Lugar: Auditorio Phillippe Flajolet, Depto. In his research he focuses on combinatorial optimization and approximation algorithms, i.e., on algorithms that are efficient and compute solutions that are provably close to the optimum.įecha: 12 de octubre de 2018, 12.30 a 13.30 horas. He finished his PhD in 2011 at TU Berlin and was a postdoc at TU Berlin, La Sapienza in Rome and at the MPI for Informatics in Saarbruecken. Key to all results is to show that there are good solutions that have a relatively simple structure.īio: Andreas Wiese is an assistant professor at the Industrial Engineering department of the Universidad de Chile. I will present an algorithm with an approximation ratio of 1.89+eps and varios other results for the problem. This problem generalizes the well-studied (one-dimensional) knapsack problem. The goal is to pack a subset of the given items non-overlappingly into the knapsack in order to maximize the total profit of the packed items. The Knapsack Problem is an NP-Hard optimization problem, which means it is unlikely that a polynomial time algorithm exists that will solve any instance of the problem.
Each item has a profit associated with it. Therefore, efficient algorithms for the Knapsack Problem allow for effective algorithms for a variety of other problems. For the bicriteria problem of minimizing utilized capacity subject to a minimum requirement on assigned weight, we give an (1/3,2)-approximation algorithm. Given are a square knapsack and a set of items that are axis-parallel rectangles. We give two different 1/2-approximation algorithms: the first one solves single knapsack problems successively and the second one is based on rounding the LP relaxation solution.
In this talk I will present approximation algorithms for the 2-dimensional knapsack problem. Therefore, we are interested in approximation algorithms which are algorithms that run in polynomial time and provably find solutions that differ from the optimum by at most some bounded factor, called the approximation ratio. Trust-Region Truncated Generalized Lanczos / Conjugate Gradient Algorithm ( methodtrust-krylov ). Abstract: Many optimization problems are NP-hard and therefore we do not expect to find algorithms for them that are efficient, i.e., run in polynomial time, and find the optimal solution for any given instance.
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