Approximation Algorithms for Minimum

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)

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...

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...

A Static 2-Approximation Algorithm for Vertex Connectivity and Incremental Approximation Algorithms for Edge and Vertex Connectivity

This paper presents insertions-only algorithms for maintaining the exact and/or approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact size k in time O(1) and a cut of size k in time linear in its size. For the minimum edge cut problem and for any 0 < 1, the amortized time per insertion is O(1= ) for a (2 + )-approximation,...

Approximation Algorithms for Outlier Removal in Convex Hulls

Given n points in R, we give approximation algorithms to find a subset of k of the points that has minimum-area or minimum-perimeter convex hull. We give algorithms that individually yield constantfactor approximations to the minimum-perimeter problem with different running times for differing values of k. Together, these algorithms provide a constant-factor approximation of the minimumperimete...