Approximation Algorithms for QMA-Complete Problems

QMA-complete problems

In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date . Such problems are believed to be difficult to solve, even with a quantum computer, but have the property that if a purported solution to the problem is given, a quantum computer would easily be able to verify whether it is correct. An attempt has been ma...

Approximation Algorithms for Geometric Problems

This chapter surveys approximation algorithms for hard geometric problems. The problems we consider typically take inputs that are point sets or polytopes in twoor three-dimensional space, and seek optimal constructions, (which may be trees, paths, or polytopes). We limit attention to problems for which no polynomial-time exact algorithms are known, and concentrate on bounds for worst-case appr...

Approximation Algorithms for Segmentation Problems

We introduce and study a novel genre of optimization problems, which we call segmentation problems, motivated in part by certain aspects of clustering and data mining. For any classical optimization problem, the corresponding segmentation problem seeks to partition a set of cost vectors into several segments, so that the overall cost is optimized. We focus on two natural and interesting (but MA...

Approximation algorithms for network problems

Approximation Algorithms for Clustering Problems