrators, medical staff, and affected patients. Given the information available in this scenario, I really only see one filter that really stands out that blocked effective communication. That filter is called role expectations and is defined in the reading as how people expect themselves, and others, to act on the basis of the roles they play, such as boss, customer, or subordinate. In the scenario, the role expectations that weren’t met were; the fluids that were placed in the empty should have been, at the very least, relabeled, furthermore in a hospital setting like this, the fluid should have been removed all together; the supervisors should have contacted the patients who came into contact with the fluid immediately. 2. Evaluate how the original problem could have been intercepted before it became a health care crisis. In my time working for a big box hardware store, there were many OSHA approved processes involved where dangerous chemicals were concerned. I can only assume that a hospital has the strictest of procedures to follow where it could affect and/or harm so many people. The people who changed the hydraulic fluid should have had their own process for disposing of the old fluid and most definitely should have relabeled these barrels as hazardous. 3. Let’s assume that you have been hired to study the series of mix-ups that involved personnel employed by Automatic...
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...and professionally though leadership, networking education and national recognition, it is said that almost 50% of all micro, small and medium enterprises in Brunei are made of women. From there, to be on an equal standing with the men can be seen, be it in terms of salary or position. Hence, women today began to accept the equal opportunity given to men and women, due to the factors such as people’s prejudice towards working women, government policies such as the Legislation on Women in Brunei and others. These women do see themselves as a part of the “bread-winners”, a role usually hold by the men. Quality Work-Life balance, as stated by Cherrington (1991), generally refers to any programs that are employed to change the traditional approaches to working. Therefore, quality of work-life programs are highly encouraged in some organisations. Thien (2014) believed that the new role that working women have and how to balance their work is a problem faced by many women. Because they have to work early in the morning, taking care...
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...human service program/agency runs. Without grants the program/agency would be unable to operate. Grants play one of the most important roles in a human services program/agency. Grants are important to a program/agency, because it allows the program/agency to serve their clients. The program/agency clients are dependent on the amount of services the program/agency is able to provide. A grant is an amount of money a program/agency is given to operate sufficiently. Not all programs/agencies are dependent on grants. The reason why some programs/agencies may not need grants in order to operate depends greatly on their financial needs. Some programs/agencies help their clients with expenses such as their utilities, rent, or security deposit. A program that operates on this level would be in need of a grant, because the cost to help clients is greater than say a program/agency that helps with food. Often a program/agency that helps with food is given food through donations. Grants are vital in how a program/agency runs. A program/agency that receives grants may be better able to serve their clients, because they have the necessary funds to do so. Grants are an important part in the human services field. Without grants a program/agency might not be possible. Tee, you did an excellent job on this assignment. You have a clear understanding of the role and importance of grants in the human services. Nice work!...
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...Case Management Overview Diana G. Resendiz BSHS/ 405 September 21, 2015 James Reeves Case Management Overview Case managers play an essential role in the helping process. Case managers take into account the person as a whole and focus not just on one problem, but also all the other variables (Summers, 2011). The case manager ensures the client receives the most individualized and effective treatments and plan for service possible. The many roles and responsibilities are carried professionally and ethically. The case manager also can use theoretical models to identify problem and cause of the client's behavior. Many times, case managers work with specific special populations and encounter issues that must be prepared to address. Roles and Responsibilities Case management primary purpose is to improve the quality of life the client by assessing their total situation (Summers, 2011). It is imperative that the case manager knows what their client wants not only for service but to have a productive and useful life. Case managers develop a comprehensive picture of each client and identify the specific intervention the client may need. Case management entails being respectful to the client, their family, and the diversity of the human experience. It also requires listening carefully and encouraging people to hope and work towards a productive and healthy life. Case managers utilize funding sources to support standard formal services, in some cases, medication, as well as community...
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...A. Groups and Teams 1. Identify the dysfunctional and functional properties of the group in the film as they pertain to the problem the group is working on. In this film, the numerous functional and dysfunctional properties of the 12-jury men play a big role in analysing and evaluating the main purpose at hand, namely identifying the young man guilty or innocent for the murder of his father. The different roles the 12-jury men play in the deliberation of the capital murder case is prominent. Firstly, a role can be defined as a set of expected behaviour patterns attributed to someone occupying a given position in a social unit. Different groups enforce different role requirements on individuals namely; role expectation, role perception and role conflict. (i) Role expectation: Role expectation can be defined as the role others believe a person should play or the way others believe a person should act in a given situation. When looking at the Jurors’ main role in any court system and in the film, it is expected of them to decide whether or not the defendant should be declared guilty or not guilty. (ii) Role perception: Role perception can be defined as the individual’s view of how he or she should act in a given situation. When looking at the film the Jurors individual frame of position and prejudices influence how they individually perceive the case. Because the Jurors perceptions are unique it leads to complications in the communication process. In the film “12 Angry men”...
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...42XX: Leadership and Change Management Professor: XXXXX College: XXXX Date: XXXXX Main Problems One of the problems with this scenario is the on-going conflict between Richard Leeman, Public Relations Chief over the chemical division, and Donna Olson, Public Relations Chief over the mechanical division. Gene Robertson, Public Relations Director for the Western Area Regional Office, has had to review seven cases in the past six months where Richard and Donna have been at odds with one another. As long as they continue to have problems working cohesively together, the issues will have an impact on the entire company. Richard and Donna, though they may be very talented in their respective roles, are a weakness in the strength of the company as a whole. If allowed to continue, the problems between the two will filter through the respective departments individually and collectively when there is a need to interact. Another problem deals with Gene. As the director over Richard and Donna, he has allowed problems to continue. With seven reported issues over the past six months, and now the current problem at the public relations dinner, Gene is not doing his job as an effective leader to fix a problem that could cause long-term damage to the organization as a whole. If the problems with setting up for the event had been visible to the guests, the effects could have had a negative impact on the company’s future business relationships...
