The Golden Ticket

2017 ◽  
Author(s):  
Lance Fortnow
Keyword(s):  
Traveling Salesman ◽  
Open Problems ◽  
Mathematical Objects ◽  
Shortest Route ◽  
The Status ◽  
Np Problem

This introductory chapter provides an overview of the P versus NP problem. The P versus NP problem asks, among other things, whether one can quickly find the shortest route for a traveling salesman. P and NP are named after their technical definitions, but it is best not to think of them as mathematical objects but as concepts. “NP” is the collection of problems that have a solution that one wants to find. “P” consists of the problems to which one can find a solution quickly. “P = NP” means one can always quickly compute these solutions, like finding the shortest route for a traveling salesman. “P ≠ NP” means one cannot. Ultimately, the P versus NP problem has achieved the status of one of the great open problems in all of mathematics.

History and Theory

2018 ◽  
Author(s):  
Chris Lorenz
Keyword(s):  
Philosophy Of History ◽  
Point Of View ◽  
History Writing ◽  
True Nature ◽  
The Status ◽  
Current Return ◽  
Theoretical Reflection ◽  
Three Phases

This introductory chapter assesses the role of theory in history and traces the developments in the discipline of history. Theoretical reflection about the ‘true nature’ of history fulfils three interrelated practical functions. First, theory legitimizes a specific historical practice—a specific way of ‘doing history’—as the best one from an epistemological and a methodological point of view. Second, theory sketches a specific programme of doing history. Third, theoretical reflections demarcate a specific way of ‘doing history’ from other ways of ‘doing history’, which are excluded or degraded. The chapter then considers three phases of theoretical changes from analytical to narrative philosophy of history, and then on to ‘history from below’ and the ‘presence’ of history, ultimately leading to the current return of fundamental ontological and normative questions concerning the status of history and history-writing.

scholarly journals PENYELESAIAN MULTI TRAVELING SALESMAN PROBLEM DENGAN ALGORITMA GENETIKA

2017 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
NI KADEK MAYULIANA ◽  
EKA N. KENCANA ◽  
LUH PUTU IDA HARINI
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Heuristic Algorithm ◽  
Minimum Distance ◽  
Processing Time ◽  
Traveling Salesman ◽  
Running Time ◽  
Shortest Route ◽  
Time Required

Genetic algorithm is a part of heuristic algorithm which can be applied to solve various computational problems. This work is directed to study the performance of the genetic algorithm (GA) to solve Multi Traveling Salesmen Problem (multi-TSP). GA is simulated to determine the shortest route for 5 to 10 salesmen who travelled 10 to 30 cities. The performance of this algorithm is studied based on the minimum distance and the processing time required for 10 repetitions for each of cities-salesmen combination. The result showed that the minimum distance and the processing time of the GA increase consistently whenever the number of cities to visit increase. In addition, different number of sales who visited certain number of cities proved significantly affect the running time of GA, but did not prove significantly affect the minimum distance.

Spinoza’s Jewish Modernities

2012 ◽  
Author(s):  
Daniel B. Schwartz
Keyword(s):  
National Identity ◽  
Jewish Identity ◽  
Jewish History ◽  
Modern State ◽  
Jewish Culture ◽  
The Status ◽  
Modern Jewish History ◽  
Great Culture

This introductory chapter considers why the hallmark of modern Jewish identity is its resistance to—and, at the same time, obsession with—definition. Like battles over national identity in the modern state, clashes over the nature and limits of Jewishness have frequently taken the shape of controversies over the status—and stature—of marginal Jews past and present. The Jewish rehabilitation of historical heretics and apostates with a vexed relationship to Judaism has become so much a part of contemporary discourse that it is difficult to imagine secular Jewish culture without it. Yet this tendency has a beginning as well as a template in modern Jewish history, which the chapter introduces in the figure of Baruch (or Benedictus) Spinoza (1632–1677)—“the first great culture-hero of modern secular Jews,” and still the most oft-mentioned candidate for the title of first modern secular Jew.

Introduction

2014 ◽  
pp. 1-20
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Planning Under Uncertainty ◽  
Problems And Solutions ◽  
The Status ◽  
The Game Theory ◽  
Close Study ◽  
Competitive Nature ◽  
Area Of Application

The situations to which game theory has actually been applied reflect its selective usefulness for problems and solutions of an individualistic and competitive nature, building in the values of the status quo. The main principal area of application has been economics. In economics, game theory has been used in studying competition for markets, advertising, planning under uncertainty, and so forth. Recently, game theory has also been applied to many other fields, such as law, ethics, sociology, biology, and of course, computer science. In all these applications, a close study of the formulation of the problem in the game theory perspective shows a strong inclination to work from existing values, to consider only currently contending parties and options, and in other ways, to exclude significant redefinitions of the problems at hand. This introductory chapter explores these and forms a basis for the rest of the book.

Introduction

2020 ◽  
pp. 1-13
Author(s):  
Rajnaara C. Akhtar ◽  
Patrick Nash ◽  
Rebecca Probert
Keyword(s):  
Family Law ◽  
Law Reform ◽  
Legal Recognition ◽  
The Poor ◽  
Cohabiting Couples ◽  
The Status ◽  
Relationship Norms ◽  
Relationship Breakdown ◽  
Poor Outcomes

This introductory chapter focusses on the status of cohabitants and those in religious only marriages, the similarities in how they are treated by the law and the potential solutions that could be adopted. It shows that law reform is needed in the light of new and evolving relationship norms and the poor outcomes on relationship breakdown for all cohabiting couples, including those in religious-only marriages. It considers legal solutions which fall broadly within two categories: (1) amend wedding laws to facilitate simpler procedures for legal recognition thereby encouraging more couples to legally marry; and (2) extend family law rights available to all legally recognised couples to include those in cohabiting relationships.

