The set-based particle swarm optimisation algorithm is a swarm-based meta-heuristic that
has gained popularity in recent years. In contrast to the original particle swarm optimisation …

We show that every language in NP has a probablistic verifier that checks membership
proofs for it using logarithmic number of random bits and by examining a constant number of …

Approximation algorithms have developed in response to the impossibility of solving a great
variety of important optimization problems. Too frequently, when attempting to get a solution …

We define a natural variant of NP, MAX NP, and also a subclass called MAX SNP. These are
classes of optimization problems, and in fact contain several natural, well-studied ones. We …

N COMPUTER applications we are used to live with approximation. Var I ious notions of
approximation appear, in fact, in many circumstances. One notable example is the type of …

Algorithmic design, especially for hard problems, is more essential for success in solving
them than any standard improvement of current computer tech nologies. Because of this, the …

This tutorial provides an introduction into the area of polynomial time approximation
schemes. The underlying ideas, the main tools, and the standard approaches for the …

We derive results of the following flavor: If a combinatorial optimization problem can be
formulated via a dynamic program of a certain structure and if the involved cost and …

We show that for some positive constant c it is not feasible to approximate Independent Set
(for graphs of n vertices) within a factor of nc, provided Maximum 2-Satisfiability does not …

This dissertation establishes a surprising new characterization of NP, the class of languages
for which membership proofs can be checked in polynomial time deterministically. The class …