Slides on Approximation algorithms

Minimizing a General Penalty Function on a Single Machine via Developing Approximation Algorithms and FPTASs

This paper addresses the Tardy/Lost penalty minimization on a single machine. According to this penalty criterion, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Besides its application in real world problems, Tardy/Lost measure is a general form for popular objective functions like weighted tardiness, late work and tardiness with reje...

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)

Approximation Solutions for Time-Varying Shortest Path Problem

Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

Approximation Algorithms for 2-dimensional Packing and Related Scheduling Problems

Main subject of this thesis are approximation algorithms for scheduling and packing, two classical geometrical problems in combinatorial optimization. It is divided into three parts. In the first part we consider a generalization of the strip packing problem or geometrical cutting stock problem. In strip packing a given set of rectangles has to be placed into a strip of fixed width and infinite...