The Simulated Annealing Algorithm Based on Multi-Populations Application of TSP

2013 ◽  
Vol 457-458 ◽  
pp. 1037-1041
Author(s):  
Qin Hui Gong
Keyword(s):  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Simulated Annealing Algorithm ◽  
Traveling Salesman ◽  
Local Minima ◽  
Multiple Populations ◽  
Annealing Algorithm ◽  
Np Problem ◽  
Very High ◽  
Collateral Mechanism

Traveling salesman problem (TSP) is not only a combinatorial optimization problem but also a classical NP problem, which has has high application value. Simulated annealing algorithm is especially effective for solving TSP problems. Based on the deficiency of simulated annealing algorithm on avoiding local minima, this paper has improved the traditional simulated annealing algorithm, proposed simulated annealing algorithm of multiple populations to solve the classical TSP problem. This algorithm has introduced collateral mechanism of multiple populations and increased the initial populations so that it can include more solution set, avoid local minima, thus it has improved the optimization efficiency.This algorithm has very high use value in solving the TSP problem. Keywords: Traveling salesman problem, NP (Non-deterministic Polynomial) problem, simulated annealing algorithm, multiple populations

scholarly journals OPTIMIZATION OF GOODS DISTRIBUTION ROUTE ASSISTED BY GOOGLE MAP WITH CHEAPEST INSERTION HEURISTIC ALGORITHM (CIH)

SINERGI ◽  
2018 ◽  
Vol 22 (2) ◽  
pp. 132
Author(s):  
L. Virginayoga Hignasari ◽  
Eka Diana Mahira
Keyword(s):  
Minimum Distance ◽  
Traveling Salesman ◽  
Optimal Distribution ◽  
Total Distance ◽  
Completion Problem ◽  
Shortest Route ◽  
The Difference ◽  
The Traveling Salesman Problem ◽  
The Relationship ◽  
Insertion Heuristic

In the distribution of goods, the efficiency of goods delivery one of which was determined by the path that passed to deliver the goods. The problem of choosing the shortest route was known as the Traveling Salesman Problem (TSP). To solve the problem of choosing the shortest route in the distribution of goods, the algorithm to be used was Cheapest Insertion Heuristic (CIH). This study aims to determine the minimum distance traveled by using the CIH algorithm.  Researchers determine the route and distance of each place visited by using google map. The concept in the CIH algorithm was to insert an unexpired city with an additional minimum distance until all cities are passed to get the solution of the problem. The step completion problem with CIH algorithm was: 1) search, 2) making sub tour; 3) change the direction of the relationship, 4) repeat the steps so that all places are included in the sub tour. Theoretically, the total distance calculated using the CIH algorithm is 20.2 km, while the total distance calculated previously traveled with the ordered route is 25.2 km. There was a difference of 5 km with the application of CIH algorithm. The difference between the distance certainly has an impact on the optimal distribution of goods to the destination. Therefore, CIH algorithm application can provide a solution for determining the shortest route from the distribution of goods delivery.

scholarly journals P vs NP: P is Equal to NP: Desired Proof

2021 ◽  
pp. 1-11
Author(s):  
Zulfia A. Chotchaeva
Keyword(s):  
Artificial Intelligence ◽  
Computer Science ◽  
Structure Prediction ◽  
Complexity Classes ◽  
Open Problems ◽  
Exponential Time ◽  
Running Time ◽  
Algorithmic Problems ◽  
Np Problems ◽  
Np Problem

Computations and computational complexity are fundamental for mathematics and all computer science, including web load time, cryptography (cryptocurrency mining), cybersecurity, artificial intelligence, game theory, multimedia processing, computational physics, biology (for instance, in protein structure prediction), chemistry, and the P vs. NP problem that has been singled out as one of the most challenging open problems in computer science and has great importance as this would essentially solve all the algorithmic problems that we have today if the problem is solved, but the existing complexity is deprecated and does not solve complex computations of tasks that appear in the new digital age as efficiently as it needs. Therefore, we need to realize a new complexity to solve these tasks more rapidly and easily. This paper presents proof of the equality of P and NP complexity classes when the NP problem is not harder to compute than to verify in polynomial time if we forget recursion that takes exponential running time and goes to regress only (every problem in NP can be solved in exponential time, and so it is recursive, this is a key concept that exists, but recursion does not solve the NP problems efficiently). The paper’s goal is to prove the existence of an algorithm solving the NP task in polynomial running time. We get the desired reduction of the exponential problem to the polynomial problem that takes O(log n) complexity.

scholarly journals Sparse complete sets for coNP: Solution of the P versus NP problem

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Computer Science ◽  
Fundamental Question ◽  
Complexity Class ◽  
Open Problems ◽  
Precise Statement ◽  
Complete Sets ◽  
Np Problem

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.

Introduction

2005 ◽  
Author(s):  
Martin Daunton
Keyword(s):  
Social Networks ◽  
Royal Society ◽  
Victorian Britain ◽  
Geographical Society ◽  
Victorian Period ◽  
The Status ◽  
Power And Authority

This book places the establishment of the British Academy in the context of the Victorian organisation of knowledge. In this introductory chapter, the nature of academic, official, and legitimate knowledge in the Victorian period is discussed. It also considers the epistemological sites of Victorian Britain and how they were ordered. These sites included social networks, clubs, or societies such as provincial literary and philosophical societies and archaeological societies, national bodies such as the Royal Geographical Society, and the most exclusive, closed bodies of the elect, such as the Royal Society and the British Academy. These bodies have their own distinctive structures of power and authority. The Royal Society and British Academy for example, were designed to stabilise knowledge and the status of those claiming knowledge.

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