Introduction to Algorithm

... clockwork to find the required solution, but most are less tractable and require either a very long computation or a compromise on a solution that may not be optimal.” (Richard Karp, UC berkeley) ...

... clockwork to find the required solution, but most are less tractable and require either a very long computation or a compromise on a solution that may not be optimal.” (Richard Karp, UC berkeley) ...

An optimal consumption problem with partial information

... We consider an optimal consumption problem where an investor tries to maximize the finite horizon expected discounted HARA utility of consumption. We treat a stochastic factor model that the mean returns of risky assets depend on underlying economic factors formulated as the solution of a linear sto ...

... We consider an optimal consumption problem where an investor tries to maximize the finite horizon expected discounted HARA utility of consumption. We treat a stochastic factor model that the mean returns of risky assets depend on underlying economic factors formulated as the solution of a linear sto ...

Additional Problems: Problem 1. K-means clustering. Given are the

... Use pseudo-code. Specify both the code in the mapper function and the reducer function. Problem 6. If I run K-means on a data set with n points, where each points has d dimensions for a total of m integrations in order to compute k clusters how much time will it take? (answer is a function of n, m, ...

... Use pseudo-code. Specify both the code in the mapper function and the reducer function. Problem 6. If I run K-means on a data set with n points, where each points has d dimensions for a total of m integrations in order to compute k clusters how much time will it take? (answer is a function of n, m, ...

Name_____________________________________ /110 Math

... 9. Use the Pythagorean Theorem to find the distance between (-1, -6) and (4, 6). ...

... 9. Use the Pythagorean Theorem to find the distance between (-1, -6) and (4, 6). ...

Bilevel programming, pricing problems and Stackelberg games

... A bilevel optimization problem consists in an optimization problem in which some of the constraints specify that a subset of variables must be an optimal solution to another optimization problem. This paradigm is particularly appropriate to model competition between agents, a leader and a follower, ...

... A bilevel optimization problem consists in an optimization problem in which some of the constraints specify that a subset of variables must be an optimal solution to another optimization problem. This paradigm is particularly appropriate to model competition between agents, a leader and a follower, ...

Honors Algebra 2 and Trig

... 1. The area of a rectangular garden cannot exceed 105 square feet. If the length of the garden is 6 more than 5 times the width of the garden, what are the largest possible integral values for each dimension of the garden? Only an algebraic solution will be accepted. ...

... 1. The area of a rectangular garden cannot exceed 105 square feet. If the length of the garden is 6 more than 5 times the width of the garden, what are the largest possible integral values for each dimension of the garden? Only an algebraic solution will be accepted. ...

MAT 200, Logic, Language and Proof, Fall 2015 Practice Questions

... Problem 3. Let n ∈ N. Prove that if there are no non-zero integer solutions to the equation xn + y n = z n , then there are no non-zero rational solutions. Problem 4. Find all integers x such that 3x ≡ 15 ...

... Problem 3. Let n ∈ N. Prove that if there are no non-zero integer solutions to the equation xn + y n = z n , then there are no non-zero rational solutions. Problem 4. Find all integers x such that 3x ≡ 15 ...

The travelling salesman problem (TSP) asks the following question: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.TSP is a special case of the travelling purchaser problem and the Vehicle routing problem.In the theory of computational complexity, the decision version of the TSP (where, given a length L, the task is to decide whether the graph has any tour shorter than L) belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (perhaps, specifically, exponentially) with the number of cities.The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved completely and even problems with millions of cities can be approximated within a small fraction of 1%.The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing. In these applications, the concept city represents, for example, customers, soldering points, or DNA fragments, and the concept distance represents travelling times or cost, or a similarity measure between DNA fragments. The TSP also appears in astronomy, as astronomers observing many sources will want to minimise the time spent slewing the telescope between the sources. In many applications, additional constraints such as limited resources or time windows may be imposed.