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...Team and Team Processes Shelitta Myers MHA601: Principles of Health Care Administration Dr. Bob 2 July 2012 Team and Team Processes In the following paper I will identify a minimum of three interventions to recommend that address the concerns expressed by Nurse B. The following are the three interventions that I will speak about: conflict management, role conflict, and striving toward the same goal. In closing I will support the recommended interventions with justification/explanation. A group consists of two or more people who interact with each other and share a common purpose (Erofeev, Glazer, & Ivanitskaya, 2009). A team is a type of group (Erofeev, Glazer, & Ivanitskaya, 2009). Teams are an essential part of any organization, especially within the healthcare organization. Each individual on a team plays a vital role in ensuring that all needs are met, task are completed daily and patients are being cared for properly. Teamwork and collaboration between all health professionals results in high quality clinical care, and increased job satisfaction for staff (Begley, 2009). When team members do not agree on the same goal, conflicts will arise. It is important for healthcare managers to control and management all conflicts within the organization. The key to successful conflict management is for both sides to try and solve the problem instead of trying to prove the other side wrong. In the case study presented, Nurse B voices concerns about working...
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...performance on job satisfaction. The authors show that conflicting findings in the literature are the result of inconsistency in both the measurement and the definition of constructs across studies that do not fully account for all the relationships between constructs. The current findings emphasize the need to distinguish clearly between factors that represent employees’ inputs in a work relationship (i.e., effort) and those that represent their outputs (i.e., job performance). The article also demonstrates the importance of properly accounting or controlling for all key variables to eliminate biases that can arise in empirical research on work relationships. here is an extensive body of research in organizational psychology that considers the role of job satisfaction in managing effective work relationships. Similarly, job satisfaction is a widely studied construct in marketing research...
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...are much interested to stay out on the streets, either in cars or on a beat instead of doing paper work while sitting in the office. They frequently put off the job or do it inadequately which results in unclear and ambiguous reports which cause the police department to lose court cases. Another problem is that the captain is finding it difficult to figure out the possible ways to motivate them to do the paper work effectively and efficiently. There are various problems related to the employee motivation, ability of officers to perform task, lack of role perception and different situational factors. Question # 2 Use the mars model of individual behaviour and performance to diagnose the possible causes of the unacceptable behaviour? Answer- According to the MARS model of individual behaviour there are four factors that directly influence voluntary individual behaviour and performance. Those factors are Motivation, Ability, Role perceptions and Situational factors. We can use the mars model to diagnose the causes responsible for different problems in the given scenario. The causes are as follows - 1. Lack of motivation – Motivation is the force within the person that affects his or her direction, intensity and persistence of voluntary behaviour. As the captain has stated in the scenario that he is facing problem to find ways to motivate the employees. He doesn’t have any financial rewards at his disposal and since the nature of job is very boring and none of the employees...
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...care needed, while assessing areas for teaching and the possibility of additional care from outside sources such as home health or hospice care. Utilizing the family structural and developmental theory the nurse could then evaluate the family structure and cultural sensitivity of the family, evaluating the ages and developmental/cognitive levels of the children to see what effect this transition might have on their lives and identify what roles and responsibilities they might assume in the care of their grandmother. “Knowing the family’s composition, interrelationships, and particular life cycles helps nurses predict overall family pattern (Edelman, 152).” The nurse could then evaluate the need for social service or support groups to assist the family with any issues that might arise, as well as providing the support needed for Susie to prevent potential caregiver role strain as she tries to balance the added responsibility. The family should be united, educated and able to communicate effectively to ensure a cohesive transition in their new roles as a family. References: Edelman, Carole. Health Promotion Throughout the Life Span. 8th Edition. Mosby, 2014. VitalBook file. Pageburst. Knowing a family’s composition, interrelationships, and particular life cycle helps nurses predict overall family pattern (Edelman 152) Edelman, Carole, Elizabeth Kudzma, Carol Mandle. Health Promotion Throughout...
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...competition.”1 C. Most common types of role strain II. Role Overload A. “Occurs when the combination of all the role demands placed on an individual exceed that individual’s ability to meet them.” 1 B. “Work related stress, lowers productivity and lowered emotional and physical health such as chronic headaches, fatigue, depression and malaise” 2, 6 III. Interpersonal conflicts within role sets A. “Problems and difficulties that arise within complementary role sets, such as wife-husband, parent-child, and worker-supervisor” 1, IV. Interrole conflict A. “Occurs when demands of two or more roles held by a person are incompatible and the demands cannot simultaneously be met.” 1 B. Employees face balancing demands of work and family responsibilities 3 V. Role Captivity A. “An individual is in an unwanted role and feels an obligation to do one thing but prefers to do something else.” 1 B. “ One is an unwilling incumbent of a role like housewives or retirees” 4 VI. Role Restructuring A. “Occurs in situations in which long-established patterns or expectations undergo considerable restructuring.” 1 B. “New expectations such as adult-child adjusting to the demands of caring for aging parents” 5 VII. Conclusion References: 1. Weiss, G.L., & Lonnquist, L.E. (2009). The Sociology of Health, Healing, and Illness. 7th Ed. 2. Idris, M. (2011). Over Time Effects of Role Stress on Psychological Strain among...
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