Fast algorithms for N -dimensional restrictions of hard problems

Hard Problems for CSP Algorithms

We prove exponential lower bounds on the running time of many algorithms for Constraint Satisfaction, by giving a simple family of instances on which they always take exponential time. Although similar lower bounds for most of these algorithms have been shown before, we provide a uniform treatment which illustrates a powerful general approach and has stronger impfications for the practice of al...

Approximation algorithms for NP-hard optimization problems

In this chapter, we discuss approximation algorithms for optimization problems. An optimization problem consists in finding the best (cheapest, heaviest, etc.) element in a large set P, called the feasible region and usually specified implicitly, where the quality of elements of the set are evaluated using a function f(x), the objective function, usually something fairly simple. The element tha...

Fast Algorithms for Hard Graph Problems: Bidimensionality, Minors, and Local Treewidth

This paper surveys the theory of bidimensional graph problems. We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems.

Fast high-order algorithms and well-conditioned integral equations for high-frequency sound-hard scattering problems

This text introduces 1) New Regularized Combined Field Integral Equations (CFIE-R) for the solution of frequency-domain sound-hard scattering problems, and, 2) Fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Like the classical Combined Field Integral Equation (CFIE), the CFIE-R are unikely-solvable integral equations based on use of single an...

Fast search algorithms for layout permutation problems